HCl + Zn + H3AsO4 = H2O + ZnCl2 + AsH3

HCl hydrogen chloride + Zn zinc + H_3AsO_4 arsenic acid, solid ⟶ H_2O water + ZnCl_2 zinc chloride + AsH_3 arsine

Balance the chemical equation algebraically: HCl + Zn + H_3AsO_4 ⟶ H_2O + ZnCl_2 + AsH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Zn + c_3 H_3AsO_4 ⟶ c_4 H_2O + c_5 ZnCl_2 + c_6 AsH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Zn, As and O: Cl: | c_1 = 2 c_5 H: | c_1 + 3 c_3 = 2 c_4 + 3 c_6 Zn: | c_2 = c_5 As: | c_3 = c_6 O: | 4 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 = 8 c_2 = 4 c_3 = 1 c_4 = 4 c_5 = 4 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + 4 Zn + H_3AsO_4 ⟶ 4 H_2O + 4 ZnCl_2 + AsH_3

+ + ⟶ + +

hydrogen chloride + zinc + arsenic acid, solid ⟶ water + zinc chloride + arsine

| hydrogen chloride | zinc | arsenic acid, solid | water | zinc chloride | arsine molecular enthalpy | -92.3 kJ/mol | 0 kJ/mol | -906.3 kJ/mol | -285.8 kJ/mol | -415.1 kJ/mol | 66.4 kJ/mol total enthalpy | -738.4 kJ/mol | 0 kJ/mol | -906.3 kJ/mol | -1143 kJ/mol | -1660 kJ/mol | 66.4 kJ/mol | H_initial = -1645 kJ/mol | | | H_final = -2737 kJ/mol | | ΔH_rxn^0 | -2737 kJ/mol - -1645 kJ/mol = -1093 kJ/mol (exothermic) | | | | |

Construct the equilibrium constant, K, expression for: HCl + Zn + H_3AsO_4 ⟶ H_2O + ZnCl_2 + AsH_3 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: 8 HCl + 4 Zn + H_3AsO_4 ⟶ 4 H_2O + 4 ZnCl_2 + AsH_3 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 | 8 | -8 Zn | 4 | -4 H_3AsO_4 | 1 | -1 H_2O | 4 | 4 ZnCl_2 | 4 | 4 AsH_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) Zn | 4 | -4 | ([Zn])^(-4) H_3AsO_4 | 1 | -1 | ([H3AsO4])^(-1) H_2O | 4 | 4 | ([H2O])^4 ZnCl_2 | 4 | 4 | ([ZnCl2])^4 AsH_3 | 1 | 1 | [AsH3] 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])^(-8) ([Zn])^(-4) ([H3AsO4])^(-1) ([H2O])^4 ([ZnCl2])^4 [AsH3] = (([H2O])^4 ([ZnCl2])^4 [AsH3])/(([HCl])^8 ([Zn])^4 [H3AsO4])

Construct the rate of reaction expression for: HCl + Zn + H_3AsO_4 ⟶ H_2O + ZnCl_2 + AsH_3 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: 8 HCl + 4 Zn + H_3AsO_4 ⟶ 4 H_2O + 4 ZnCl_2 + AsH_3 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 | 8 | -8 Zn | 4 | -4 H_3AsO_4 | 1 | -1 H_2O | 4 | 4 ZnCl_2 | 4 | 4 AsH_3 | 1 | 1 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 | 8 | -8 | -1/8 (Δ[HCl])/(Δt) Zn | 4 | -4 | -1/4 (Δ[Zn])/(Δt) H_3AsO_4 | 1 | -1 | -(Δ[H3AsO4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) ZnCl_2 | 4 | 4 | 1/4 (Δ[ZnCl2])/(Δt) AsH_3 | 1 | 1 | (Δ[AsH3])/(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 = -1/8 (Δ[HCl])/(Δt) = -1/4 (Δ[Zn])/(Δt) = -(Δ[H3AsO4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/4 (Δ[ZnCl2])/(Δt) = (Δ[AsH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | zinc | arsenic acid, solid | water | zinc chloride | arsine formula | HCl | Zn | H_3AsO_4 | H_2O | ZnCl_2 | AsH_3 Hill formula | ClH | Zn | AsH_3O_4 | H_2O | Cl_2Zn | AsH_3 name | hydrogen chloride | zinc | arsenic acid, solid | water | zinc chloride | arsine IUPAC name | hydrogen chloride | zinc | arsoric acid | water | zinc dichloride | arsane