HCl + Zn + HAsO2 = H2O + ZnCl2 + AsH3

HCl hydrogen chloride + Zn zinc + HAsO2 ⟶ H_2O water + ZnCl_2 zinc chloride + AsH_3 arsine

Balance the chemical equation algebraically: HCl + Zn + HAsO2 ⟶ H_2O + ZnCl_2 + AsH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Zn + c_3 HAsO2 ⟶ 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 + c_3 = 2 c_4 + 3 c_6 Zn: | c_2 = c_5 As: | c_3 = c_6 O: | 2 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 = 6 c_2 = 3 c_3 = 1 c_4 = 2 c_5 = 3 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + 3 Zn + HAsO2 ⟶ 2 H_2O + 3 ZnCl_2 + AsH_3

+ + HAsO2 ⟶ + +

hydrogen chloride + zinc + HAsO2 ⟶ water + zinc chloride + arsine

Construct the equilibrium constant, K, expression for: HCl + Zn + HAsO2 ⟶ 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: 6 HCl + 3 Zn + HAsO2 ⟶ 2 H_2O + 3 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 | 6 | -6 Zn | 3 | -3 HAsO2 | 1 | -1 H_2O | 2 | 2 ZnCl_2 | 3 | 3 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 | 6 | -6 | ([HCl])^(-6) Zn | 3 | -3 | ([Zn])^(-3) HAsO2 | 1 | -1 | ([HAsO2])^(-1) H_2O | 2 | 2 | ([H2O])^2 ZnCl_2 | 3 | 3 | ([ZnCl2])^3 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])^(-6) ([Zn])^(-3) ([HAsO2])^(-1) ([H2O])^2 ([ZnCl2])^3 [AsH3] = (([H2O])^2 ([ZnCl2])^3 [AsH3])/(([HCl])^6 ([Zn])^3 [HAsO2])

Construct the rate of reaction expression for: HCl + Zn + HAsO2 ⟶ 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: 6 HCl + 3 Zn + HAsO2 ⟶ 2 H_2O + 3 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 | 6 | -6 Zn | 3 | -3 HAsO2 | 1 | -1 H_2O | 2 | 2 ZnCl_2 | 3 | 3 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 | 6 | -6 | -1/6 (Δ[HCl])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) HAsO2 | 1 | -1 | -(Δ[HAsO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) ZnCl_2 | 3 | 3 | 1/3 (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 = -1/6 (Δ[HCl])/(Δt) = -1/3 (Δ[Zn])/(Δt) = -(Δ[HAsO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/3 (Δ[ZnCl2])/(Δt) = (Δ[AsH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | zinc | HAsO2 | water | zinc chloride | arsine formula | HCl | Zn | HAsO2 | H_2O | ZnCl_2 | AsH_3 Hill formula | ClH | Zn | HAsO2 | H_2O | Cl_2Zn | AsH_3 name | hydrogen chloride | zinc | | water | zinc chloride | arsine IUPAC name | hydrogen chloride | zinc | | water | zinc dichloride | arsane

| hydrogen chloride | zinc | HAsO2 | water | zinc chloride | arsine molar mass | 36.46 g/mol | 65.38 g/mol | 107.93 g/mol | 18.015 g/mol | 136.3 g/mol | 77.946 g/mol phase | gas (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | gas (at STP) melting point | -114.17 °C | 420 °C | | 0 °C | 293 °C | -111.2 °C boiling point | -85 °C | 907 °C | | 99.9839 °C | | -62.5 °C density | 0.00149 g/cm^3 (at 25 °C) | 7.14 g/cm^3 | | 1 g/cm^3 | | 0.003186 g/cm^3 (at 25 °C) solubility in water | miscible | insoluble | | | soluble | surface tension | | | | 0.0728 N/m | | dynamic viscosity | | | | 8.9×10^-4 Pa s (at 25 °C) | | 1.47×10^-5 Pa s (at 0 °C) odor | | odorless | | odorless | odorless |