Mechanistic Evidence for Hg Removal from Wastewater by Biologically Produced Sulfur

A significant quantity of biologically produced sulfur (BPS) is generated as a by-product of chemical and biological desulfurization processes applied to landfill gas treatment. The beneficial upcycling of BPS has seen limited use in the environmental context. The effectiveness and underlying mechanism of BPS as an adsorbent for removing Hg2+ from both solution and wastewater were elucidated based on experiments encompassing surface characterization, adsorption isotherms, kinetics, and thermodynamics. The BPS exhibited remarkable efficacy in removing Hg2+ from solution, with the Langmuir model accurately describing the adsorption process and showing a maximum adsorption capacity of 244 mg g−1. Surface analysis through X-ray photoelectron spectroscopy and scanning electron microscopy revealed that Hg2+ complexed with sulfide on BPS surfaces, forming stable HgS. The adsorbed Hg was strongly retained in BPS, with less than 0.2% of the adsorbed Hg desorbed by strong acids. Adsorption kinetics followed the double-exponential first-order model, showing an initial rapid adsorption phase wherein 75% of the initial Hg2+ was removed within 5 min, followed by a slower adsorption rate. The thermodynamic parameters suggested that adsorption of Hg2+ by BPS was a spontaneous and endothermic process. Additionally, BPS effectively removed Hg2+ from wastewater, showing preference for Hg over other co-existing metals. These findings underscore the potential of BPS as an effective adsorbent for Hg2+ removal from wastewater.


Introduction
Mercury (Hg) pollution poses a significant threat to environmental quality and public health globally.The World Health Organization (WHO) considers Hg as one of the ten most harmful elements to public health [1].Exposure to Hg can lead to various human health problems, including issues with child growth during pregnancy or childhood.It impacts the digestive and immune systems [2,3], as well as functions of organs such as the lungs, kidneys, and skin [4,5].In recognition of this critical issue, the United Nations Minamata Convention on Mercury (MCM) came into effect on 16 August 2017 with the primary goal of reducing emissions (air) and discharge (water) of anthropogenic Hg and aiming to protect the environment and human health.However, Hg continues to be released into the environment from various sources, including the battery and paint industries, metal mining, and the chlorine-alkali and pesticide sectors [6,7].
Various technologies have been implemented to prevent Hg pollution in wastewater, such as adsorption, membrane separation, flotation, electro-chemical treatment, and ion exchange [8][9][10][11].Among these, adsorption technology stands out as the most widely adopted method for effectively removing Hg from water [12].For instance, activated carbon Toxics 2024, 12, 278 2 of 15 prepared from rice husks exhibited a maximum Hg removal capacity of 55.87 mg g −1 through an adsorption process, and this was attributed to its favorable pore structure and oxygen-containing functional groups [13].
According to the hard and soft acids and bases (HSAB) theory, metals can be classified as Lewis acids, which accept electron pairs from ligands.Ligands are electron donors and anions that are classified as Lewis bases.Generally, a hard electron pair acceptor (hard acid) prefers to form a complex with a hard donor (hard base).Inorganic Hg acts as a soft acceptor and, thus, can strongly interact with soft donors such as sulfur-containing compounds, including sulfides, thiols, thiourea, and thioether groups [14][15][16].In efforts to enhance Hg adsorption capacity, researchers have attempted to modify adsorbents with S-containing compounds [16][17][18].
The practical application of using adsorbents in wastewater treatment is, however, limited due to their high cost and the requirement for a large quantity of them [19,20].Recently, there has been growing interest in finding alternative adsorbents that are readily available and cost-effective, including adsorbents derived from natural materials or industrial by-products [20,21].
Hydrogen sulfide (H 2 S) gas emitted from landfill sites causes many detrimental problems, such as equipment damage, environmental toxicity, and odor pollution [22].To mitigate these issues, chemical and biological desulfurization technology has been successfully adopted for the removal of H 2 S [23].During the desulfurization process, H 2 S gas is converted into a solid, biologically produced sulfur (BPS), which is primarily composed of elemental sulfur (S 8 ) with a small amount of sulfides [23][24][25].This conversion occurs via a chemical reaction using NaOH (see Equation (1)) and biological oxidation (see Equation ( 2)) with Thiobacilli [23].A significant quantity of BPS, exceeding 10,000 tons per year, is generated from landfill sites in Seoul, Korea.Hence, there is an urgent need for the efficient and sustainable recycling of BPS in an environmentally friendly manner.
According to the HSAB theory, it is anticipated that the sulfur-containing BPS will selectively form complexes with Hg in wastewater, demonstrating significant potential as a cost-effective and environmentally sound adsorbent for Hg, because it is a by-product of the landfill desulfurization process.In this study, BPS was evaluated as an adsorbent for removing Hg 2+ from both aqueous solutions and wastewater.The efficacy and underlying mechanisms of using BPS for this application were elucidated through experiments involving surface characterization, adsorption isotherms, kinetics, and thermodynamics.

Characterization of BPS
BPS samples were obtained in slurry form from the landfill gas desulfurization plant located at the Seoul landfill site (Eco-Bio Holdings Co., Ltd., Seoul, Republic of Korea), then centrifuged to separate the solid BPS.The solid was subsequently oven-dried at 65 • C for 24 h and ground to pass through a 1 mm sieve.The chemical and mineralogical composition of BPS was determined using an X-ray fluorescence spectrometer (XRF, ZSX Primus II, Rigaku, Japan) and an X-ray diffractometer (XRD, X'Pert PRO MPD, PANalytical, Almelo, The Netherlands) with Cu Kα radiation operating at 40 kV and 250 mA, respectively.The size classes and surface areas of BPS were determined using the laser particle size analyzer (Mastersizer 3000, Malvern Instruments Ltd., Worcestershire, UK).The specific surface area of BPS was determined from N 2 adsorption isotherms at 77 K using a Brunauer Emmett Teller (BET) Analyzer (BELSORP MAX X, MicrotracBEL, Osaka, Japan).The point of zero charge of BPS was determined using 0.1 M NaCl at pH 2.0-11.0.The pH values were adjusted using HCl and NH 4 OH.The BPS was stirred for 24 h with 0.1 M NaCl solutions of different pH values.After 24 h, the pH of resulting solution was measured after equilibrium.
The difference in the initial and final pH (∆pH) was calculated, and the pH value where ∆pH was zero indicated the point of zero charge of BPS.

Hg Removal Efficiency
The performance of BPS in removing Hg 2+ was evaluated through batch experiments.A stock solution containing Hg 2+ was prepared by dissolving 99.5% mercury chloride (HgCl 2 , Daejung Chemical, Seoul, Korea) in deionized water and diluting it to the required initial concentration before use.Table 1 presents the conditions under which batch experiments were conducted, including different pH levels, reacting times, temperatures, and Hg concentrations.Each batch of BPS and Hg solution under a specific condition was equilibrated for 24 h in a mechanical shaker (150 rpm) at 298 K, then filtered through a 0.45 µm membrane filter.The concentration of Hg in the filtrate was determined using a cold-vapor Hg analyzer (Hydra II AA, Teledyne Leeman Labs, Hudson, NH, USA).The removal efficiency and capacity of BPS for Hg 2+ at equilibrium were calculated using the following Equations ( 3) and (4), respectively.
where R is the removal percentage of Hg 2+ (%); C 0 and C e refer to the initial and equilibrium Hg 2+ concentrations (mg L −1 ), respectively; q e is the removal capacity of Hg 2+ at equilibrium (mg g −1 ); V is the volume of the solution (mL), and m is the weight of BPS (mg).All experiments were conducted in triplicate, and mean values are reported.Following the batch experiments, the surface morphology of the BPS and the distribution map of Hg 2+ were examined using a scanning electron microscope equipped with an energy-dispersive X-ray spectrometer (FE-SEM, S-4800, Hitachi, Tokyo, Japan) at 5 kV accelerating voltage, with a working distance of 15 mm.Also, the chemical state of elements on the BPS surface was analyzed via X-ray photoelectron spectroscopy (XPS, K Alpha+, Thermo Scientific, Loughborough, UK) using an Al K α X-ray source.

Hg Adsorption Isotherm
The adsorption capacity of the Hg 2+ on BPS was analyzed using the Langmuir (see Equation ( 5)) and Freundlich (see Equation ( 6)) isotherm models. ) where q e is the amount of adsorbed Hg 2+ at equilibrium (mg g −1 ); C e is the equilibrium concentration of Hg 2+ (mg L −1 ) in solution; and Q m and b are the maximum adsorption capacity (mg g −1 ) and Langmuir constant (L mg −1 ) related to free energy of adsorption, respectively.K f is a constant (mg g −1 ) related to the adsorption capacity and intensity of the Freundlich model, and 1/n is the Freundlich constant (unitless) related to the surface heterogeneity.The goodness of fit of these models to Hg adsorption onto BPS was evaluated based on a higher coefficient of determination (r 2 ) and a lower standard error.

Hg Adsorption Kinetics
The adsorption kinetics of Hg 2+ onto BPS were evaluated using pseudo-first order, pseudo-second order, and double-exponential models.The linear form of the pseudo-first order kinetic model is given as Equation ( 7) [26]: where q e (mg g −1 ) and q t (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibrium and time t (min), respectively.K 1 (min −1 ) is the rate constant of the pseudo-first-order model.The linear form of the pseudo-second-order kinetic model is shown as Equation ( 8) [26]: where K 2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order model.The nonlinear form of the double-exponential kinetic model is given as Equation ( 9) [27]: where m ads (g L −1 ) is the adsorbent amount in the solution; D 1 and D 2 are adsorption rate constants (g L −1 ) of the rapid and the slow step, respectively; and K D1 and K D2 (min −1 ) are the rate constants of the double exponential model for the fast and slow steps, respectively.The best fit of Hg adsorption onto BPS using the above three models was evaluated based on a high coefficient of determination (r 2 ) and a low root mean square error (RMSE) (see Equation (10)).(10) where q i,exp and q i,cal are the experimental and calculated values of the adsorption capacity, respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch experiments at 288, 298, and 308 K under the various conditions specified in Table 1.The change in Gibbs free energy of activation (∆G o capacity (mg g ) and Langmuir constant (L mg ) related to free energy of adsorption, respectively.Kf is a constant (mg g −1 ) related to the adsorption capacity and intensity of the Freundlich model, and 1/n is the Freundlich constant (unitless) related to the surface heterogeneity.The goodness of fit of these models to Hg adsorption onto BPS was evaluated based on a higher coefficient of determination (r 2 ) and a lower standard error.

Hg Adsorption Kinetics
The adsorption kinetics of Hg 2+ onto BPS were evaluated using pseudo-first order, pseudo-second order, and double-exponential models.The linear form of the pseudo-first order kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibrium and time t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order model.The linear form of the pseudo-second-order kinetic model is shown as Equation ( 8) [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order model.The nonlinear form of the double-exponential kinetic model is given as Equation ( 9) [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption rate constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 ) are the rate constants of the double exponential model for the fast and slow steps, respectively.
The best fit of Hg adsorption onto BPS using the above three models was evaluated based on a high coefficient of determination (r 2 ) and a low root mean square error (RMSE) (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capacity, respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch experiments at 288, 298, and 308 K under the various conditions specified in Table 1.The change in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol equation (see Equation (11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( 12)), the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ ⧧ ) were determined from the slope and intercept of the linear relation, respectively.
) ) was calculated using the Gibbs-Helmholtz equation (see Equation (11)).By plotting ln(K e ) vs. 1/T (van't Hoff equation: see Equation ( 12)), the change in enthalpy of activation (∆H o   where qe is the amount of adsorbed Hg at equilibrium (mg g ); Ce is the equilibrium concentration of Hg 2+ (mg L −1 ) in solution; and Qm and b are the maximum adsorption capacity (mg g −1 ) and Langmuir constant (L mg −1 ) related to free energy of adsorption, respectively.Kf is a constant (mg g −1 ) related to the adsorption capacity and intensity of the Freundlich model, and 1/n is the Freundlich constant (unitless) related to the surface heterogeneity.The goodness of fit of these models to Hg adsorption onto BPS was evaluated based on a higher coefficient of determination (r 2 ) and a lower standard error.

Hg Adsorption Kinetics
The adsorption kinetics of Hg 2+ onto BPS were evaluated using pseudo-first order, pseudo-second order, and double-exponential models.The linear form of the pseudo-first order kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibrium and time t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order model.The linear form of the pseudo-second-order kinetic model is shown as Equation ( 8) [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order model.The nonlinear form of the double-exponential kinetic model is given as Equation ( 9) [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption rate constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 ) are the rate constants of the double exponential model for the fast and slow steps, respectively.
The best fit of Hg adsorption onto BPS using the above three models was evaluated based on a high coefficient of determination (r 2 ) and a low root mean square error (RMSE) (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capacity, respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch experiments at 288, 298, and 308 K under the various conditions specified in Table 1.The change in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol equation (see Equation (11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( 12)), the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ ⧧ ) were determined from the slope and intercept of the linear relation, respectively.
) and the change in entropy of activation (∆S o   where qe is the amount of adsorbed Hg concentration of Hg 2+ (mg L −1 ) in solution capacity (mg g −1 ) and Langmuir constant respectively.Kf is a constant (mg g −1 ) relat the Freundlich model, and 1/n is the Freun heterogeneity.The goodness of fit of these ated based on a higher coefficient of determ

Hg Adsorption Kinetics
The adsorption kinetics of Hg 2+ onto pseudo-second order, and double-exponen order kinetic model is given as Equation ( 7( −  where qe (mg g −1 ) and qt (mg g −1 ) are the amo t (min), respectively.K1 (min −1 ) is the rate c The linear form of the pseudo-second [26]: where K2 (g mg −1 min −1 ) is the rate constant The nonlinear form of the double-exp [27]: where mads (g L −1 ) is the adsorbent amount constants (g L −1 ) of the rapid and the slow the rate constants of the double exponent tively.
The best fit of Hg adsorption onto BP based on a high coefficient of determination (see Equation (10)).

RMSE = 1 𝑁 −
where qi,exp and qi,cal are the experimental an respectively, and N is the number of observ

Pseudo-Thermodynamic Parameters of Hg
Pseudo-thermodynamic parameters w ments at 288, 298, and 308 K under the vari in Gibbs free energy of activation (∆ ⧧ ) wa tion (see Equation ( 11)).By plo ing ln(Ke) v the change in enthalpy of activation (∆ ⧧ ) were determined from the slope and interc ) were determined from the slope and intercept of the linear relation, respectively.
where qe is the amount of adsorbed Hg 2+ at equilibrium (mg g −1 ); Ce is the equilibrium concentration of Hg 2+ (mg L −1 ) in solution; and Qm and b are the maximum adsorption capacity (mg g −1 ) and Langmuir constant (L mg −1 ) related to free energy of adsorption, respectively.Kf is a constant (mg g −1 ) related to the adsorption capacity and intensity of the Freundlich model, and 1/n is the Freundlich constant (unitless) related to the surface heterogeneity.The goodness of fit of these models to Hg adsorption onto BPS was evaluated based on a higher coefficient of determination (r 2 ) and a lower standard error.

Hg Adsorption Kinetics
The adsorption kinetics of Hg 2+ onto BPS were evaluated using pseudo-first order, pseudo-second order, and double-exponential models.The linear form of the pseudo-first order kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibrium and time t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order model.The linear form of the pseudo-second-order kinetic model is shown as Equation ( 8) [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order model.The nonlinear form of the double-exponential kinetic model is given as Equation ( 9) [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption rate constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 ) are the rate constants of the double exponential model for the fast and slow steps, respectively.
The best fit of Hg adsorption onto BPS using the above three models was evaluated based on a high coefficient of determination (r 2 ) and a low root mean square error (RMSE) (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capacity, respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch experiments at 288, 298, and 308 K under the various conditions specified in Table 1.The change in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol equation (see Equation ( 11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( 12)), the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ ⧧ ) were determined from the slope and intercept of the linear relation, respectively.
where qe is the amount of adsorbed Hg 2+ at equilibrium (mg g −1 ); Ce is the equilibrium concentration of Hg 2+ (mg L −1 ) in solution; and Qm and b are the maximum adsorption capacity (mg g −1 ) and Langmuir constant (L mg −1 ) related to free energy of adsorption, respectively.Kf is a constant (mg g −1 ) related to the adsorption capacity and intensity of the Freundlich model, and 1/n is the Freundlich constant (unitless) related to the surface heterogeneity.The goodness of fit of these models to Hg adsorption onto BPS was evaluated based on a higher coefficient of determination (r 2 ) and a lower standard error.

Hg Adsorption Kinetics
The adsorption kinetics of Hg 2+ onto BPS were evaluated using pseudo-first order, pseudo-second order, and double-exponential models.The linear form of the pseudo-first order kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibrium and time t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order model.The linear form of the pseudo-second-order kinetic model is shown as Equation ( 8) [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order model.The nonlinear form of the double-exponential kinetic model is given as Equation ( 9) [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption rate constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 ) are the rate constants of the double exponential model for the fast and slow steps, respectively.
The best fit of Hg adsorption onto BPS using the above three models was evaluated based on a high coefficient of determination (r 2 ) and a low root mean square error (RMSE) (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capacity, respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch experiments at 288, 298, and 308 K under the various conditions specified in Table 1.The change in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol equation (see Equation ( 11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( 12)), the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ ⧧ ) were determined from the slope and intercept of the linear relation, respectively.
where qe is the amount of adsorbed Hg 2+ at equilibrium (mg g −1 ); Ce is the equi concentration of Hg 2+ (mg L −1 ) in solution; and Qm and b are the maximum ads capacity (mg g −1 ) and Langmuir constant (L mg −1 ) related to free energy of adso respectively.Kf is a constant (mg g −1 ) related to the adsorption capacity and inte the Freundlich model, and 1/n is the Freundlich constant (unitless) related to the heterogeneity.The goodness of fit of these models to Hg adsorption onto BPS wa ated based on a higher coefficient of determination (r 2 ) and a lower standard error

Hg Adsorption Kinetics
The adsorption kinetics of Hg 2+ onto BPS were evaluated using pseudo-firs pseudo-second order, and double-exponential models.The linear form of the pseu order kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibrium a t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order mode The linear form of the pseudo-second-order kinetic model is shown as Equa [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order model.The nonlinear form of the double-exponential kinetic model is given as Equa [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorpt constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (mi the rate constants of the double exponential model for the fast and slow steps, tively. The best fit of Hg adsorption onto BPS using the above three models was ev based on a high coefficient of determination (r 2 ) and a low root mean square error (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption ca respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch ments at 288, 298, and 308 K under the various conditions specified in Table 1.The in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol tion (see Equation ( 11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equatio the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation were determined from the slope and intercept of the linear relation, respectively. ) where qe is the amount of adsorbed Hg 2+ at equilibrium (mg g −1 ); Ce is the equilibr concentration of Hg 2+ (mg L −1 ) in solution; and Qm and b are the maximum adsorp capacity (mg g −1 ) and Langmuir constant (L mg −1 ) related to free energy of adsorpt respectively.Kf is a constant (mg g −1 ) related to the adsorption capacity and intensit the Freundlich model, and 1/n is the Freundlich constant (unitless) related to the sur heterogeneity.The goodness of fit of these models to Hg adsorption onto BPS was ev ated based on a higher coefficient of determination (r 2 ) and a lower standard error.

Hg Adsorption Kinetics
The adsorption kinetics of Hg 2+ onto BPS were evaluated using pseudo-first or pseudo-second order, and double-exponential models.The linear form of the pseudoorder kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibrium and t t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order model.
The linear form of the pseudo-second-order kinetic model is shown as Equation [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order model.The nonlinear form of the double-exponential kinetic model is given as Equation [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 ) the rate constants of the double exponential model for the fast and slow steps, res tively.
The best fit of Hg adsorption onto BPS using the above three models was evalu based on a high coefficient of determination (r 2 ) and a low root mean square error (RM (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capa respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch exp ments at 288, 298, and 308 K under the various conditions specified in Table 1.The cha in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol eq tion (see Equation (11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ were determined from the slope and intercept of the linear relation, respectively. where qe is the amount of adsorbed Hg 2+ at equilibrium (mg g −1 ); Ce is the concentration of Hg 2+ (mg L −1 ) in solution; and Qm and b are the maximum capacity (mg g −1 ) and Langmuir constant (L mg −1 ) related to free energy o respectively.Kf is a constant (mg g −1 ) related to the adsorption capacity and the Freundlich model, and 1/n is the Freundlich constant (unitless) related t heterogeneity.The goodness of fit of these models to Hg adsorption onto BP ated based on a higher coefficient of determination (r 2 ) and a lower standard

Hg Adsorption Kinetics
The adsorption kinetics of Hg 2+ onto BPS were evaluated using pseud pseudo-second order, and double-exponential models.The linear form of the order kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibri t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order m The linear form of the pseudo-second-order kinetic model is shown as [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order mod The nonlinear form of the double-exponential kinetic model is given as [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are ad constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and K the rate constants of the double exponential model for the fast and slow s tively.
The best fit of Hg adsorption onto BPS using the above three models w based on a high coefficient of determination (r 2 ) and a low root mean square e (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorpt respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting b ments at 288, 298, and 308 K under the various conditions specified in Table 1 in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Hel tion (see Equation (11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Eq the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of acti were determined from the slope and intercept of the linear relation, respectiv where R is the ideal gas constant (8.314J•mol −1 •K −1 ); T is the absolute temperature (K); and K e is the binding constant (L g −1 ), which is derived from the Langmuir constant (L mg −1 ) and from the adsorption isotherms [28,29].

Hg Desorption
Desorption studies were conducted using batch conditions similar to those of the adsorption study (Table 1).After Hg was adsorbed onto BPS under specific conditions (adsorbent dose of 1 g L −1 , initial concentration of Hg 300 mg L −1 , pH 5, contact time of 24 h, and temperature 298 K), the BPS was separated by filtration and dried.Subsequently, the dried BPS was mixed with desorbing solution using different acids (HCl, HNO 3 , or H 2 SO 4 ) at varying molarities (0.1 M, 0.5 M, and 1 M) and shaken for 24 h at a temperature of 298 K.The batch was then filtered through a 0.45 µm membrane filter.The Hg 2+ concentrations in the filtrate were measured using the cold-vapor AAS Hg analyzer (Hydra II AA, Teledyne Leeman Labs, Hudson, NH, USA).The desorption percentage of Hg 2+ (DES(Hg), %) was calculated according to the following Equation ( 13): Amount o f desrobed Hg 2+ into the desorption solution Amount o f adsorbed Hg 2+ (13)

Hg Removal from Waste Water
Wastewater was collected from a Zn plating plant located in Daegu, Korea, and filtered through a 0.45 µm membrane filter to determine the concentrations of Hg and other metals.Mercury and other heavy metals (As, Cd, Cr, Cu, Ni, Pb, and Zn) co-existed in the collected wastewater (Table 2).Concentrations of Hg in wastewater (0.13 mg L −1 ) exceeded the allowable limit (5 µg L −1 ) for wastewater discharges from the individual industry, as specified by the Korea Water Environment Conservation Act [30].Because the concentration of Hg was relatively low as compared to other metals, Hg-spiked wastewater was additionally prepared using the same wastewater to compare the Hg removal efficiency.The wastewater was spiked with Hg using HgCl 2 to prepare a final Hg concentration of 1.5 mg/L.The BPS was added to both actual and spiked wastewaters at a 1 g L −1 batch ratio, and the mixture was shaken at 150 rpm at 298 K for 60 min to evaluate the Hg 2+ removal efficiency using Equation (3).The Hg removal efficiencies of BPS from actual wastewater and spiked wastewater were comparatively assessed.

Biologically Produced S Characteristics
The BPS samples collected from the landfill gas desulfurization plant exhibited a light yellow color (Figure 1a) with a slight odor of sulfide.The scanning electron micrographs (SEM) of the BPS (Figure 1b) depicted an amorphous structure composed of spherical sulfur globules with diameters of 10~20 µm.According to Janssen et al. [31], BPS particles are often covered with a negatively charged polymeric protein layer, which could render the particles hydrophilic, despite elemental sulfur being inherently hydrophobic [32,33].The point of zero charge of BPS was found to be 2.3.
XRF analysis revealed that BPS was composed of various elements, with S being the dominant one, constituting 76% of the composition (Table 3).The elemental composition of BPS used in this experiment was found to be similar to that reported in a previous study [23], despite BPS samples being collected at different times.This suggested that BPS generated from the landfill gas desulfurization plant has a consistent composition.particles hydrophilic, despite elemental sulfur being inherently hydrophobic [32,33].The point of zero charge of BPS was found to be 2.3.XRF analysis revealed that BPS was composed of various elements, with S being the dominant one, constituting 76% of the composition (Table 3).The elemental composition of BPS used in this experiment was found to be similar to that reported in a previous study [23], despite BPS samples being collected at different times.This suggested that BPS generated from the landfill gas desulfurization plant has a consistent composition.The spectra of X-ray diffractometry (XRD) for BPS powder are depicted in Figure 2. The peaks at 2θ values of 15.38°, 23.07°, 25.83°, 26.71°, and 27.70° were assigned to (113), (222), (026), (311), and (206) reflections of S8 (Reference No. 01-078-1889), respectively, while the weak diffraction peaks of BPS corresponded to inorganic sulfides, such as Na2S and NaHS [34,35].The XRD pattern confirmed that BPS was composed of elemental sulfur (S8) and sulfides, supporting its strong potential for use as an adsorbent for Hg removal through adsorption processes between Hg-and S-containing ligands.The distribution of BPS particles is relatively broad, with the standard percentiles for particle size D10, D50, and D90 values being 7.4 µm, 125 µm, and 488 µm, respectively.D10, D50, and D90 represent particle sizes at 10%, 50%, and 90% in the cumulative size distribution, respectively.Surface areas of the BPS sample were estimated to be 1.36 m 2 g −1 .026), (311), and (206) reflections of S 8 (Reference No. 01-078-1889), respectively, while the weak diffraction peaks of BPS corresponded to inorganic sulfides, such as Na 2 S and NaHS [34,35].The XRD pattern confirmed that BPS was composed of elemental sulfur (S 8 ) and sulfides, supporting its strong potential for use as an adsorbent for Hg removal through adsorption processes between Hg-and S-containing ligands.The distribution of BPS particles is relatively broad, with the standard percentiles for particle size D10, D50, and D90 values being 7.4 µm, 125 µm, and 488 µm, respectively.D10, D50, and D90 represent particle sizes at 10%, 50%, and 90% in the cumulative size distribution, respectively.Surface areas of the BPS sample were estimated to be 1.36 m 2 g −1 .

Effect of pH and Adsorbent Dose on Hg Removal
The pH of the batch solution significantly influences the adsorption process, because it affects the surface charge of the adsorbent and the ionization degree and speciation of the adsorbate [36].To assess the effect of the pH of Hg 2+ adsorption onto BPS, the initial

Effect of pH and Adsorbent Dose on Hg Removal
The pH of the batch solution significantly influences the adsorption process, because it affects the surface charge of the adsorbent and the ionization degree and speciation of the adsorbate [36].To assess the effect of the pH of Hg 2+ adsorption onto BPS, the initial solution pH values were adjusted to pH 2.0~7.0.The percentage of Hg 2+ removal by BPS was pH-dependent, showing a sharp increase with increasing pH from 2.0 to 6.0 (Figure 3), followed by a gradual increase at pH values higher than 6.Under strong acidic conditions, high concentrations of H + would compete with Hg 2+ for adsorption sites on the BPS surface, leading to low Hg 2+ removal efficiency [37].Under higher pH conditions, more S 2− dissociated from sulfide (NaHS) could favorably complex with free Hg 2+ to produce HgS precipitates [38].Additionally, the presence of OH − at a higher pH would facilitate the transformation of Hg 2+ to Hg(OH) + or Hg(OH) 2 precipitates [39].

Effect of pH and Adsorbent Dose on Hg Removal
The pH of the batch solution significantly influences the adsorption process, because it affects the surface charge of the adsorbent and the ionization degree and speciation of the adsorbate [36].To assess the effect of the pH of Hg 2+ adsorption onto BPS, the initial solution pH values were adjusted to pH 2.0~7.0.The percentage of Hg 2+ removal by BPS was pH-dependent, showing a sharp increase with increasing pH from 2.0 to 6.0 (Figure 3), followed by a gradual increase at pH values higher than 6.Under strong acidic conditions, high concentrations of H + would compete with Hg 2+ for adsorption sites on the BPS surface, leading to low Hg 2+ removal efficiency [37].Under higher pH conditions, more S 2− dissociated from sulfide (NaHS) could favorably complex with free Hg 2+ to produce HgS precipitates [38].Additionally, the presence of OH − at a higher pH would facilitate the transformation of Hg 2+ to Hg(OH) + or Hg(OH)2 precipitates [39].

Adsorption Isotherms
The Langmuir and Freundlich isotherm models were employed to evaluate Hg adsorption onto BPS (Figure 4).Table 4 presents the adsorption parameters obtained from both isotherm models.The results of this study confirmed that the Langmuir isotherm model was more applicable, based on a higher coefficient determination (r 2 ), than the Freundlich isotherm model in describing the adsorption of Hg 2+ by BPS.This suggests that Hg adsorption onto BPS occurred uniformly on the finite monolayer sorption sites of BPS.The maximum Hg adsorption capacity (Q m ) of BPS was found to be 244 mg g −1 .
The Q m values of BPS were compatible to, or even higher than, those reported previously (Table 5), where Q m values were assessed using various adsorbents, such as activated carbon, functional polymers, and bentonite by-products.These results demonstrate that BPS can be recycled as an effective adsorbent for removing Hg from wastewater.

Adsorption Isotherms
The Langmuir and Freundlich isotherm models were employed to evaluate Hg adsorption onto BPS (Figure 4).Table 4 presents the adsorption parameters obtained from both isotherm models.The results of this study confirmed that the Langmuir isotherm model was more applicable, based on a higher coefficient determination (r 2 ), than the Freundlich isotherm model in describing the adsorption of Hg 2+ by BPS.This suggests that Hg adsorption onto BPS occurred uniformly on the finite monolayer sorption sites of BPS.The maximum Hg adsorption capacity (Qm) of BPS was found to be 244 mg g −1 .The Qm values of BPS were compatible to, or even higher than, those reported previously (Table 5), where Qm values were assessed using various adsorbents, such as activated carbon, functional polymers, and bentonite by-products.These results demonstrate that BPS can be recycled as an effective adsorbent for removing Hg from wastewater.5) and ( 6) for parameter descriptions.

Adsorption Kinetics
Three kinetic models, i.e., the pseudo-first order, pseudo-second order, and the doubleexponential models, were employed to investigate the mechanism of Hg adsorption onto BPS. Figure 5 illustrates the rate curves of the three models, and Table 6 summarizes the relevant kinetic parameters.Based on higher r 2 and lower root mean square error (RMSE) values, the double-exponential first-order kinetic model was found to be the best fit for the Hg adsorption process, even though the other two models showed higher r 2 , as well as higher RSME values.contribute to the fast adsorption kinetics.Once rapid adsorption occurs, then the Hg removal efficiency becomes relatively constant even with longer contact times due to the saturation of active sites on the adsorbent surface [23].7)-( 10) for parameter descriptions.** Significant at p < 0.001.Table 6.Kinetic model parameters for Hg 2+ adsorption onto BPS.
The Hg adsorption process appears to involve two stages: a fast initial stage followed by a slow stage.The fast adsorption occurred within 5 min, with 75% of Hg removed, followed by a slower and more static adsorption phase.The rate constants of D 1 and K D1 for the fast step of the double-exponential first order kinetic model were 237.2 g L −1 and 4.9 min −1 , respectively, significantly higher than D 2 (11.72 g L −1 ) and K D2 (0.0015 min −1 ) for the slow step.The rate constants for the pseudo-first order kinetic model (K 1 ) and pseudo-second order kinetic model (K 2 ) were very low, with values of 0.0012 min −1 and 0.0013 g mg −1 min −1 , respectively.
The initial fast adsorption process could be interpreted as an adsorption reaction, where Hg species (soft Lewis acid) rapidly complexed with the sulfide functional groups (soft Lewis base) on the BPS surface [31,54].Studies by Molavi et al. [55] and Li et al. [56] suggest that a greater interaction between adsorbents with high surface area and Hg could contribute to the fast adsorption kinetics.Once rapid adsorption occurs, then the Hg removal efficiency becomes relatively constant even with longer contact times due to the saturation of active sites on the adsorbent surface [23].

Adsorption Thermodynamics
The pseudo-thermodynamic parameters for Hg adsorption onto BPS, including the Gibbs free energy of activation where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption rate constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 ) are the rate constants of the double exponential model for the fast and slow steps, respectively.
The best fit of Hg adsorption onto BPS using the above three models was evaluated based on a high coefficient of determination (r 2 ) and a low root mean square error (RMSE) (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capacity, respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch experiments at 288, 298, and 308 K under the various conditions specified in Table 1.The change in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol equation (see Equation ( 11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( 12)), the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ ⧧ ) were determined from the slope and intercept of the linear relation, respectively.
where mads (g L −1 ) is the adsorbent amount in the solution; D1 a constants (g L −1 ) of the rapid and the slow step, respectively; an the rate constants of the double exponential model for the fas tively.
The best fit of Hg adsorption onto BPS using the above thr based on a high coefficient of determination (r 2 ) and a low root m (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values o respectively, and N is the number of observations in the experim

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by ments at 288, 298, and 308 K under the various conditions specifi in Gibbs free energy of activation (∆ ⧧ ) was calculated using th tion (see Equation ( 11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equ the change in enthalpy of activation (∆ ⧧ ) and the change in en were determined from the slope and intercept of the linear relat ), and entropy of activation (∆S o [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption rate constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 ) are the rate constants of the double exponential model for the fast and slow steps, respectively.
The best fit of Hg adsorption onto BPS using the above three models was evaluated based on a high coefficient of determination (r 2 ) and a low root mean square error (RMSE) (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capacity, respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch experiments at 288, 298, and 308 K under the various conditions specified in Table 1.The change in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol equation (see Equation ( 11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( 12)), the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ ⧧ ) were determined from the slope and intercept of the linear relation, respectively.∆ ⧧ = ∆ ⧧ − ∆ ⧧ = − (11) ), were calculated using the Gibbs-Helmholtz equation (see Equation (11)) and the van't Hoff equation (see Equation ( 12)) based on results obtained from the isothermal batch adsorption experiment at different temperatures ranging from 288 to 308 K (Table 7).where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 the rate constants of the double exponential model for the fast and slow steps, res tively. The best fit of Hg adsorption onto BPS using the above three models was evalu based on a high coefficient of determination (r 2 ) and a low root mean square error (RM (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capa respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch ex ments at 288, 298, and 308 K under the various conditions specified in Table 1.The ch in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol e tion (see Equation ( 11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ were determined from the slope and intercept of the linear relation, respectively. where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-o The nonlinear form of the double-exponential kinetic model i [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and constants (g L −1 ) of the rapid and the slow step, respectively; and K the rate constants of the double exponential model for the fast a tively.
The best fit of Hg adsorption onto BPS using the above three based on a high coefficient of determination (r 2 ) and a low root mea (see Equation (10)).
where qi,exp and qi,cal are the experimental and calculated values of th respectively, and N is the number of observations in the experimen

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by con ments at 288, 298, and 308 K under the various conditions specified in Gibbs free energy of activation (∆ ⧧ ) was calculated using the G tion (see Equation ( 11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equat the change in enthalpy of activation (∆ ⧧ ) and the change in entro were determined from the slope and intercept of the linear relation where K2 (g mg −1 min −1 ) is the rate constant of the The nonlinear form of the double-exponenti [27]: where mads (g L −1 ) is the adsorbent amount in the constants (g L −1 ) of the rapid and the slow step, r the rate constants of the double exponential mo tively.
The best fit of Hg adsorption onto BPS usin based on a high coefficient of determination (r 2 ) a (see Equation (10)).

RMSE = 1 𝑁 − 2
where qi,exp and qi,cal are the experimental and calcu respectively, and N is the number of observations

Pseudo-Thermodynamic Parameters of Hg Adsor
Pseudo-thermodynamic parameters were c ments at 288, 298, and 308 K under the various co in Gibbs free energy of activation (∆ ⧧ ) was calc tion (see Equation ( 11)).By plo ing ln(Ke) vs. 1/T the change in enthalpy of activation (∆ ⧧ ) and th were determined from the slope and intercept of As shown in Table 7, the adsorption process of Hg 2+ onto BPS was spontaneous, as evidenced by the negative value of ∆G o order kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibrium and time t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order model.The linear form of the pseudo-second-order kinetic model is shown as Equation ( 8) [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order model.The nonlinear form of the double-exponential kinetic model is given as Equation ( 9) [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption rate constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 ) are the rate constants of the double exponential model for the fast and slow steps, respectively.
The best fit of Hg adsorption onto BPS using the above three models was evaluated based on a high coefficient of determination (r 2 ) and a low root mean square error (RMSE) (see Equation ( 10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capacity, respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch experiments at 288, 298, and 308 K under the various conditions specified in Table 1.The change in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol equation (see Equation (11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( 12)), the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ ⧧ ) were determined from the slope and intercept of the linear relation, respectively.∆ ⧧ = ∆ ⧧ − ∆ ⧧ = − (11) , and endothermic, as indicated by the positive value of ∆H o pseudo-second order, and double-exponential models.The linear form of the pseudo-first order kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibrium and time t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order model.The linear form of the pseudo-second-order kinetic model is shown as Equation ( 8) [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order model.The nonlinear form of the double-exponential kinetic model is given as Equation ( 9) [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are adsorption rate constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and KD2 (min −1 ) are the rate constants of the double exponential model for the fast and slow steps, respectively.
The best fit of Hg adsorption onto BPS using the above three models was evaluated based on a high coefficient of determination (r 2 ) and a low root mean square error (RMSE) (see Equation ( 10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorption capacity, respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting batch experiments at 288, 298, and 308 K under the various conditions specified in Table 1.The change in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-Helmhol equation (see Equation (11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see Equation ( 12)), the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of activation (∆ ⧧ ) were determined from the slope and intercept of the linear relation, respectively.∆ ⧧ = ∆ ⧧ − ∆ ⧧ = − (11) .Additionally, the positive value of ∆S o pseudo-second order, and double-exponential models.The linear form of th order kinetic model is given as Equation ( 7) [26]: where qe (mg g −1 ) and qt (mg g −1 ) are the amounts of Hg 2+ adsorbed at equilibr t (min), respectively.K1 (min −1 ) is the rate constant of the pseudo-first-order The linear form of the pseudo-second-order kinetic model is shown as [26]: where K2 (g mg −1 min −1 ) is the rate constant of the pseudo-second-order mod The nonlinear form of the double-exponential kinetic model is given as [27]: where mads (g L −1 ) is the adsorbent amount in the solution; D1 and D2 are ad constants (g L −1 ) of the rapid and the slow step, respectively; and KD1 and K the rate constants of the double exponential model for the fast and slow tively.
The best fit of Hg adsorption onto BPS using the above three models w based on a high coefficient of determination (r 2 ) and a low root mean square (see Equation ( 10)).
where qi,exp and qi,cal are the experimental and calculated values of the adsorp respectively, and N is the number of observations in the experiment.

Pseudo-Thermodynamic Parameters of Hg Adsorption
Pseudo-thermodynamic parameters were calculated by conducting ments at 288, 298, and 308 K under the various conditions specified in Table in Gibbs free energy of activation (∆ ⧧ ) was calculated using the Gibbs-He tion (see Equation (11)).By plo ing ln(Ke) vs. 1/T (van't Hoff equation: see E the change in enthalpy of activation (∆ ⧧ ) and the change in entropy of act were determined from the slope and intercept of the linear relation, respecti ∆ ⧧ = ∆ ⧧ − ∆ ⧧ = − suggests increased disorder and randomness at the solid-liquid interface, which is considered to be a favorable condition during the adsorption process.Results from thermodynamic parameters (Table 7) supported the fact that Hg adsorption onto BPS was a thermodynamically favorable process, because adsorption proportionally increased with increasing temperatures.

Desorption of Hg from HgS Complex
The stability of the adsorbed Hg on BPS was assessed by desorption tests using strong acids, such as HCl, HNO 3 , and H 2 SO 4 , at different ionic strengths ranging from 0.1 to 1.0 M (Figure 6).The percentages of desorbed Hg were highest using HCl, followed by HNO 3 and H 2 SO 4 .However, the percentages of the desorbed Hg by HCl were lower than 0.17% of the adsorbed Hg, even at 1 M ionic strength.When the ionic strength of the HCl and HNO 3 solutions increased from 0.1 to 1 M, the amount of desorbed Hg 2+ increased, but that by H 2 SO 4 remained relatively constant (Figure 6).These results demonstrate that Hg 2+ was strongly and irreversibly adsorbed on the BPS due to the high affinity of sulfide anions in BPS (soft Lewis base) towards the Hg 2+ ion (the soft Lewis acid), according to the HSAB theory [57].Additionally, the results support the observation that the adsorbed Hg onto BPS would not be released under natural conditions, thereby preventing secondary pollution.
Hg 2+ was strongly and irreversibly adsorbed on the BPS due to the high affinity of sulfide anions in BPS (soft Lewis base) towards the Hg 2+ ion (the soft Lewis acid), according to the HSAB theory [57].Additionally, the results support the observation that the adsorbed Hg onto BPS would not be released under natural conditions, thereby preventing secondary pollution.

BPS Surface Morphology after Hg Adsorption
To elucidate the mechanism of Hg 2+ adsorption onto BPS, SEM images and XPS spectra were employed to observe the changes in the BPS surface after Hg adsorption (Figure 7).The SEM images (Figure 7a) revealed that numerous fine particles were spiked onto the surface of BPS after Hg adsorption, indicating the attachment of Hg 2+ onto the BPS surface.Furthermore, the XPS pattern analysis of Hg4f confirmed that a certain amount of Hg 2+ was adsorbed onto BPS (Figure 7b).Hg4f refers to the photoelectrons ejected from the 4f orbital of Hg atoms in a sample.The 4f orbital of Hg atom splits into two spin-orbit components when it reacts with X-ray, i.e., 4f5/2 and 4f7/2 [58][59][60].The Hg4f binding energies for BPS after Hg 2+ adsorption were mainly centered at 100.94 and 104.98 eV, suggesting that the Hg species adsorbed onto BPS was HgS [61,62].Therefore, these results demonstrate that Hg 2+ adsorption onto BPS was mainly governed by chemical complexation on the outer sphere of the BPS surface to form HgS.

BPS Surface Morphology after Hg Adsorption
To elucidate the mechanism of Hg 2+ adsorption onto BPS, SEM images and XPS spectra were employed to observe the changes in the BPS surface after Hg adsorption (Figure 7).The SEM images (Figure 7a) revealed that numerous fine particles were spiked onto the surface of BPS after Hg adsorption, indicating the attachment of Hg 2+ onto the BPS surface.Furthermore, the XPS pattern analysis of Hg4f confirmed that a certain amount of Hg 2+ was adsorbed onto BPS (Figure 7b).Hg4f refers to the photoelectrons ejected from the 4f orbital of Hg atoms in a sample.The 4f orbital of Hg atom splits into two spin-orbit components when it reacts with X-ray, i.e., 4f5/2 and 4f7/2 [58][59][60].The Hg4f binding energies for BPS after Hg 2+ adsorption were mainly centered at 100.94 and 104.98 eV, suggesting that the Hg species adsorbed onto BPS was HgS [61,62].Therefore, these results demonstrate that Hg 2+ adsorption onto BPS was mainly governed by chemical complexation on the outer sphere of the BPS surface to form HgS.

Application of BPS for Wastewater Treatment
The effectiveness of BPS in removing Hg 2+ from both actual wastewater and spiked wastewater was evaluated to assess its performance under realistic conditions.As depicted in Figure 8, the Hg 2+ removal percentages by BPS from actual and spiked

Figure 1 .
Figure 1.Photo (a) and SEM image (b) of the biologically produced sulfur (BPS).

Figure 3 .
Figure 3.Effect of pH on the removal of Hg 2+ by BPS.Vertical bars represent standard deviations from the mean values (n = 3).

Figure 3 .
Figure 3.Effect of pH on the removal of Hg 2+ by BPS.Vertical bars represent standard deviations from the mean values (n = 3).

Figure 5 .
Figure 5. Rate curves of three kinetic models for Hg 2+ adsorption onto BPS: (a) pseudo-first-order kinetic, (b) pseudo-second-order, and (c) non-linear multiple first-order kinetic model.

Figure 5 .
Figure 5. Rate curves of three kinetic models for Hg 2+ adsorption onto BPS: (a) pseudo-first-order kinetic, (b) pseudo-second-order, and (c) non-linear multiple first-order kinetic model.

Figure 6 .
Figure 6.Effect of kind and concentration of acid solutions on the desorption of Hg 2+ from BPSadsorbed Hg.

Figure 6 .
Figure 6.Effect of kind and concentration of acid solutions on the desorption of Hg 2+ from BPSadsorbed Hg.

Figure 7 .
Figure 7. Scanning electron microscope images of BPS, with EDS mapping of S and Hg elements (a) and high-resolution XPS spectra of BPS after Hg adsorption (b).

Figure 7 .
Figure 7. Scanning electron microscope images of BPS, with EDS mapping of S and Hg elements (a) and high-resolution XPS spectra of BPS after Hg adsorption (b).
was in part supported by USDA-National Institute of Food and Agriculture (NIFA) Capacity Grant No. 21-0008.Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.

Table 1 .
Descriptions of conditions of the batch adsorption experiments.

Table 2 .
Metal concentrations of wastewater sample used in this study and allowable limit of each metal in discharging water.
† Allowable limit for wastewater discharges from the individual industry specified by the Korea Water Environment Conservation Act.

Table 3 .
Elemental composition of biologically produced S (BPS) determined by X-ray fluorescence spectrometry.

Table 3 .
Elemental composition of biologically produced S (BPS) determined by X-ray fluorescence spectrometry.

Table 4 .
Adsorption parameters of the Langmuir and Freundlich isotherm models.

Table 5 .
Lists of maximum capacities (Q max ) for Hg 2+ adsorption by various adsorbents reported in selected literature.

Table 4 .
Adsorption parameters of the Langmuir and Freundlich isotherm models.
†Refer to Equations (

Table 7 .
Thermodynamic parameters for adsorption of Hg 2+ onto BPS.