<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">JEP</journal-id><journal-title-group><journal-title>Journal of Environmental Protection</journal-title></journal-title-group><issn pub-type="epub">2152-2197</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/jep.2014.515138</article-id><article-id pub-id-type="publisher-id">JEP-51789</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Earth&amp;Environmental Sciences</subject></subj-group></article-categories><title-group><article-title>
 
 
  Evaluation of Biosorptive Capacity of Banana (&lt;i&gt;Musa paradisiaca&lt;/i&gt;) Stalk for Lead(II) Removal from Aqueous Solution
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>ladipupo</surname><given-names>O. Ogunleye</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Mary</surname><given-names>A. Ajala</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Samuel</surname><given-names>E. Agarry</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib></contrib-group><aff id="aff1"><addr-line>Department of Chemical Engineering, Ladoke Akintola University of Technology, Ogbomoso, Nigeria</addr-line></aff><author-notes><corresp id="cor1">* E-mail:<email>ooogunleye@yahoo.com(LOO)</email>;</corresp></author-notes><pub-date pub-type="epub"><day>25</day><month>11</month><year>2014</year></pub-date><volume>05</volume><issue>15</issue><fpage>1451</fpage><lpage>1465</lpage><history><date date-type="received"><day>27</day>	<month>August</month>	<year>2014</year></date><date date-type="rev-recd"><day>21</day>	<month>September</month>	<year>2014</year>	</date><date date-type="accepted"><day>11</day>	<month>October</month>	<year>2014</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  Raw Banana Stalk (RBS), Acid Activated Banana Stalk (AABS) and Base Activated Banana Stalk (BABS) prepared from banana stalk were used as biosorbents to remove Lead(II) from aqueous solution. The biosorbents were characterised using proximate analysis and Fourier Transform Infrared (FTIR) spectroscopy. Pb(II) of 1000 mg/L concentration was prepared from Pb(NO
  <sub>3</sub>)
  <sub>2 </sub>salt and other concentrations were obtained from this stock through serial dilution. Effects of adsorbent dose, temperature, initial metal concentration, contact time and pH on the percentage Pb(II) removal were evaluated. The Pb(II) concentrations in the solutions were analysed using Atomic Absorption Spectrophotometer. Kinetic, isotherm and thermodynamic parameters were determined. FTIR spectroscopy showed that RBS, AABS and BABS are rich in carboxyl, hydroxyl and phenolic functional groups. At an equilibrium time of 180 minutes, the percentage Pb(II) removal was 63.97%, 96.13% and 66.90% for RBS, AABS and BABS, respectively. Pseudo-second order kinetics best described the process with 
  R
  <sup>2 </sup>(0.95, 0.98, 0.97) for RBS, AABS and BABS, respectively. Langmuir isotherm (AABS) has the maximum adsorption capacity (
  q
  <sub>max</sub>) of 13.53 mg/g and 
  R
  <sup>2</sup> (0.99). Thermodynamic parameters obtained were 
  △
  <em>G</em><sup>0</sup> (?18.75 kJ/mol), 
  △
  <em>H</em><sup>0</sup> (12.63 kJ/mol), 
  △
  <em>S</em><sup>0</sup> (0.05 kJ/mol&#183;K) and Ea (4.37 kJ/mol). Banana stalk has viable characteristics for preparing biosorbents. Acid activated banana biosorbent is more efficient for removal of lead ions from its aqueous solution. 
 
</p></abstract><kwd-group><kwd>Biosorption</kwd><kwd> Isotherm</kwd><kwd> Banana Stalk</kwd><kwd> Kinetics</kwd><kwd> Lead(II)</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>Lead is one of the heavy metals that are often found in industrial wastewater and its discharge into the environment poses serious threat due to its toxicity to aquatic and terrestrial lives [<xref ref-type="bibr" rid="scirp.51789-ref1">1</xref>] [<xref ref-type="bibr" rid="scirp.51789-ref2">2</xref>] . It is a group IV element on the periodic table which is remarkably highly resistant to corrosion in most acid and naturally occur as element buried in the earth crust in insoluble and biologically inoffensive forms [<xref ref-type="bibr" rid="scirp.51789-ref3">3</xref>] . Enhanced industrialization such as manufacturing of storage batteries, television tube, printing, paints, pigments, photographic materials, gasoline additives, matches and explosives brought about lead bearing wastewater [<xref ref-type="bibr" rid="scirp.51789-ref4">4</xref>] - [<xref ref-type="bibr" rid="scirp.51789-ref7">7</xref>] .</p><p>Exposure to Lead is widely recognized as a major risk factor for several human diseases once it goes beyond the World Health Organisation (WHO) maximum permissible limit (3 - 10 mg・L<sup>−1</sup>) in drinking water [<xref ref-type="bibr" rid="scirp.51789-ref8">8</xref>] - [<xref ref-type="bibr" rid="scirp.51789-ref12">12</xref>] . It forms complexes with oxo-groups in enzymes to affect virtually all steps in the process of haemoglobin synthesis and porphyrin metabolism [<xref ref-type="bibr" rid="scirp.51789-ref13">13</xref>] . Other problems associated with toxic levels of lead exposure are encephalopathy, seizures and mental retardation, anemia and nephropathy [<xref ref-type="bibr" rid="scirp.51789-ref14">14</xref>] [<xref ref-type="bibr" rid="scirp.51789-ref15">15</xref>] . Hence, lead must be removed as much as possible from industrial effluents to prevent environmental hazard from its discharge.</p><p>Adsorption technology has been widely preferred to other traditional methods such as coagulation, flocculation, filtration, ozonation or sedimentation in the removal of pollutants from wastewater [<xref ref-type="bibr" rid="scirp.51789-ref16">16</xref>] - [<xref ref-type="bibr" rid="scirp.51789-ref18">18</xref>] . In this technology, activated carbons are commonly used adsorbent due to their high adsorption capacity, a result of their high surface area and surface reactivity but their regeneration is, however, difficult and expensive [<xref ref-type="bibr" rid="scirp.51789-ref19">19</xref>] [<xref ref-type="bibr" rid="scirp.51789-ref20">20</xref>] .</p><p>Quest for effective and economical technologies have brought about biosorption. It is based on metal binding capacities of various biological materials mainly composed of cellulose, hemicelluloses and lignin that make them effective adsorbents for a wide range of pollutants due to the presence of functional groups such as hydroxyl, carboxyl, methoxyl and phenols [<xref ref-type="bibr" rid="scirp.51789-ref21">21</xref>] -[<xref ref-type="bibr" rid="scirp.51789-ref25">25</xref>] . Recent studies have shown that heavy metals can be removed using plant materials such as empty palm oil fruit bunch [<xref ref-type="bibr" rid="scirp.51789-ref26">26</xref>] , sour soup seeds [<xref ref-type="bibr" rid="scirp.51789-ref27">27</xref>] , modified cassava fibre [<xref ref-type="bibr" rid="scirp.51789-ref28">28</xref>] , coconut shell [<xref ref-type="bibr" rid="scirp.51789-ref29">29</xref>] , duck weed [<xref ref-type="bibr" rid="scirp.51789-ref30">30</xref>] , sago waste [<xref ref-type="bibr" rid="scirp.51789-ref31">31</xref>] , African spinach stalk [<xref ref-type="bibr" rid="scirp.51789-ref32">32</xref>] , palm fruit fibre [<xref ref-type="bibr" rid="scirp.51789-ref33">33</xref>] , hop [<xref ref-type="bibr" rid="scirp.51789-ref34">34</xref>] , orange peels [<xref ref-type="bibr" rid="scirp.51789-ref35">35</xref>] - [<xref ref-type="bibr" rid="scirp.51789-ref37">37</xref>] and spent tea leaves [<xref ref-type="bibr" rid="scirp.51789-ref18">18</xref>] [<xref ref-type="bibr" rid="scirp.51789-ref38">38</xref>] .</p><p>Banana Stalks (BS) are generated in large amount as waste product after the consumption of banana and these constitute environmental menace due to the fact that they are left to decompose being of non-economic importance [<xref ref-type="bibr" rid="scirp.51789-ref39">39</xref>] . However, BS is a rich lignocellulosic agricultural waste whose previous application has been limited to the production of activated carbon for malachite green dye removal [<xref ref-type="bibr" rid="scirp.51789-ref40">40</xref>] and not yet applied to Pb(II) removal [<xref ref-type="bibr" rid="scirp.51789-ref41">41</xref>] - [<xref ref-type="bibr" rid="scirp.51789-ref48">48</xref>] . The present study investigated the adsorptive capacity of BS as a low-cost adsorbent for the biosorption of Lead(II) from aqueous solution. The effects of physical parameters such as initial concentration, pH, and temperature and biosorbent dosage on the biosorption process have been investigated. In addition, the biosorption equilibrium isotherms, kinetics and thermodynamic parameters have been determined.</p></sec><sec id="s2"><title>2. Materials and Method</title><sec id="s2_1"><title>2.1. Preparation and Characterization of Adsorbent</title><p>Banana Stalks were first sundried, cut into small pieces and washed with distilled water to remove dirt particles. BS pieces were then dried in the oven at 100˚C for 24 hours to constant weight before being grounded and screened to 300 - 425 mm mesh particle size. It was then stored as Raw Banana Stalk (RBS). RBS of 200 g was soaked with 1 M H<sub>3</sub>PO<sub>4</sub> in ratio 1:1, kept in the oven for 24 hours at 80˚C for activation and stored as Acid Activated Banana Stalk (AABS). Similarly, Base Activated Banana Stalk (BABS) was prepared by soaking another 200 g of the RBS in 0.1 M KOH for 24 hours at 80˚C in an oven and stored as BABS. The Proximate analysis of the biosorbents was carried out to know the percentage compositions of its constituents. Fourier Transform Infrared (FTIR) spectroscopic analysis was performed on RBS, AABS and BABS using FTIR spectroscope (FTIR-2000, Perkin-Elmer). The spectra were measured from 4000 to 400 cm<sup>−</sup><sup>1</sup>.</p></sec><sec id="s2_2"><title>2.2. Preparation of Simulated Wastewater</title><p>Simulated wastewater samples containing Pb(II) was prepared from Pb(NO<sub>3</sub>)<sub>2</sub> of 1000 mg・L<sup>−1</sup> stock solutions. Reagents used were of analytical grade and deionized water was used in solution preparation. Other concentrations (20 - 100 mg/L) were obtained from this stock solution by serial dilution. Fresh dilutions were used for each experiment. The concentration of Pb(II) in simulated wastewater was analysed by Atomic Absorption Spectrophotometer (model PyeUnicam SP-9 Cambridge, UK).</p></sec><sec id="s2_3"><title>2.3. Batch Biosorption Equilibrium Studies</title><p>Batch equilibrium tests were carried out on the adsorption of Pb(II) on RBS. The effect of initial metal ion concentration, contact time, temperature, solution pH and adsorbent dose were investigated. Sample solutions were withdrawn at time interval and equilibrium to determine residual concentrations. Solutions were filtered prior to analysis in order to minimise the interference of the RBS. For equilibrium studies, the experiment was carried out for 360 minutes to ensure that equilibrium was reached. The linear Beer-Lambert relationship between absorbance and concentration with the calibration curve was established by plotting the graph of absorbance versus concentration of the lead solution. The concentration of lead solution before and after adsorption was determined using an Atomic Absorption Spectrophotometer (model PyeUnicam SP-9 Cambridge, UK). This experiment was done in turns for AABS and BABS.</p><p>The adsorbed phase concentration (<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x10.png" xlink:type="simple"/></inline-formula>, in mg/g) at time (t) was calculated using Equation (1)</p><disp-formula id="scirp.51789-formula129"><label>(1)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x11.png"  xlink:type="simple"/></disp-formula><p>where, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x12.png" xlink:type="simple"/></inline-formula>and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x13.png" xlink:type="simple"/></inline-formula> are the initial and the final lead concentration (mg/L), respectively; <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x14.png" xlink:type="simple"/></inline-formula>is the water sample volume (L); and m is the mass of adsorbent used (g).</p><p>The biosorption at equilibrium, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x15.png" xlink:type="simple"/></inline-formula>(mg/g), was calculated according to Equation (2)</p><disp-formula id="scirp.51789-formula130"><label>(2)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x16.png"  xlink:type="simple"/></disp-formula><p>where, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x17.png" xlink:type="simple"/></inline-formula>and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x18.png" xlink:type="simple"/></inline-formula> are the initial and the final (equilibrium) lead concentration (mg/L) respectively; <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x19.png" xlink:type="simple"/></inline-formula>is the water sample volume (L); and m is the mass of adsorbent used (g). The percentage of lead ion removal was calculated using Equation (3):</p><disp-formula id="scirp.51789-formula131"><label>(3)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x20.png"  xlink:type="simple"/></disp-formula></sec><sec id="s2_4"><title>2.4. Effects of Adsorption Conditions</title><p>RBS of 1 g was measured into a 125 ml Erlenmeyer flask with 100 ml of 100 mg/l of Pb(II) solution with pH of 7 monitored using a pH meter (model CD70 WPA) and controlled with 0.1 M NaOH and 0.1 M HCl. The flask was agitated at 30˚C at a constant 125 rpm using the Thermostatic water bath shaker, the sorption experiment carried out for sufficient time of 360 minutes. The supernatant was filtered using Watman Filter Paper and Lead(II) concentration was analysed using Atomic Absorption Spectrophotometer (AAS). The effect of contact time (30, 60, 90, 120, 150, 180, 210, 240, 300, 360 minutes), biosorbent dose (0.2, 0.4, 0.6, 0.8, 1.0, 1.5 and 2.0 g), initial metal ion concentration (20, 40, 60, 80, 100 and 120 mg/L), pH (4, 6 and 8) and temperature (30, 40 and 50˚C) were evaluated during the study. During the experiment, the particular parameter considered was varied while the other four were kept constant variously for RBS, BABS and AABS biosorbents.</p></sec></sec><sec id="s3"><title>3. Results and Discussion</title><sec id="s3_1"><title>3.1. Characterisation of Biosorbent</title><p>The result of proximate analysis carried out on the biosorbent samples are as presented in <xref ref-type="table" rid="table1">Table 1</xref>. It revealed that the AABS, BABS and RBS are rich in crude fibre of 67.69%, 62.07% and 58.47%, respectively. This rich crude fibre comprise of lignin, cellulose and hemicellulose content. Lignin is a compound rich with functional groups, such as carbonyl, ether and hydroxyl [<xref ref-type="bibr" rid="scirp.51789-ref21">21</xref>] [<xref ref-type="bibr" rid="scirp.51789-ref41">41</xref>] and has been used for metals adsorption by some researchers [<xref ref-type="bibr" rid="scirp.51789-ref40">40</xref>] [<xref ref-type="bibr" rid="scirp.51789-ref49">49</xref>] . The implication of this is that the presence of the active site presupposes that banana stalks are good biosorbents. The FTIR spectra characteristics for the three biosorbents are as shown on <xref ref-type="table" rid="table2">Table 2</xref> while main spectra are on <xref ref-type="fig" rid="fig1">Figure 1</xref>. The analysis revealed that the biosorbents are rich in hydroxyl, carboxyl and the phenolic groups which indicates that RBS, AABS and BABS are viable for the adsorption of Pb(II) onto the biosorbents.</p></sec><sec id="s3_2"><title>3.2. Effect of Initial Concentration and Contact Time</title><p>The rate of biosorption is a function of the initial concentration and contact time of the sorbate and these makes them important factors for effective biosorption. <xref ref-type="fig" rid="fig2">Figure 2</xref> shows the effect of contact time on Pb(II) adsorption onto RBS, BABS and AABS. It was found that the adsorption of Pb(II) by the three banana stalks increased with contact time until equilibrium was reached at around 180 minutes. The biosorption process was rapid initially</p><table-wrap id="table1" ><label><xref ref-type="table" rid="table1">Table 1</xref></label><caption><title> Proximate analysis of banana stalks</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Sample</th><th align="center" valign="middle" >Moisture content (%)</th><th align="center" valign="middle" >Ash content (%)</th><th align="center" valign="middle" >Crude fibre (%)</th><th align="center" valign="middle" >Protein (%)</th><th align="center" valign="middle" >Carbohydrate (%)</th></tr></thead><tr><td align="center" valign="middle" >AABS</td><td align="center" valign="middle" >10.38</td><td align="center" valign="middle" >5.52</td><td align="center" valign="middle" >67.69</td><td align="center" valign="middle" >6.29</td><td align="center" valign="middle" >10.12</td></tr><tr><td align="center" valign="middle" >BABS</td><td align="center" valign="middle" >10.88</td><td align="center" valign="middle" >5.93</td><td align="center" valign="middle" >62.07</td><td align="center" valign="middle" >7.93</td><td align="center" valign="middle" >13.26</td></tr><tr><td align="center" valign="middle" >RBS</td><td align="center" valign="middle" >12.19</td><td align="center" valign="middle" >7.40</td><td align="center" valign="middle" >58.47</td><td align="center" valign="middle" >8.58</td><td align="center" valign="middle" >14.10</td></tr></tbody></table></table-wrap><table-wrap id="table2" ><label><xref ref-type="table" rid="table2">Table 2</xref></label><caption><title> FTIR spectra characteristics for RBS, BABS and AABS</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >IR peak</th><th align="center" valign="middle"  colspan="3"  >Band wave number (cm<sup>−1</sup>)</th><th align="center" valign="middle" >Assigned functional group</th></tr></thead><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >RBS</td><td align="center" valign="middle" >BABS</td><td align="center" valign="middle" >AABS</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >1</td><td align="center" valign="middle" >3889.63</td><td align="center" valign="middle" >3287.10</td><td align="center" valign="middle" >3327.12</td><td align="center" valign="middle" >O-H stretching vibration of alcohol or carbonyl acid</td></tr><tr><td align="center" valign="middle" >2</td><td align="center" valign="middle" >2918.26</td><td align="center" valign="middle" >2920.86</td><td align="center" valign="middle" >2918.94</td><td align="center" valign="middle" >C-H stretching vibration of alkane</td></tr><tr><td align="center" valign="middle" >3</td><td align="center" valign="middle" >2184.23</td><td align="center" valign="middle" >2541.21</td><td align="center" valign="middle" >2209.05</td><td align="center" valign="middle" >C-H stretching of alkyne</td></tr><tr><td align="center" valign="middle" >4</td><td align="center" valign="middle" >1916.51</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >C-O stretching vibration of alkene and ketones</td></tr><tr><td align="center" valign="middle" >5</td><td align="center" valign="middle" >1636.18</td><td align="center" valign="middle" >1604.94</td><td align="center" valign="middle" >1628.34</td><td align="center" valign="middle" >C-H stretching of alkene</td></tr><tr><td align="center" valign="middle" >6</td><td align="center" valign="middle" >1029.54</td><td align="center" valign="middle" >897.33</td><td align="center" valign="middle" >660.63</td><td align="center" valign="middle" >CH bending vibration of C-H<sub>2</sub> and C-H<sub>3</sub> (finger print region)</td></tr></tbody></table></table-wrap><fig-group id="fig1"><label><xref ref-type="fig" rid="fig1">Figure 1</xref></label><caption><title> FTIR Spectroscopy for the biosorbents, (a) RBS; (b) BABS; (c) AABS.</title></caption><fig id ="fig1_1"><label>(b)</label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x21.png"/></fig><fig id ="fig1_2"><label>(c)</label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x22.png"/></fig><fig id ="fig1_3"><label></label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x23.png"/></fig></fig-group><fig id="fig2"  position="float"><label><xref ref-type="fig" rid="fig2">Figure 2</xref></label><caption><title> Effect of contact time on the percentage removal of Lead(II)</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x24.png"/></fig><p>due to increased availability of active binding site on the biosorbent surface and this is controlled by diffusion process from the bulk to the surface. However, during the last stages, biosorption is likely to be attachment- controlled process due to reduction in the available active sites. AABS has 96.00% removal at equilibrium, followed by BABS (66.90%) while RBS had the least percentage removal and adsorptive capacity even beyond 180 minutes of 63.9% and 6.39 mg・g<sup>−1</sup>, respectively. <xref ref-type="fig" rid="fig3">Figure 3</xref> reveals that, at lower concentrations of 20 - 40 mg・L<sup>−1</sup>, biosorption was completed at about 60 minutes while at higher concentration, the biosorption process became constant at 180 mins as observed in Figures 3(a)-3(c), respectively. At lower concentrations, all metal ions present in the solution interacted with binding sites and then facilitated about 70.1% on RBS (<xref ref-type="fig" rid="fig3">Figure 3</xref>(a)) 74.6% on BABS (<xref ref-type="fig" rid="fig3">Figure 3</xref>(b)) with 93% Pb(II) removal on AABS (<xref ref-type="fig" rid="fig3">Figure 3</xref>(c)). At higher concentrations between 80 - 120 mg・L<sup>−1</sup>, more Pb(II) is left unabsorbed in the solution due to the saturation of binding sites. This may be due to the increase in the number of ions competing for available binding sites on the three Banana Stalks considered in this study. This result is similar to other researcher findings [<xref ref-type="bibr" rid="scirp.51789-ref18">18</xref>] [<xref ref-type="bibr" rid="scirp.51789-ref50">50</xref>] .</p></sec><sec id="s3_3"><title>3.3. Effect of Adsorbent Dose</title><p>Varying adsorbent dosage of 0.2 to 2.0 g were used to test for the effect of adsorbent dose on the biosorption process keeping the initial lead concentration at 100 mg・L<sup>−1</sup>, while all other parameters were kept constant. It was observed as shown on <xref ref-type="fig" rid="fig4">Figure 4</xref> that, when the adsorbent dose was increased from 0.2 g to 2.0 g, the percentage adsorption generally increased from 30.2% to 97.3%, but the amount adsorbed per unit mass of adsorbent decreased considerably. The increase in the adsorption percentage or decrease in unit adsorption with increased dose of the biosorbent is due to the increase in active sites on the adsorbent and thus making easier penetration of the metal ions to the adsorption sites which is in agreement with previous researcher [<xref ref-type="bibr" rid="scirp.51789-ref33">33</xref>] . When the adsorbent added is beyond 0.6 g, the decrease in lead ion adsorption is not very prominent which is perhaps due to the formation of adsorbent agglomerates reducing available surface area and blocking some of the adsorption sites. Maximum adsorption capacity of lead ions was observed with adsorbent dose of 0.6 g with adsorption capacity of 15.8 mg・g<sup>−1</sup> and thereafter, a slow increase in the percentage removal was seen reaching a constant value with respect to adsorbent dosage.</p></sec><sec id="s3_4"><title>3.4. Effect of pH</title><p>Surface charges on the adsorbent and degree of ionization of the sorbate are affected by the pH of the solution and this makes pH and important factor in adsorptive studies. <xref ref-type="fig" rid="fig5">Figure 5</xref> reveals that, the adsorptive capacity was best at pH 8 with 89% removal of the lead ion. This is because biosorption is low at strong acidic medium (pH 2 - 4) because the surface charge on the biosorbents is positive, thus, Pb(II) is not favourable attached because of electrostatic repulsion between the RBS, BABS and AABS surfaces and the positively charged Pb(II). At higher pH, uptake increased because more metal binding sites could be exposed and carried negative charges, with</p><fig-group id="fig3"><label><xref ref-type="fig" rid="fig3">Figure 3</xref></label><caption><title> Effect of different initial lead concentration on the percentage removal of Pb(II) on Raw banana stalk biosorbent, (a) RBS; (b) BABS; (c) AABS.</title></caption><fig id ="fig3_1"><label>(b)</label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x25.png"/></fig><fig id ="fig3_2"><label>(c)</label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x26.png"/></fig><fig id ="fig3_3"><label></label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x27.png"/></fig></fig-group><fig id="fig4"  position="float"><label><xref ref-type="fig" rid="fig4">Figure 4</xref></label><caption><title> Effect of adsorbent dose on the percentage removal of Pb(II) removal using different biosorbents</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x28.png"/></fig><p>subsequent attraction of the positively charged metal ions with the biosorbent surface and this agreed with Bello et al. [<xref ref-type="bibr" rid="scirp.51789-ref40">40</xref>] on the adsorptive features of banana stalk-based activated carbon for malachite green dye removal. Experiments were carried out with the pH values of up to 8 due to the fact that metal precipitation appeared at higher pH values and interfered with the accumulation or biosorbent deterioration which was in agreement with the result obtained by Puranik and Paknikar [<xref ref-type="bibr" rid="scirp.51789-ref51">51</xref>] .</p></sec><sec id="s3_5"><title>3.5. Effect of Temperature</title><p>The percentage Pb(II) removal decreased with increased temperature for AABS as shown on <xref ref-type="fig" rid="fig6">Figure 6</xref> while BABS and RBS followed a reverse trend. AABS highest percentage removal was at 30˚C (82.4%) and declined with increasing temperature. The reverse in the trend of result obtained for AABS compared with the other two may be due to the fact that at increased temperature, AABS surface for adsorption has acquire the maximum energy for adsorption while RBS and BABS had not. A similar result, in which adsorptive capacity is inversely proportional to temperature was obtained by Paresh et al. [<xref ref-type="bibr" rid="scirp.51789-ref52">52</xref>] using a biosorbent. Lower temperature of 30˚C also favoured the Biosorption of Lead(II) and Nickel(II) using Pigeon peas hulls waste by Ramana et al. [<xref ref-type="bibr" rid="scirp.51789-ref53">53</xref>] .</p></sec><sec id="s3_6"><title>3.6. Adsorption Kinetics for Biosorption</title><sec id="s3_6_1"><title>3.6.1. The Pseudo-First-Order Kinetics Model</title><p>The pseudo-first-order kinetics equation is expressed as Equation (4) according to Lagergren [<xref ref-type="bibr" rid="scirp.51789-ref54">54</xref>]</p><disp-formula id="scirp.51789-formula132"><label>(4)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x29.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula> are the adsorption capacities at equilibrium (mg/g) and time<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula>, respectively. <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x33.png" xlink:type="simple"/></inline-formula>is the rate constant for Pseudo-first-order adsorption (min<sup>−1</sup>). Plots of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x34.png" xlink:type="simple"/></inline-formula> against <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x34.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x35.png" xlink:type="simple"/></inline-formula> at various temperatures resulted in linear graphs with negative slopes <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x34.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x35.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x36.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x34.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x35.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x36.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x37.png" xlink:type="simple"/></inline-formula> values were calculated as intercepts. All the values as well as their correlation coefficient <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x34.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x35.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x36.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x37.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x38.png" xlink:type="simple"/></inline-formula> are as shown on <xref ref-type="table" rid="table3">Table 3</xref> for biosorbents. Though values of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x34.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x35.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x36.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x37.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x38.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x39.png" xlink:type="simple"/></inline-formula> were high but high SSE and the various disparity between the values of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x34.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x35.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x36.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x37.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x38.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x39.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x40.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x34.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x35.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x36.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x37.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x38.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x39.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x40.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x41.png" xlink:type="simple"/></inline-formula> is an indication that the biosorption of Pb(II) unto AABS, BABS and RBS do not follow the pseudo-first-order kinetics.</p></sec><sec id="s3_6_2"><title>3.6.2. The Pseudo-Second-Order Kinetics Model</title><p>The pseudo-second-order kinetics equation is expressed as Equation (5) according to Ho and Mckay [<xref ref-type="bibr" rid="scirp.51789-ref55">55</xref>]</p><fig id="fig5"  position="float"><label><xref ref-type="fig" rid="fig5">Figure 5</xref></label><caption><title> Effect of pH on the percentage removal of Lead(II) using biosorbents</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x42.png"/></fig><fig id="fig6"  position="float"><label><xref ref-type="fig" rid="fig6">Figure 6</xref></label><caption><title> Effect of temperature on the percentage removal of Pb(II) using different banana stalk biosorbents</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/1-6702422x43.png"/></fig><table-wrap id="table3" ><label><xref ref-type="table" rid="table3">Table 3</xref></label><caption><title> Pseudo-first-order and pseudo-second-order kinetic parameters and correlation coefficients obtained for the biosorption of Pb(II)</title></caption><table><tbody><thead><tr><th align="center" valign="middle"  colspan="3"  ></th><th align="center" valign="middle"  colspan="4"  >Pseudo-first-order</th><th align="center" valign="middle"  colspan="4"  >Pseudo-second-order</th></tr></thead><tr><td align="center" valign="middle" >Adsorbents</td><td align="center" valign="middle" >T(˚C)</td><td align="center" valign="middle" >q<sub>e</sub>(exp) (mg・L<sup>−1</sup>)</td><td align="center" valign="middle" >k<sub>1</sub> (min<sup>−1</sup>)</td><td align="center" valign="middle" >q<sub>e</sub>(cal) (mg・L<sup>−1</sup>)</td><td align="center" valign="middle" >R<sup>2</sup></td><td align="center" valign="middle" >SSE</td><td align="center" valign="middle" >k<sub>2</sub> (g・mg<sup>−1</sup>・min<sup>−1</sup>)</td><td align="center" valign="middle" >q<sub>e</sub>(cal) (mg・L<sup>−1</sup>)</td><td align="center" valign="middle" >R<sup>2</sup></td><td align="center" valign="middle" >SSE</td></tr><tr><td align="center" valign="middle" >AABS</td><td align="center" valign="middle" >30</td><td align="center" valign="middle" >9.967</td><td align="center" valign="middle" >0.0091</td><td align="center" valign="middle" >7.184</td><td align="center" valign="middle" >0.969</td><td align="center" valign="middle" >1.14</td><td align="center" valign="middle" >0.0013</td><td align="center" valign="middle" >9.950</td><td align="center" valign="middle" >0.999</td><td align="center" valign="middle" >0.01</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >40</td><td align="center" valign="middle" >9.338</td><td align="center" valign="middle" >0.0105</td><td align="center" valign="middle" >11.413</td><td align="center" valign="middle" >0.855</td><td align="center" valign="middle" >0.85</td><td align="center" valign="middle" >0.0011</td><td align="center" valign="middle" >10.468</td><td align="center" valign="middle" >0.992</td><td align="center" valign="middle" >0.46</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >50</td><td align="center" valign="middle" >9.232</td><td align="center" valign="middle" >0.0114</td><td align="center" valign="middle" >2.436</td><td align="center" valign="middle" >0.684</td><td align="center" valign="middle" >2.77</td><td align="center" valign="middle" >0.0010</td><td align="center" valign="middle" >10.136</td><td align="center" valign="middle" >0.983</td><td align="center" valign="middle" >0.36</td></tr><tr><td align="center" valign="middle" >BABS</td><td align="center" valign="middle" >30</td><td align="center" valign="middle" >3.756</td><td align="center" valign="middle" >0.0056</td><td align="center" valign="middle" >8.602</td><td align="center" valign="middle" >0.864</td><td align="center" valign="middle" >1.98</td><td align="center" valign="middle" >0.0489</td><td align="center" valign="middle" >2.749</td><td align="center" valign="middle" >1.000</td><td align="center" valign="middle" >0.41</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >40</td><td align="center" valign="middle" >8.042</td><td align="center" valign="middle" >0.0059</td><td align="center" valign="middle" >6.181</td><td align="center" valign="middle" >0.884</td><td align="center" valign="middle" >0.76</td><td align="center" valign="middle" >0.0261</td><td align="center" valign="middle" >8.117</td><td align="center" valign="middle" >0.999</td><td align="center" valign="middle" >0.03</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >50</td><td align="center" valign="middle" >8.052</td><td align="center" valign="middle" >0.0091</td><td align="center" valign="middle" >8.355</td><td align="center" valign="middle" >0.932</td><td align="center" valign="middle" >0.10</td><td align="center" valign="middle" >0.0067</td><td align="center" valign="middle" >8.389</td><td align="center" valign="middle" >0.997</td><td align="center" valign="middle" >0.10</td></tr><tr><td align="center" valign="middle" >RBS</td><td align="center" valign="middle" >30</td><td align="center" valign="middle" >8.968</td><td align="center" valign="middle" >0.0069</td><td align="center" valign="middle" >8.737</td><td align="center" valign="middle" >0.887</td><td align="center" valign="middle" >0.08</td><td align="center" valign="middle" >0.0012</td><td align="center" valign="middle" >10.460</td><td align="center" valign="middle" >0.968</td><td align="center" valign="middle" >0.60</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >40</td><td align="center" valign="middle" >9.011</td><td align="center" valign="middle" >0.0056</td><td align="center" valign="middle" >7.448</td><td align="center" valign="middle" >0.862</td><td align="center" valign="middle" >0.64</td><td align="center" valign="middle" >0.0066</td><td align="center" valign="middle" >9.259</td><td align="center" valign="middle" >0.998</td><td align="center" valign="middle" >0.10</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >50</td><td align="center" valign="middle" >2.352</td><td align="center" valign="middle" >0.0118</td><td align="center" valign="middle" >1.553</td><td align="center" valign="middle" >0.841</td><td align="center" valign="middle" >0.33</td><td align="center" valign="middle" >0.0010</td><td align="center" valign="middle" >4.730</td><td align="center" valign="middle" >0.957</td><td align="center" valign="middle" >0.96</td></tr></tbody></table></table-wrap><disp-formula id="scirp.51789-formula133"><label>(5)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x44.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x45.png" xlink:type="simple"/></inline-formula> is the rate constant of pseudo-second-order adsorption (g・mg<sup>−1</sup>・min<sup>−1</sup>). For the boundary conditions <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x46.png" xlink:type="simple"/></inline-formula> to <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x47.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x48.png" xlink:type="simple"/></inline-formula> the integrated form of the equation becomes</p><disp-formula id="scirp.51789-formula134"><label>(6)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x49.png"  xlink:type="simple"/></disp-formula><p>Rearranging this equation, we have a linear form:</p><disp-formula id="scirp.51789-formula135"><label>(7)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x50.png"  xlink:type="simple"/></disp-formula><p>A plot of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x51.png" xlink:type="simple"/></inline-formula> versus <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x52.png" xlink:type="simple"/></inline-formula> was made and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x53.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x53.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x54.png" xlink:type="simple"/></inline-formula> value was estimated from the slopes and intercepts of the plot. The Sum of Error Square (SSE%) was also used to evaluate the difference between the <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x53.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x54.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x55.png" xlink:type="simple"/></inline-formula> and<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x53.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x54.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x55.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x56.png" xlink:type="simple"/></inline-formula>, giving as</p><disp-formula id="scirp.51789-formula136"><label>(8)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x57.png"  xlink:type="simple"/></disp-formula><p>where, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x58.png" xlink:type="simple"/></inline-formula>is the number of experiments.</p><p>The <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x59.png" xlink:type="simple"/></inline-formula> values were as high as 0.99 and the sum of square error was lower when compared to that of pseudo-first-order as there was good agreement between the <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x59.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x60.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x59.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x60.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x61.png" xlink:type="simple"/></inline-formula> of the pseudo-second-order kinetics as shown on <xref ref-type="table" rid="table3">Table 3</xref>. Therefore the biosorption of Pb(II) onto AABS,BABS and RBS follows a pseudo-second- order kinetics.</p></sec></sec><sec id="s3_7"><title>3.7. Adsorption Isotherms AABS</title><sec id="s3_7_1"><title>3.7.1. Langmuir Isotherm Model</title><p>Langmuir isotherm is based on the monolayer sorption of Pb(II) on the surface of carbon sites and is represented linearly by the following equation [<xref ref-type="bibr" rid="scirp.51789-ref56">56</xref>] :</p><disp-formula id="scirp.51789-formula137"><label>(10)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x62.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x63.png" xlink:type="simple"/></inline-formula> (mg/L) and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x63.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x64.png" xlink:type="simple"/></inline-formula> (mg/g) are the concentration of Pb(II) solution (mg/L) and the amount of adsorbed lead at equilibrium, respectively, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x63.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x64.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x65.png" xlink:type="simple"/></inline-formula>or <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x63.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x64.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x65.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x66.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x63.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x64.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x65.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x66.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x67.png" xlink:type="simple"/></inline-formula> are Langmuir constants related to sorption capacity (mg/g) and the energy of sorption (L/mg) respectively.</p><p>The essential characteristics of the Langmuir isotherm can be expressed in terms of a dimensionless equilibrium parameter <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x68.png" xlink:type="simple"/></inline-formula> which confirms the favourability of the adsorption process. Given as,</p><disp-formula id="scirp.51789-formula138"><label>(11)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x69.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x70.png" xlink:type="simple"/></inline-formula> is the Langmuir constant and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x70.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x71.png" xlink:type="simple"/></inline-formula> is the highest Pb(II) concentration (mg/L).</p><p>The value of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x72.png" xlink:type="simple"/></inline-formula> indicates the type of the isotherm to be either unfavourable<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x72.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x73.png" xlink:type="simple"/></inline-formula>, linear<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x72.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x73.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x74.png" xlink:type="simple"/></inline-formula>, favourable <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x72.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x73.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x74.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x75.png" xlink:type="simple"/></inline-formula> or irreversible<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x72.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x73.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x74.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x75.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x76.png" xlink:type="simple"/></inline-formula>. The values of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x72.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x73.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x74.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x75.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x76.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x77.png" xlink:type="simple"/></inline-formula> reported in <xref ref-type="table" rid="table4">Table 4</xref> obtained at various temperatures were &lt;1, indicating that the adsorption of Pb(II) onto AABS is favourable. The value of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x72.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x73.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x74.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x75.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x76.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x77.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x78.png" xlink:type="simple"/></inline-formula> obtained was compared with those of other adsorbents used for Pb(II) removal from aqueous solution and the present study gave the best as shown on <xref ref-type="table" rid="table5">Table 5</xref>.</p></sec><sec id="s3_7_2"><title>3.7.2. Freundlich Isotherm Model</title><p>Freundlich isotherm describes the heterogeneous surface energies by multilayer sorption and is expressed by the following equation [<xref ref-type="bibr" rid="scirp.51789-ref57">57</xref>] :</p><disp-formula id="scirp.51789-formula139"><label>(12)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x79.png"  xlink:type="simple"/></disp-formula><table-wrap id="table4" ><label><xref ref-type="table" rid="table4">Table 4</xref></label><caption><title> Comparison of the Isotherms for the adsorption of lead onto AABS at different temperatures</title></caption><table><tbody><thead><tr><th align="center" valign="middle" ></th><th align="center" valign="middle"  colspan="3"  >Temperature (K)</th></tr></thead><tr><td align="center" valign="middle" >Models</td><td align="center" valign="middle" >303</td><td align="center" valign="middle" >318</td><td align="center" valign="middle" >333</td></tr><tr><td align="center" valign="middle" >Langmuir isotherm</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x80.png" xlink:type="simple"/></inline-formula>(mg・g<sup>−1</sup>)</td><td align="center" valign="middle" >13.53</td><td align="center" valign="middle" >16.50</td><td align="center" valign="middle" >18.12</td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x81.png" xlink:type="simple"/></inline-formula>(L・mg<sup>−</sup><sup>1</sup>)</td><td align="center" valign="middle" >0.083</td><td align="center" valign="middle" >0.49</td><td align="center" valign="middle" >1.08</td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x82.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >0.98</td><td align="center" valign="middle" >0.99</td><td align="center" valign="middle" >0.99</td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x83.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >0.099</td><td align="center" valign="middle" >0.095</td><td align="center" valign="middle" >0.090</td></tr><tr><td align="center" valign="middle" >Freudlich isotherm</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x84.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >1.49</td><td align="center" valign="middle" >1.04</td><td align="center" valign="middle" >0.62</td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x85.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >1.69</td><td align="center" valign="middle" >1.44</td><td align="center" valign="middle" >1.66</td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x86.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >0.99</td><td align="center" valign="middle" >0.99</td><td align="center" valign="middle" >0.90</td></tr><tr><td align="center" valign="middle" >Temkin isotherm</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >B</td><td align="center" valign="middle" >2.74</td><td align="center" valign="middle" >3.16</td><td align="center" valign="middle" >2.04</td></tr><tr><td align="center" valign="middle" >A</td><td align="center" valign="middle" >1.04</td><td align="center" valign="middle" >0.63</td><td align="center" valign="middle" >0.40</td></tr><tr><td align="center" valign="middle" >B</td><td align="center" valign="middle" >0.92</td><td align="center" valign="middle" >0.82</td><td align="center" valign="middle" >1.32</td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x87.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >0.96</td><td align="center" valign="middle" >0.97</td><td align="center" valign="middle" >0.86</td></tr><tr><td align="center" valign="middle" >D-R isotherm</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x88.png" xlink:type="simple"/></inline-formula>(mg・g<sup>−</sup><sup>1</sup>)</td><td align="center" valign="middle" >6.85</td><td align="center" valign="middle" >42.20</td><td align="center" valign="middle" >5.16</td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x89.png" xlink:type="simple"/></inline-formula>(mol<sup>2</sup>・J<sup>−</sup><sup>2</sup>) &#215; 10<sup>−</sup><sup>6</sup></td><td align="center" valign="middle" >0.80</td><td align="center" valign="middle" >0.24</td><td align="center" valign="middle" >6.01</td></tr><tr><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x90.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >0.79</td><td align="center" valign="middle" >0.91</td><td align="center" valign="middle" >0.83</td></tr><tr><td align="center" valign="middle" >E (kJ・mol<sup>−</sup><sup>1</sup>)</td><td align="center" valign="middle" >0.79</td><td align="center" valign="middle" >1.58</td><td align="center" valign="middle" >0.28</td></tr></tbody></table></table-wrap><table-wrap id="table5" ><label><xref ref-type="table" rid="table5">Table 5</xref></label><caption><title> Comparison of adsorption capacities of various adsorbents for Pb(II)</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Adsorbent</th><th align="center" valign="middle" >Adsorptive capacity (<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x91.png" xlink:type="simple"/></inline-formula>in mg・g<sup>−</sup><sup>1</sup>)</th><th align="center" valign="middle" >Reference</th></tr></thead><tr><td align="center" valign="middle" >Saracaindica leaf powder</td><td align="center" valign="middle" >1.19</td><td align="center" valign="middle" >Goyal et al. [<xref ref-type="bibr" rid="scirp.51789-ref60">60</xref>]</td></tr><tr><td align="center" valign="middle" >Bentolite</td><td align="center" valign="middle" >7.56</td><td align="center" valign="middle" >Mishra and Patel [<xref ref-type="bibr" rid="scirp.51789-ref61">61</xref>]</td></tr><tr><td align="center" valign="middle" >Activated carbon</td><td align="center" valign="middle" >6.68</td><td align="center" valign="middle" >Mishra and Patel [<xref ref-type="bibr" rid="scirp.51789-ref61">61</xref>]</td></tr><tr><td align="center" valign="middle" >Fly ash</td><td align="center" valign="middle" >4.98</td><td align="center" valign="middle" >Mishra and Patel [<xref ref-type="bibr" rid="scirp.51789-ref61">61</xref>]</td></tr><tr><td align="center" valign="middle" >Kaolin</td><td align="center" valign="middle" >4.50</td><td align="center" valign="middle" >Mishra and Patel [<xref ref-type="bibr" rid="scirp.51789-ref61">61</xref>]</td></tr><tr><td align="center" valign="middle" >Banana stalk</td><td align="center" valign="middle" >13.53</td><td align="center" valign="middle" >This study</td></tr></tbody></table></table-wrap><p>Linearised as,</p><disp-formula id="scirp.51789-formula140"><label>(13)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x92.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x93.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x93.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x94.png" xlink:type="simple"/></inline-formula> are the Freundlich constants incorporating the factors affecting the adsorption capacity and the degree of non-linearity between the solute concentration in the solution and the amount adsorbed at equilibrium respectively. Plots of log <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x93.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x94.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x95.png" xlink:type="simple"/></inline-formula> versus log <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x93.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x94.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x95.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x96.png" xlink:type="simple"/></inline-formula> gave linear graphs with high to<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x93.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x94.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x95.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x96.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x97.png" xlink:type="simple"/></inline-formula>. Comparing the <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x93.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x94.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x95.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x96.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x97.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x98.png" xlink:type="simple"/></inline-formula><sup> </sup>values of the two isotherms (<xref ref-type="table" rid="table4">Table 4</xref>), the adsorption fits the Langmuir model better. Value of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x93.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x94.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x95.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x96.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x97.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x98.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x99.png" xlink:type="simple"/></inline-formula> indicates that the adsorption is favourable.</p></sec><sec id="s3_7_3"><title>3.7.3. Temkin Isotherm Model</title><p>Temkin isotherm based on the ions sorption heat, which is due to the sorbate and adsorbent interactions, is given by Temkin and Pyzhev [<xref ref-type="bibr" rid="scirp.51789-ref58">58</xref>]</p><disp-formula id="scirp.51789-formula141"><label>(14)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x100.png"  xlink:type="simple"/></disp-formula><p>where:</p><disp-formula id="scirp.51789-formula142"><label>(15)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x101.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula> is the concentration of sorbate at equilibrium (mg・L<sup>−1</sup>), <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula>is the quantity of sorbate bioadsorbed at equilibrium (mg・g<sup>−1</sup>), <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x104.png" xlink:type="simple"/></inline-formula>is the equilibrium binding constant (L/mol) corresponding to the maximum binding energy and constant <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x104.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x105.png" xlink:type="simple"/></inline-formula> is related to the heat of sorption. <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x104.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x105.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x106.png" xlink:type="simple"/></inline-formula>is the temperature<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x104.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x105.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x106.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x107.png" xlink:type="simple"/></inline-formula>, and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x104.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x105.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x106.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x107.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x108.png" xlink:type="simple"/></inline-formula> is the ideal gas constant (8.314 &#215; 10<sup>−3</sup> kJ・mol<sup>−1</sup>・K<sup>−1</sup>). The values of<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x104.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x105.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x106.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x107.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x108.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x109.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x104.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x105.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x106.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x107.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x108.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x109.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x110.png" xlink:type="simple"/></inline-formula>and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x104.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x105.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x106.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x107.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x108.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x109.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x110.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x111.png" xlink:type="simple"/></inline-formula> are given in <xref ref-type="table" rid="table4">Table 4</xref>, the lower value of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x102.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x103.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x104.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x105.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x106.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x107.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x108.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x109.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x110.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x111.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x112.png" xlink:type="simple"/></inline-formula> being 1.32 kJ・mol<sup>−1</sup> (&lt;8 kJ・mol<sup>−1</sup>) indicates that the interaction between lead ions and AABS can be expressed as a physisorption process.</p></sec><sec id="s3_7_4"><title>3.7.4. Dubinin-Radushkevich Isotherm (D-R) Model</title><p>The Dubinin-Radushkevich (D-R) model was used to estimate the characteristic porosity of the AABS and the apparent energy of adsorption. The non-linear form of the D-R isotherm equation is given in Equation (16) according to Dubinin-Rasdushkevich [<xref ref-type="bibr" rid="scirp.51789-ref59">59</xref>] :</p><disp-formula id="scirp.51789-formula143"><label>(16)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x113.png"  xlink:type="simple"/></disp-formula><p>The equation is linearised by taking the logarithm on both sides of equation and is expressed as,</p><disp-formula id="scirp.51789-formula144"><label>(17)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x114.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x115.png" xlink:type="simple"/></inline-formula> is the heavy metal amount that is adsorbed per unit mass of AABS in mg・g<sup>−1</sup>; <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x115.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x116.png" xlink:type="simple"/></inline-formula> is the maximum adsorption capacity in mg・g<sup>−1</sup>; <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x115.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x116.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x117.png" xlink:type="simple"/></inline-formula>is the free energy of sorption per mole of the sorbate as it migrates to the surface of AABS from an infinite distance in the solution in mol<sup>2</sup>・kJ<sup>−2</sup>, and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x115.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x116.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x117.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x118.png" xlink:type="simple"/></inline-formula> is the Polanyi potential. The Polanyi potential <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x115.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x116.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x117.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x118.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x119.png" xlink:type="simple"/></inline-formula> can be given as:</p><disp-formula id="scirp.51789-formula145"><label>(18)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x120.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x121.png" xlink:type="simple"/></inline-formula> is the gas constant in kJ・K<sup>−1</sup>・mol<sup>−1</sup>, and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x121.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x122.png" xlink:type="simple"/></inline-formula> is the absolute temperature in<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x121.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x122.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x123.png" xlink:type="simple"/></inline-formula>. A plot of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x121.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x122.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x123.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x124.png" xlink:type="simple"/></inline-formula> versus <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x121.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x122.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x123.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x124.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x125.png" xlink:type="simple"/></inline-formula> gave a linear plot (not shown) from which <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x121.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x122.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x123.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x124.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x125.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x126.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x121.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x122.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x123.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x124.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x125.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x126.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x127.png" xlink:type="simple"/></inline-formula> are obtained from the slopes and the intercepts respectively (<xref ref-type="table" rid="table4">Table 4</xref>). Similarly, the <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x121.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x122.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x123.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x124.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x125.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x126.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x127.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x128.png" xlink:type="simple"/></inline-formula> value obtained was then used to estimate the mean free energy of adsorption <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x121.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x122.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x123.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x124.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x125.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x126.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x127.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x128.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x129.png" xlink:type="simple"/></inline-formula> which is calculated by,</p><disp-formula id="scirp.51789-formula146"><label>(19)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x130.png"  xlink:type="simple"/></disp-formula><p>The values of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x131.png" xlink:type="simple"/></inline-formula> were found to be in the range 0.29 - 1.58 kJ・mol<sup>−1</sup> over the range of temperatures used in this study. Because E &lt; 8 kJ・mol<sup>−1</sup>, it suggests that the biosorption of lead ion onto AABS is physically controlled.</p></sec></sec><sec id="s3_8"><title>3.8. Thermodynamics Studies for AABS</title><p>Thermodynamic parameters; standard free energy<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x132.png" xlink:type="simple"/></inline-formula>, standard enthalpy <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x132.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x133.png" xlink:type="simple"/></inline-formula> and standard entropy<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x132.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x133.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x134.png" xlink:type="simple"/></inline-formula> were calculated using the following equation:</p><disp-formula id="scirp.51789-formula147"><label>(20)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x135.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.51789-formula148"><label>(21)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x136.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula> is the Langmuir constant (L/mol), <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x138.png" xlink:type="simple"/></inline-formula>is the temperature in <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x138.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x139.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x138.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x139.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x140.png" xlink:type="simple"/></inline-formula> is the gas constant (kJ・mol<sup>−1</sup>・K<sup>−1</sup>). A plot of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x138.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x139.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x140.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x141.png" xlink:type="simple"/></inline-formula> against <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x138.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x139.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x140.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x141.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x142.png" xlink:type="simple"/></inline-formula> gave linear plot from which <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x138.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x139.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x140.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x141.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x142.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x143.png" xlink:type="simple"/></inline-formula><sup> </sup>and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x138.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x139.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x140.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x141.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x142.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x143.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x144.png" xlink:type="simple"/></inline-formula> values were obtained from the slope and intercept respectively. From the pseudo-second-order rate constant, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x138.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x139.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x140.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x141.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x142.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x143.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x144.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x145.png" xlink:type="simple"/></inline-formula>(<xref ref-type="table" rid="table3">Table 3</xref>), the activation energy <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x137.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x138.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x139.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x140.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x141.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x142.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x143.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x144.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x145.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x146.png" xlink:type="simple"/></inline-formula> for the adsorption of Pb(II) onto AABS could be determined using equation</p><disp-formula id="scirp.51789-formula149"><label>(22)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/1-6702422x147.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x148.png" xlink:type="simple"/></inline-formula> is the biosorption rate constant, A is the Arrhenius constant, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x148.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x149.png" xlink:type="simple"/></inline-formula>is the activation energy (kJ・mol<sup>−1</sup>). By plotting <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x148.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x149.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x150.png" xlink:type="simple"/></inline-formula> versus<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x148.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x149.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x150.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x151.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x148.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x149.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x150.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x151.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x152.png" xlink:type="simple"/></inline-formula>can be obtained from the slope of the linear plot and is presented in <xref ref-type="table" rid="table6">Table 6</xref>. The negative free energy values at various temperature as shown on <xref ref-type="table" rid="table6">Table 6</xref> indicates that the adsorption of Pb(II) unto AABS is spontaneous and thermodynamically favoured. In addition, the range of values between 0 to −20 kJ・mol<sup>−1</sup> further confirms that the adsorption process is a physisorption process. The positive value of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x148.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x149.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x150.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x151.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x152.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x153.png" xlink:type="simple"/></inline-formula> obtained shows that the process is endothermic in nature and it range of values (2.1 - 20.9 kJ・mol<sup>−1</sup>) implies that the process is physically controlled. The values of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x148.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x149.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x150.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x151.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x152.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x153.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x154.png" xlink:type="simple"/></inline-formula> is positive indicating that there was randomness at the solid-liquid interface during the adsorption of the Pb(II) onto AABS.</p></sec></sec><sec id="s4"><title>4. Conclusion</title><p>The biosorption experiment carried out using banana stalk (Musa paradisiaca) was found suitable for the adsorption of Pb(II). Considering the three modified banana stalk (AABS, BABS and RBS) used in this study, AABS was established to be the best adsorbent of Pb(II) with 96.76% metal removal. The operational parameter (Adsorbent dose, temperature, initial metal ion concentration, time and pH) had varied effects on the percentage Pb(II) removal. It was found out that Pseudo-second order kinetic model was suitable for the adsorption of</p><table-wrap id="table6" ><label><xref ref-type="table" rid="table6">Table 6</xref></label><caption><title> Thermodynamic parameters for the biosorption of Pb(II) by AABS</title></caption><table><tbody><thead><tr><th align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x155.png" xlink:type="simple"/></inline-formula>(˚C)</th><th align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x156.png" xlink:type="simple"/></inline-formula>(kJ・mol<sup>−</sup><sup>1</sup>)</th><th align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x157.png" xlink:type="simple"/></inline-formula>(kJ・mol<sup>−</sup><sup>1</sup>)</th><th align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x158.png" xlink:type="simple"/></inline-formula>(kJ・mol<sup>−</sup><sup>1</sup>)</th><th align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x159.png" xlink:type="simple"/></inline-formula>(kJ・mol<sup>−</sup><sup>1</sup>)</th></tr></thead><tr><td align="center" valign="middle" >30</td><td align="center" valign="middle" >−18.75</td><td align="center" valign="middle" >12.63</td><td align="center" valign="middle" >0.049</td><td align="center" valign="middle" >4.365</td></tr><tr><td align="center" valign="middle" >40</td><td align="center" valign="middle" >−24.02</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >50</td><td align="center" valign="middle" >−26.00</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap><p>Pb(II). Four adsorption Isotherms (Langmuir, Freudlich, Temkin and Dubinin-Radushkevich) were tested and confirmed suitable to describe the nature of the adsorption process of Pb(II) removal from aqueous solution, but Langmuir Isotherm was the best. The thermodynamics studies showed that <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x160.png" xlink:type="simple"/></inline-formula> values were negative indicating that the process of Pb(II) adsorption onto AABS was spontaneous and the positive <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x160.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x161.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x160.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x161.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-6702422x162.png" xlink:type="simple"/></inline-formula> suggests that the biosorption process is an endothermic reaction.</p></sec><sec id="s5"><title>Acknowledgements</title><p>The authors acknowledge the support given by Dr. O. S. Bello of Department of Pure and Applied Chemistry, Ladoke Akintola University of Technology, Ogbomoso-Nigeria in making some laboratory facilities available for this work from his Third World Academy of Science (TWAS) Research Grant (Grant number: 11-249 RG/CHE/AF/AC_1_UNESCO FR: 3240262674).</p></sec><sec id="s6"><title>NOTES</title></sec></body><back><ref-list><title>References</title><ref id="scirp.51789-ref1"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">Ko, D.C.K., Porter, J.F. and Mckay, G. (2000) Optimized Correlation for the Fixed Bed Adsorption of Metal Ions on Bone Char. Chemical Engineering Science, 55, 5819-5829. http://dx.doi.org/10.1016/S0009-2509(00)00416-4</mixed-citation></ref><ref id="scirp.51789-ref2"><label>2</label><mixed-citation publication-type="other" xlink:type="simple">Koller, K.B.T., Spurgeon, A. and Levy, L. (2004) Recent Development in Low Level Exposure and Intellectual Impairment in Children. 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