All the selected reagents were of analytical grade and purchased from Merck. The stock solutions for preparation of lead solution were prepared by dissolving Pb(CH₃OO)₂∙3H₂O in deionized water.TiCl₄ and NH₄ were used to synthesize TiO₂ nanoparticles by the sol-gel method. For adjusting pH, 1 M HNO₃, NaOH and NH₃ solutions as well as a Metrohm pH meter model 744 were used. Sartorius Electrical Balans Model BP 221S, Laboren oven, mixer HT Infors AG model CH-4103-BOT Tmingen, Centrifuge model MSE ministral1000 were used to conduct the experiments, and analysis of heavy metals was carried out using Inductivity Coupled Plasma (ICP) model Optima 2000 DV.

TiCl₄ (30 mL) was added to deionized water (1L) under vigorous stirring (1000 rpm). pH of the solution was adjusted by adding NH₃ (drop wise) to reach 7.8, and the mixing was continued until gel was formed. The gel was left for 7 days until colloidal sediment of TiOH₂ was formed. Then, TiOH₂ sediment was separated by filtration. The reaction was performed as presented by Equation (1).

The separated sediment was placed in oven for 24 hours at 70˚C. Then, calcination was performed at 400˚C for 4 hours.

Adsorption experiments were performed by adding 0.15 g of adsorbent to 50 mL of solution with the initial Pb²⁺ ions concentration of 25 mg/L in a flask. The effect of pH on sorption ions was studied in the range of 3 - 6.5, at the temperature of 25˚C and contact time of 4 h. The effect of contact time was investigated by varying the time from 10 to 240 min, at a temperature of 25˚C, with the obtained pH values. The effect of adsorbent weight on sorption metal ions was studied in the range of 1 to 4 g/L (0.05, 0.10, 0.15 and 0.20 g of adsorbent in 50 mL of metal ions solution) at the contact time of 4 h, temperature of 25˚C and the obtained pH values.

The concentration of lead ions before and after equilibrium sorption was determined using ICP. The uptake percentages of the lead ions were calculated according to Equation (2) [5] :

where, C₀ and C_e are initial and equilibrium concentrations of ions (mg/L), respectively.

Characterization of crystalline size of the adsorbent was determined by XRD (model STV_MP STOE Company, Germany).For this purpose, Cu radiation (λCu = 1.5405 A) was used and the sample was scanned in a 2θ range of 8 - 108.5˚ at a scanning rate of 0.015˚/S. The crystalline size was determined from the characteristic peak at 2θ = 25.326˚ (corresponding to the 440 plane) using Scherrer formula crystalline size, nm = Kλ/W cosθ, where K is shape factor = 0.9, λ is wavelength of the X-ray used (1.5405), and W is (Wb-Ws, width of peak at half-height at 2θ = 25.326) the difference of broadened profile width of the experimental sample and the standard width of reference TiO₂ sample(reference code 01-073-1764, pdf2-2003) [15] . Comparison of the graphs shows that all peaks are in good agreement with the standard spectrum [16] . The mean crystalline size was obtained to be 21.1 nm. Figure 1 shows the XRD graph of synthesized nano TiO₂ sample (Figure 1(a)) in comparison of reference sample of TiO₂ (Figure 1(b)).

Figure 2 shows the FT-IR (model Vector 22 Brucker Company, USA) analysis of nano TiO₂. All the adsorption bands were at 3446, 1635, 1031 and 455 cm⁻¹. The strong IR band at 3446 cm⁻¹ was assigned to the stretching bands of adsorbed water [15] . The bands around the peak of 1635 cm⁻¹ were assigned to Hydroxyl bond. The strong bands around 1031 cm⁻¹ were related to the titanium, oxygen and nitrogen bonds (Ti-O-N). Broad band around the peak of 455 cm⁻¹ was related to the vibration of titanium and oxygen bonds and anatase form of TiO₂ [17] .

The TEM images (taken by PHILIPS, EM 208) of synthesized nano TiO₂ are illustrated in Figure 3. It can be observed that the nanoparticles are very aggregate, with a mean diameter of about 21.1 nm. In the present context, the discrepancy between the X-ray crystallite size and that measured in the TEM can be interpreted as being attributed to lattice distortions in the prepared powder. As a result of a sub-structure much smaller than the nano-crystalline, the grain size measured in the TEM is in good agreement with the findings of Chandramouli et al. [17] .

Specific surface area was determined through nitrogen adsorption isotherms method. Using the BET (model

Quantachrome NOVA 2200e) method, the surface area of the sample was calculated to be 55.35 m²/g. Also, the pore size distribution was attained by Barrett-Joyner-Halenda (BJH method revealed the mesoporosity) [18] . The pore size obtained by this method was 19.21 nm.

Figure 5 indicates the variation in amount of lead ions adsorbed at different time intervals for a fixed initial ion concentration of 25 mg/L. The data revealed that the amount of adsorbed ions studied increased with the increase of contact time. To describe changes of metal ions sorption with time, two simple kinetic models were tested. The experimental kinetic data for lead ions adsorption from aqueous solutions on the TiO₂ nano particles were modeled using pseudo-first and second-order kinetic models. In order to investigate the accuracy of the models in predicting the lead ions adsorption behavior, the correlation coefficient (R) of each model, which is an important factor, was used.Success of the models in predicting the kinetics of adsorbate sorption was described by a relatively high R value [5] . The rate constant of lead ion removal from the solution by nano TiO₂ was also determined using pseudo-first and second-order rate models. The Lagergren’s pseudo first-order expression is given by Equation (3) [5] [21] :

where, q_e and q_t are amounts of the lead adsorbed onto the sorbent (mg/g) at equilibrium and at time t respectively, and k₁ is the rate constant of the first-order adsorption (min⁻¹). The straight line plots of against t were used to determine the rate constant, k₁ and correlation coefficient; R² values of the lead were calculated from this plot. The calculated correlation coefficient for pseudo-first-order and the values of constants are shown in Table 2. The pseudo second-order rate model is expressed by Equation (4) [5] [22] :

where, K₂ is the rate constant of adsorption (gr∙mg⁻¹∙min⁻¹), q_e is the amount adsorbed at equilibrium, and q_t is the amount adsorbed at any time. The equilibrium adsorption amount (q_e) and the pseudo-second-order rate parameters (K₂) can be calculated from the slope and intercept of t/q_t plotted versus t. The values of constants and calculated correlation coefficients for pseudo-second-order are presented in Table 2.

In adsorption of lead ions, correlation coefficient of the pseudo-second-order equation was larger than that of the pseudo-first-order equation, indicating that lead ion adsorption onto the TiO₂ nanoparticles followed the pseudo-second-order kinetic model. It was observed that the predicted q_e value for the pseudo-second-order model well agreed with the experimental value. Therefore, the pseudo-second-order kinetic model was found to be more suitable for predicting the kinetic sorption process of lead ion onto the TiO₂ nanoparticles. The kinetic sorption fitted plots are illustrated in Figure 7.

Adsorption equilibrium is usually described by an isotherm equation whose parameters express the surface properties and affinity of the sorbent at a fixed temperature and pH. An adsorption isotherm describes the relationship between the amount of adsorbate on the adsorbent and the concentration of dissolved adsorbate in the liquid at equilibrium. Having this in mind, the adsorption isotherms for the removal of lead ions from aqueous solution by nano TiO₂ were determined. Figure 8 shows the experimental and isotherm data fitted by Langmuir and Freundlich isotherm models at 298 K.