Kinetics, isothermand thermodynamic studies of S adsorption by (SBA-15)-Hg (II)

The nano-mesoporous material SBA (Santa Barbara Amorphous)-15 was synthesized using the hydrothermal method. Hg2þ was adsorbed by SBA-15 and then the S in the aqueous phase by (SBA-15)-Hg(II), with the hope that materials with better S adsorption properties can be obtained. The relevant materials were characterized by X-ray diffraction, scanning electron microscopy, 77 K nitrogen adsorption-desorption, and related product characteristics were determined. In this work, the adsorption conditions of S onto (SBA-15)-Hg(II) were optimized. Adsorption efficiency reached about 92% and the adsorption capacity 55.02 mg/g. Studies of the system’s adsorption kinetics showed that the pseudo-second-order equation applies. The thermodynamic results indicated that ΔG, 0, ΔH1⁄4 28.56 kJ/mol, ΔS1⁄4 81.136 J/(mol·K), and that adsorption is exothermic, enthalpy decreases and the reaction is spontaneous. This accords with the Freundlich isothermal adsorption equation.

Beijing Chemical Plant, China), sodium sulfide (Na 2 S·9H 2 O, Beijing Chemical Plant, China), Hg(NO 3 ) 2 ·0.5H 2 O (Tianjin Guangfu Fine Research Institute of Chemical Engineering, China), and silver nitrate and sodium hydroxide (both Beijing Chemical Plant) were used. All reagents were analytical grade. Deionized water was used.
Particle morphology and size were obtained on a scanning electron microscope (Philips XL30) running at 20 kV.
The nitrogen adsorption-desorption results were determined using a Micromeritics Corporation (USA) ASAP 2020 V3.01 H-type adsorption analyzer at 77 K. Samples were vacuum-activated at 363 K for 12 hours and the data calculated using the BdB (Broekhoff and de Boer) method (Broekhoff et al. 1968a(Broekhoff et al. , 1968b. The specific surface was analyzed and calculated by the BET (Brunauer-Emmett-Teller) method (Brunauer et al. 1938), and the pore size distribution by the BJH (Barrett-Joyner-Halenda) method (Barrett et al. 1951).

Synthesis of mesoporous molecular sieve SBA-15
Mesoporous molecular sieve SBA-15 was synthesized by the hydrothermal method (Zhai 2012). 2 g of P123 template were dissolved in 15 mL of deionized water and 60 g of 2 mol/L HCl, stirred magnetically until the template was completely dissolved. 4.25 g of TEOS were then added slowly and stirred continuously to form a homogeneous solution. Stirring continued at 40°C for 24 hours, after which it was crystallized in a polytetrafluoroethylene substrate reaction kettle at 100°C for 48 hours. The resulting product was filtered, washed with deionized water, dried at room temperature, and finally calcined in a muffle furnace at 550°C for 24 hours to remove the triblock copolymer. This yielded the mesoporous material SBA-15 molecular sieve, as a white powder.
2.3.2. Preparation of (SBA-15)-Hg(II) 0.167 g of Hg(NO 3 ) 2 ·0.5H 2 O was dissolved in 1 L of deionized water. 40 mL of the Hg 2þ standard solution were placed in a beaker, the pH was adjusted to 5 using 0.1 mol/L HNO 3 and NaOH solutions, and 0.10 g of SBA-15 was added and stirred for 40 minutes. The solution was filtered and dried at 25 + 1°C to obtain (SBA-15)-Hg(II).
The precipitate mass produced was weighed and the residual S 2À concentration in the solution calculated. The amount of S 2À adsorbed by the modified SBA-15 was calculated by subtraction, and then the adsorption capacity and rate.
The equilibrium adsorption capacity, q e , of S 2À and its adsorption capacity at time t, q t , were obtained using Equations (1) and (2): where C 0 is the initial adsorption concentration of the adsorbate, C e the equilibrium adsorption concentration, C t the adsorption concentration at time t, V the solution volume, and m the adsorbent mass. The C 0 , C e , C t are measured in mg/ml, V in ml, and m in g. 2.3.4. Adsorption kinetics 0.050 g of (SBA-15)-Hg(II) was added to 20 mL of Na 2 S solution at concentrations of 0.04, 0.1, 0.2 and 0.6 mg/mL. The pH was adjusted to 9.5 and water added to bring the volume to 40 mL, before adsorption took place at room temperature for known periods of time. After that the liquor was centrifuged and the supernatant was titrated with excess 0.1 mol-AgNO 3 /L. When precipitation was complete, the product was subjected to vacuum filtration and dried at room temperature. The mass of Ag 2 S precipitate was weighed and the residual S 2À concentration in solution calculated, so that the amount of S 2À adsorbed by the (SBA-15)-Hg(II) could be calculated by differential subtraction. Once q e and q t were calculated, quasi-first-order and quasi-second-order dynamic equations were obtained, and the corresponding parameters.
2.3.5. Adsorption isotherm 0.050 g of (SBA-15)-Hg(II) were added to 20 mL of Na 2 S solution to yield concentrations of 0.04, 0.1, 0.2 and 0.6 mg/mL. The pH was adjusted to 9.5 and water added to bring the volume to 40 mL. Adsorption was carried out for known time periods at 25, 35 and 45°C, after which the mixture was centrifuged, and the supernatant titrated with excess 0.1 mol/L AgNO 3 solution. The precipitate was vacuum filtered and dried at room temperature. The mass of precipitate was weighed and the residual S 2À concentration in solution calculated. From this, the amount of S 2À adsorbed by the (SBA-15)-Hg(II) was calculated by differential subtraction. When q e and q t were calculated, a quasi-first-order dynamic equation and Langmuir and Freundlich adsorption isotherms were drawn, and the corresponding parameters calculated.

Effect of adsorption conditions
The effect of pH on the adsorbent's ability to sorb S 2À is very important. It can be seen in Figure 1 that when the solution pH is below 9.5, the amount adsorbed increases with increasing pH, and at pH 9.5, the modified material's adsorption rate and capacity are at their maxima. Thereafter, adsorption decreases with increasing pH.
When the pH is low, the adsorption sites of modified SBA-15 adsorb mainly sulfur ions. When it is too high, however, hydroxyl ions fight S 2À for adsorption sites, reducing their adsorption capacity.
The effect of different initial Na 2 S solution concentrations on adsorption ability is shown in Figure 2. As the initial concentration of Na 2 S increases, the adsorption capacity for S 2À increases gradually. The maximum adsorption rate occurs when the solution concentration reaches 0.10 mg-Na 2 S/mL. When the concentration exceeds that, the adsorption rate decreases due to saturation of the adsorption sites. The effect of contact time is shown in Figure 3. The adsorption rate and capacity increase significantly with increasing contact time, and reach the maximum at 40 minutes, after which both are stable.
The effects of temperatureobserved at 298.15, 308.15, and 318.15 Kare shown in Figure 4. The adsorption rate decreases with increasing temperature, indicating that the adsorption process is exothermic.

Adsorption kinetics
Quasi-first-order and second-order dynamic equations were developed using the time and concentration data in linear fittingsee Figures 5 and 6, respectively. The dynamic data are listed in Table 1, where q e1 , q e2 are the theoretical q e values obtained from the quasi-first and second-order dynamic equations, respectively, and R 1 2 , R 2 2 are their respective correlation coefficients. It is clear that the S 2À adsorption process by (SBA-15)-Hg(II) is in better accord with the quasi-second-order kinetic equation than the first, the correlation coefficient being 0.9992, 0.9998 and 0.9997, respectively, and the difference between theoretical and actual q e is small. However,  most of the correlation coefficients for the quasi-first-order kinetic equation are around 0.78, when it is used to fit the adsorption process. The error is also larger and the theoretical q e differs considerably from the actual q e , indicating that the quasi-second-order kinetic equation expresses the S 2À adsorption process (SBA-15)-Hg(II) better.

Adsorption isotherm
The adsorption data were investigated in relation to the Langmuir and Freundlich adsorption isotherms. The linear Equation -(3)for the Langmuir isotherm is (Langmuir 1916(Langmuir , 1918Crini et al. 2007;Naushad 2014;Alqadami et al. 2017): where C e /q e (g/mL) is the equilibrium constant, C e (mg/mL) the adsorbate's equilibrium concentration, and q e the adsorption capacitythat is the mass by the adsorbent per unit mass. Q 0 (mg/mL) and b (mL/mg) represent the relationship among the Langmuir constant and the adsorption capacity and rate, respectively.  The linear equation -(4)for the Freundlich isotherm is (Freundlich 1906;Langmuir 1916Langmuir , 1918: where q e (mg/g) is the adsorption capacity at equilibrium, C e (mg/mL) the absorbate concentration at equilibrium. K F is the Freundlich adsorption isotherm constant (the coefficient of adsorption degree) and 1/nusually ,1indicates adsorption intensity. The results of simulating the Langmuir and Freundlich adsorption isotherms are shown in Figures 7 and 8, respectively. The related parameters are listed in Table 2. As can be seen, the S 2À adsorption process by (SBA-15)-Hg(II) is closer to the Freundlich isotherm and R 2 is 0.9951, 0.9906, 0.9914that is it always exceeds 0.99. All values of 1/n are below 1, too, indicating S 2À adsorption by (SBA-15)-Hg(II) is preferential.

Characterization of SBA-15 related material
Figures 9 and 10 show the small and wide angle XRD images, respectively, of SBA-15, (SBA-15)-Hg(II), the (SBA-15)-Hg(II) with S 2À adsorbed. The XRD small angle image of the SBA-15 molecular sieves has four peaks (Zhai 2012), which can be assigned to those obtained by (100), (110), (200) and (210) crystal plane diffraction, respectively. The peaks confirm that the SBA-15 prepared is a molecular sieve. In the wide-angle images, the (SBA-15)-Hg(II) peak is unchanged but the peak is lower, showing that modification was successful and caused no damage to the original SBA-15 skeleton. The characteristic diffraction peaks of SBA-15 exist after S 2À adsorption by (SBA-15)-Hg(II), proving that the original SBA-15 framework is still present. Figure 11 shows the SEM images of SBA-15, (SBA-15)-Hg(II), S 2À adsorbed (SBA-15)-Hg(II), respectively. As can be seen, the grain fiber diameter of the three materials is 333, 360, and 350 nm, respectively. The SBA-15 molecular sieve has a rod-like structure, and, after adsorption, the crystallinity decreases and the disorder increases. Figure 12 shows the nitrogen adsorption-desorption isotherms at low temperature, and the typical type IV adsorption isotherms in the IUPAC (International Union of Pure and Applied Chemistry) classification, with the H1 lag rings characteristic of typical mesoporous materials. The mesoporous properties were determined using the adsorption data: total surface area and pore volume, and the pore diameter in the BJH model (Barrett et al. 1951). When the relative pressure is below 0.6, the adsorption process exhibits linear correlation.
The sudden increase at about 0.65, and sharp increase in the volume of nitrogen adsorbed, are characteristic of capillary condensation in the mesopores. The curve tends to be flat after about 0.8. These characteristics show that the adsorption of S 2À resulted in decreases in mesoporous area and pore volume. Table 4 is a summary of the physicochemical characteristics of the SBA-15 in the three samples. The three samples showed similar inflection points, tending to lower relative pressure with Hg 2þ modification and subsequent S 2À adsorption. A sequential decrease in specific surface was observed for the three samples, which  occurred because the guest molecules adsorbed stayed and were tightly packed within the SBA-15 porous network.
As can be seen in Figure 13, the pore size distribution of the three samples is very narrow, indicating that they all have a regular and single mesoporous framework structure (the samples' pore size structure parameters are given in Table 4). It can be concluded from Figure 13 and Table 4 that Hg 2þ modification and subsequent S 2À adsorption do not change the original SBA-15 structure. The pore wall thickness increases gradually with increasing ionic adsorption. The reductions in BET surface area, mesoporous volume and average pore size all show that after adsorbing S 2À the SBA-15 channel was partially filled and blocked, indicating that S 2À has been adsorbed in SBA-15 channels.

CONCLUSIONS
Nano-mesoporous SBA-15 was synthesized successfully using a hydrothermal method. The adsorption conditions and kinetics, adsorption isotherms and thermodynamic-related properties of S 2À adsorption by (SBA-15)-Hg(II) were studied. XRD images were taken after adsorption. The post-adsorption materials were also characterized by SEM and low-temperature (77 K) nitrogen adsorption-desorption. It was concluded that: (1) The optimum adsorption conditions for S 2À by (SBA-15)-Hg(II) are: 1.67 g-SBA-15/L, pH 9.5, temperature and time 25°C for 40 minutes. The maximum adsorption efficiency and capacity were about 92% and 55.02 mg/g, respectively.
(2) The adsorption of S 2À by (SBA-15)-Hg(II) is best fitted by the quasi-second-order kinetic equation, and the adsorption isotherm is best fitted by the Freundlich model. (3) Thermodynamically, the entropy and Gibbs free energy changes for S 2À adsorption by (SBA-15)-Hg(II) are all below zero, indicating that the process is exothermic and accompanied by a decrease in entropy.