H2O + Cl2 + H2S = H2SO4 + HCl

H_2O (water) + Cl_2 (chlorine) + H_2S (hydrogen sulfide) ⟶ H_2SO_4 (sulfuric acid) + HCl (hydrogen chloride)

Balance the chemical equation algebraically: H_2O + Cl_2 + H_2S ⟶ H_2SO_4 + HCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cl_2 + c_3 H_2S ⟶ c_4 H_2SO_4 + c_5 HCl Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl and S: H: | 2 c_1 + 2 c_3 = 2 c_4 + c_5 O: | c_1 = 4 c_4 Cl: | 2 c_2 = c_5 S: | c_3 = c_4 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 4 c_3 = 1 c_4 = 1 c_5 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + 4 Cl_2 + H_2S ⟶ H_2SO_4 + 8 HCl

+ + ⟶ +

water + chlorine + hydrogen sulfide ⟶ sulfuric acid + hydrogen chloride

| water | chlorine | hydrogen sulfide | sulfuric acid | hydrogen chloride molecular enthalpy | -285.8 kJ/mol | 0 kJ/mol | -20.6 kJ/mol | -814 kJ/mol | -92.3 kJ/mol total enthalpy | -1143 kJ/mol | 0 kJ/mol | -20.6 kJ/mol | -814 kJ/mol | -738.4 kJ/mol | H_initial = -1164 kJ/mol | | | H_final = -1552 kJ/mol | ΔH_rxn^0 | -1552 kJ/mol - -1164 kJ/mol = -388.5 kJ/mol (exothermic) | | | |

| water | chlorine | hydrogen sulfide | sulfuric acid | hydrogen chloride molecular free energy | -237.1 kJ/mol | 0 kJ/mol | -33.4 kJ/mol | -690 kJ/mol | -95.3 kJ/mol total free energy | -948.4 kJ/mol | 0 kJ/mol | -33.4 kJ/mol | -690 kJ/mol | -762.4 kJ/mol | G_initial = -981.8 kJ/mol | | | G_final = -1452 kJ/mol | ΔG_rxn^0 | -1452 kJ/mol - -981.8 kJ/mol = -470.6 kJ/mol (exergonic) | | | |

| water | chlorine | hydrogen sulfide | sulfuric acid | hydrogen chloride molecular entropy | 69.91 J/(mol K) | 223 J/(mol K) | 206 J/(mol K) | 157 J/(mol K) | 187 J/(mol K) total entropy | 279.6 J/(mol K) | 892 J/(mol K) | 206 J/(mol K) | 157 J/(mol K) | 1496 J/(mol K) | S_initial = 1378 J/(mol K) | | | S_final = 1653 J/(mol K) | ΔS_rxn^0 | 1653 J/(mol K) - 1378 J/(mol K) = 275.4 J/(mol K) (endoentropic) | | | |

Construct the equilibrium constant, K, expression for: H_2O + Cl_2 + H_2S ⟶ H_2SO_4 + HCl Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 4 H_2O + 4 Cl_2 + H_2S ⟶ H_2SO_4 + 8 HCl Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 4 | -4 Cl_2 | 4 | -4 H_2S | 1 | -1 H_2SO_4 | 1 | 1 HCl | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 4 | -4 | ([H2O])^(-4) Cl_2 | 4 | -4 | ([Cl2])^(-4) H_2S | 1 | -1 | ([H2S])^(-1) H_2SO_4 | 1 | 1 | [H2SO4] HCl | 8 | 8 | ([HCl])^8 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2O])^(-4) ([Cl2])^(-4) ([H2S])^(-1) [H2SO4] ([HCl])^8 = ([H2SO4] ([HCl])^8)/(([H2O])^4 ([Cl2])^4 [H2S])

Construct the rate of reaction expression for: H_2O + Cl_2 + H_2S ⟶ H_2SO_4 + HCl Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 4 H_2O + 4 Cl_2 + H_2S ⟶ H_2SO_4 + 8 HCl Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 4 | -4 Cl_2 | 4 | -4 H_2S | 1 | -1 H_2SO_4 | 1 | 1 HCl | 8 | 8 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2O | 4 | -4 | -1/4 (Δ[H2O])/(Δt) Cl_2 | 4 | -4 | -1/4 (Δ[Cl2])/(Δt) H_2S | 1 | -1 | -(Δ[H2S])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) HCl | 8 | 8 | 1/8 (Δ[HCl])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/4 (Δ[H2O])/(Δt) = -1/4 (Δ[Cl2])/(Δt) = -(Δ[H2S])/(Δt) = (Δ[H2SO4])/(Δt) = 1/8 (Δ[HCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | chlorine | hydrogen sulfide | sulfuric acid | hydrogen chloride formula | H_2O | Cl_2 | H_2S | H_2SO_4 | HCl Hill formula | H_2O | Cl_2 | H_2S | H_2O_4S | ClH name | water | chlorine | hydrogen sulfide | sulfuric acid | hydrogen chloride IUPAC name | water | molecular chlorine | hydrogen sulfide | sulfuric acid | hydrogen chloride