HCl + SO2 + Zn = H2O + H2S + ZnCl2

HCl hydrogen chloride + SO_2 sulfur dioxide + Zn zinc ⟶ H_2O water + H_2S hydrogen sulfide + ZnCl_2 zinc chloride

Balance the chemical equation algebraically: HCl + SO_2 + Zn ⟶ H_2O + H_2S + ZnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 SO_2 + c_3 Zn ⟶ c_4 H_2O + c_5 H_2S + c_6 ZnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, O, S and Zn: Cl: | c_1 = 2 c_6 H: | c_1 = 2 c_4 + 2 c_5 O: | 2 c_2 = c_4 S: | c_2 = c_5 Zn: | c_3 = c_6 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 3 c_4 = 2 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + SO_2 + 3 Zn ⟶ 2 H_2O + H_2S + 3 ZnCl_2

+ + ⟶ + +

hydrogen chloride + sulfur dioxide + zinc ⟶ water + hydrogen sulfide + zinc chloride

| hydrogen chloride | sulfur dioxide | zinc | water | hydrogen sulfide | zinc chloride molecular enthalpy | -92.3 kJ/mol | -296.8 kJ/mol | 0 kJ/mol | -285.8 kJ/mol | -20.6 kJ/mol | -415.1 kJ/mol total enthalpy | -553.8 kJ/mol | -296.8 kJ/mol | 0 kJ/mol | -571.7 kJ/mol | -20.6 kJ/mol | -1245 kJ/mol | H_initial = -850.6 kJ/mol | | | H_final = -1838 kJ/mol | | ΔH_rxn^0 | -1838 kJ/mol - -850.6 kJ/mol = -987 kJ/mol (exothermic) | | | | |

Construct the equilibrium constant, K, expression for: HCl + SO_2 + Zn ⟶ H_2O + H_2S + ZnCl_2 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: 6 HCl + SO_2 + 3 Zn ⟶ 2 H_2O + H_2S + 3 ZnCl_2 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 HCl | 6 | -6 SO_2 | 1 | -1 Zn | 3 | -3 H_2O | 2 | 2 H_2S | 1 | 1 ZnCl_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) SO_2 | 1 | -1 | ([SO2])^(-1) Zn | 3 | -3 | ([Zn])^(-3) H_2O | 2 | 2 | ([H2O])^2 H_2S | 1 | 1 | [H2S] ZnCl_2 | 3 | 3 | ([ZnCl2])^3 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 = ([HCl])^(-6) ([SO2])^(-1) ([Zn])^(-3) ([H2O])^2 [H2S] ([ZnCl2])^3 = (([H2O])^2 [H2S] ([ZnCl2])^3)/(([HCl])^6 [SO2] ([Zn])^3)

Construct the rate of reaction expression for: HCl + SO_2 + Zn ⟶ H_2O + H_2S + ZnCl_2 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: 6 HCl + SO_2 + 3 Zn ⟶ 2 H_2O + H_2S + 3 ZnCl_2 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 HCl | 6 | -6 SO_2 | 1 | -1 Zn | 3 | -3 H_2O | 2 | 2 H_2S | 1 | 1 ZnCl_2 | 3 | 3 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 HCl | 6 | -6 | -1/6 (Δ[HCl])/(Δt) SO_2 | 1 | -1 | -(Δ[SO2])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) H_2S | 1 | 1 | (Δ[H2S])/(Δt) ZnCl_2 | 3 | 3 | 1/3 (Δ[ZnCl2])/(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 = -1/6 (Δ[HCl])/(Δt) = -(Δ[SO2])/(Δt) = -1/3 (Δ[Zn])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[H2S])/(Δt) = 1/3 (Δ[ZnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | sulfur dioxide | zinc | water | hydrogen sulfide | zinc chloride formula | HCl | SO_2 | Zn | H_2O | H_2S | ZnCl_2 Hill formula | ClH | O_2S | Zn | H_2O | H_2S | Cl_2Zn name | hydrogen chloride | sulfur dioxide | zinc | water | hydrogen sulfide | zinc chloride IUPAC name | hydrogen chloride | sulfur dioxide | zinc | water | hydrogen sulfide | zinc dichloride