An isotherm describes the equilibrium relationship between the adsorbate concentration in the liquid phase and that on the adsorbent’s surface at a given condition. It gives the most appropriate equilibrium correlation [11] . They are also important for comparing biosorption performance, optimization, design and prediction purposes [12] . The biosorption of benzene on clay and sandy soil was optimized by analyzing equilibrium curve of the following three isotherm models.

a) Langmuir Isotherm: The Langmuir Isotherm [13] developed by Irving Langmuir (1916) was originally used to describe the gas-solid phase and adsorption onto activated carbon but is now extended and generally applied to liquid-solid interaction. The equation is:

where q_e (mg/g) and C_e (mg/L) are the solid phase concentration and liquid phase concentration of benzene at equilibrium, respectively. Q_o (mg/g) is the maximum sorption capacity and b (L/mg) is the Langmuir constant related to the affinity of the adsorbate for the adsorbent. The linearized form of Equation (1) is given as:

b) Freundlich Isotherm: The Freundlich Isotherm, [14] relates the solute concentration on the adsorbent surface to the solute concentration in the liquid phase. The isotherm assumes that adsorption occurs on a heterogeneous adsorbent surface (i.e. multilayer adsorption). Freundlich model is represented by the equation;

Equation (3) can be linearized in logarithmic form, Equation (4) and the Freundlich constants can be determined,

where k_f and n are the Freundlich constants characteristic of the system. k_f and n are indicators of adsorption capacity and adsorption intensity, respectively.

c) Tempkin Isotherm: The Tempkin Isotherm [15] takes into account the interaction between adsorbate and adsorbent and assumes a linear decrease in the heat of adsorption instead of a logarithmic decrease. Tempkin Isotherm is expressed as;

which on linearization gives

Various parameters obtained from Langmuir, Freundlich and Tempkin Isotherms are shown in Table 1.

A kinetic model is a mathematical representation of the rate at which a chemical reaction or process takes place. The rate at which chemical reactions occur varies from very rapid to very slow [16] .

Adsorption kinetics is one of the most important parameters for determining the adsorption mechanism and also to investigate the efficacy of adsorbent for the removal of pollutants. Pseudo-first order model [17] and pseudo second order model [18] were used to analyze the kinetic data

The pseudo first order kinetics is given in its linearized form as:

where q_e and q_t are the amounts of benzene sorbed per unit weight of sorbent at equilibrium and at time t (min), respectively. k₁ is the rate constant of the pseudo first order sorption (min⁻¹). The rate constant k₁ is obtained from the linear plot of the graph.

The pseudo second order rate equation can also be expressed as

the linear plot of this graph gives the slope 1/q_e and intercept

Clay and Sandy soil samples used in this study were obtained from Ikpoba River, Benin City, Edo State, Nigeria. On collection, the clay and sandy soil samples were kept separately in double plastic bags to ensure the prevalence of anaerobic conditions. The samples were stored in a refrigerator for some days and were subsequently analyzed for their PAHs content [19] .

Ten gram (10 g) of the clay soil sample was measured and added to a beaker containing 40 ml of a solvent made up of 50% acetone and 50% dichloromethane. The clay soil-solvent mixture was then placed in a sonicator for about 20 minutes to heat it to 70˚C. To the soil-solvent mixture, 10 g of anhydrous sodium sulphate was added and then shaken gently to obtain a clear extract. The content of the beaker was separated leaving only soil in the beaker. The extracted solvent was poured into a conical flask and then put into a rotary evaporator. After evaporation for some minutes, the conical flask was withdrawn from the evaporator and 2 ml of solvent was measured with a pipette and put into vial bottle for analysis using a capillary column Gas Chromatogram equipped with a flame ionization detector (US, EPA, 2004).

For the sandy soil sample, the same procedure as outlined above was repeated. The clay and sand soil samples were washed with distilled water by a process involving agitation and dissolution. The soil samples were soaked in distilled water for two days while continuously stirring using a manual stirrer so as to remove all contaminants. The mixture was drained using a micro sieve and continuously flushed with distilled water several times. The mixture was then allowed to drain completely and put into a furnace to get heated up at a high temperature to dry the sample. It was subsequently allowed to cool naturally in open air. The sample was then analyzed using a Gas Chromatogram equipped with a flame ionization detector.

The clay and sandy soil samples were analyzed for their physico-chemical properties as shown in Table 2.

The analyzed clay sandy soil samples were used to carry out adsorption studies using benzene as adsorbate and the Iodine adsorption method was used to determine the surface area of the soil samples. These soil samples were hydrophilic in nature; this can be seen with the amount of moisture content present in them. The adsorption of benzene on clay and sandy soil was determined by carrying out the adsorption studies in tightly corked 1000 ml flasks. For each experiment, 100 ml of benzene solution with different initial concentrations (50 - 250 mg/l) was placed in a flask. The adsorbent capacity for the uptake of benzene at time t, q_t (mg/g), was calculated. This was achieved by testing the kinetics to determine the adsorption mechanism using pseudo-first order and pseudo second order adsorption models.

To determine the effect of adsorbate concentration, the concentration of benzene was varied between 50 to 250 mg/l for 1 g of clay and sandy soil particles, respectively with particle size of 220 μm, added to each flask and kept in a shaker at 120 rpm at room temperature for predetermined equilibrium times of 32 hrs, 26 hrs, 34 hrs, and 22 hrs, 20 hrs, 30 hrs, respectively. Then the samples were filtered and the residual concentration of benzene in the filtrate was analysed using UV-Visible spectrophotometer at maximum wave length of 229 nm for benzene.

To determine the effect of agitation time, 250 mg/l concentration was prepared. 100 mls from the 250 mg/l concentration was measured and placed in a container. 1 g of soil sample was measured and was added to the container. The sample was placed in a mechanical shaker for agitation. After 2 hrs the sample was removed, and it was immediately filtered to remove the adsorbent. The equilibrium concentration of the effluent solution benzene was measured using the UV spectrophotometer.

Effect of varying concentration on the adsorption of benzene.

The effect of the variation of concentration of benzene in an effluent solution is described by using the Langmuir, Freundlich and Tempkin Isotherm models. These isotherms are shown graphically below.

The above graphs show that the equilibrium concentration and the amount of benzene adsorbed increases as the initial effluent concentration increases. The Langmuir, Freundlich and Tempkin Isotherm constants were calculated from the slope and intercepts of the graphs. The linear coefficient of determination, R² was used as an error function to evaluate the fitness of each isotherm equation to the experimental data obtained from the optimization process employed. For the adsorbent clay in Figures 1-3, the Freundlich Isotherm in Figure 5 gave the highest correlation coefficient (R² = 0.8108) followed by the Langmuir isotherm (R² = 0.7999). The linear coefficient of determination for the Tempkin Isotherm was not very high (R² = 0.014). The graphs show that both the Freundlich and Langmuir Isotherms models can sufficiently describe the adsorption data well for benzene. The fact that the sorption process showed a good fit to the Langmuir Isotherm suggests a finite adsorption capacity and energetically equivalent sites [20] .

With regards to the adsorbent sandy soil, the graphs in Figures 4-6 show that the Freundlich Isotherm gave the highest correlation coefficient (R² = 0.9468) followed by the Langmuir isotherm (R² = 0.9152). The linear coefficient of determination for the Tempkin Isotherm (R² = 0.1169) was not high. Both the Freundlich and

Langmuir Isotherms models can sufficiently describe the adsorption data well for benzene in sandy soil. A comparison of the adsorbents clay and sandy soil for the adsorption of benzene indicates from this study that sandy soil sorbed less than clay.

This experimental data for this study best fits the Freundlich model. This is consistent with the work of [21] in which clay adsorbent was best used. The adsorption capacity Q_o (mg/g) and energy of adsorption n (mg⁻¹) for benzene are 0.286 (mg/g) and 0.0107 (mg⁻¹), respectively.

Benzene adsorption kinetics onto clay and sandy soil with their respective fits are shown in Figure 7. The graph shows that the variation of concentration with time for benzene sorption in clay and sandy soils took 32 hrs and 22 hrs for equilibrium to be reached for clay and sandy soils, respectively. The graph illustrates that the variation of benzene concentration with time for clay and sandy soils shows a difference of about 10 hrs. Furthermore, the graph shows that there was a steady adsorption of benzene by the two different adsorbents.

The data obtained were analyzed with the Lagergren pseudo first order kinetic model. A plot of ln(q_e − q_t) against time t (hrs) is shown in Figure 8 with the linear equations from clay and sandy soils. It shows that k₁ for the pseudo-first order adsorption is −0.256 for sandy soil and 0.0735 for clay. q_e which was also obtained from the graph is15.49 mg/g and 19.50 mg/g for clay and sandy soil, respectively. The correlation coefficient (R²) is 0.9273 for sandy soil and 0.7632 for clay, respectively.

The results obtained when the data was subjected to the pseudo-second order equation are shown in Figure 9.

From the graph in Figure 9, q_e is from the slope and k₂ is from the intercept. q_e values are 37.59 (mg/g) for clay and 36.50 (mg/g) for sandy soil. k₂ values are 0.00083 and 0.00190 for clay and sandy soil samples, respectively. Also the correlation coefficients (R²) for this model are 0.5962 for clay and 0.6732 for sandy soil, respectively. The kinetic model that best fitted the experimental data obtained for both clay and sandy soil was the pseudo second order model.