HCl + Zn + As2O3 = H2O + ZnCl2 + AsH3

HCl hydrogen chloride + Zn zinc + As_2O_3 arsenic trioxide ⟶ H_2O water + ZnCl_2 zinc chloride + AsH_3 arsine

Balance the chemical equation algebraically: HCl + Zn + As_2O_3 ⟶ H_2O + ZnCl_2 + AsH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Zn + c_3 As_2O_3 ⟶ 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 = 2 c_4 + 3 c_6 Zn: | c_2 = c_5 As: | 2 c_3 = c_6 O: | 3 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 = 12 c_2 = 6 c_3 = 1 c_4 = 3 c_5 = 6 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 HCl + 6 Zn + As_2O_3 ⟶ 3 H_2O + 6 ZnCl_2 + 2 AsH_3

+ + ⟶ + +

hydrogen chloride + zinc + arsenic trioxide ⟶ water + zinc chloride + arsine

Construct the equilibrium constant, K, expression for: HCl + Zn + As_2O_3 ⟶ 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: 12 HCl + 6 Zn + As_2O_3 ⟶ 3 H_2O + 6 ZnCl_2 + 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 | 12 | -12 Zn | 6 | -6 As_2O_3 | 1 | -1 H_2O | 3 | 3 ZnCl_2 | 6 | 6 AsH_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 12 | -12 | ([HCl])^(-12) Zn | 6 | -6 | ([Zn])^(-6) As_2O_3 | 1 | -1 | ([As2O3])^(-1) H_2O | 3 | 3 | ([H2O])^3 ZnCl_2 | 6 | 6 | ([ZnCl2])^6 AsH_3 | 2 | 2 | ([AsH3])^2 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])^(-12) ([Zn])^(-6) ([As2O3])^(-1) ([H2O])^3 ([ZnCl2])^6 ([AsH3])^2 = (([H2O])^3 ([ZnCl2])^6 ([AsH3])^2)/(([HCl])^12 ([Zn])^6 [As2O3])

Construct the rate of reaction expression for: HCl + Zn + As_2O_3 ⟶ 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: 12 HCl + 6 Zn + As_2O_3 ⟶ 3 H_2O + 6 ZnCl_2 + 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 | 12 | -12 Zn | 6 | -6 As_2O_3 | 1 | -1 H_2O | 3 | 3 ZnCl_2 | 6 | 6 AsH_3 | 2 | 2 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 | 12 | -12 | -1/12 (Δ[HCl])/(Δt) Zn | 6 | -6 | -1/6 (Δ[Zn])/(Δt) As_2O_3 | 1 | -1 | -(Δ[As2O3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) ZnCl_2 | 6 | 6 | 1/6 (Δ[ZnCl2])/(Δt) AsH_3 | 2 | 2 | 1/2 (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 = -1/12 (Δ[HCl])/(Δt) = -1/6 (Δ[Zn])/(Δt) = -(Δ[As2O3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/6 (Δ[ZnCl2])/(Δt) = 1/2 (Δ[AsH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | zinc | arsenic trioxide | water | zinc chloride | arsine formula | HCl | Zn | As_2O_3 | H_2O | ZnCl_2 | AsH_3 Hill formula | ClH | Zn | As_2O_3 | H_2O | Cl_2Zn | AsH_3 name | hydrogen chloride | zinc | arsenic trioxide | water | zinc chloride | arsine IUPAC name | hydrogen chloride | zinc | 2, 4, 5-trioxa-1, 3-diarsabicyclo[1.1.1]pentane | water | zinc dichloride | arsane