H2SO4 + Zn + As4O6 = H2O + ZnSO4 + AsH3

Input interpretation

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H_2SO_4 sulfuric acid + Zn zinc + As4O6 ⟶ H_2O water + ZnSO_4 zinc sulfate + AsH_3 arsine

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + Zn + As4O6 ⟶ H_2O + ZnSO_4 + AsH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Zn + c_3 As4O6 ⟶ c_4 H_2O + c_5 ZnSO_4 + c_6 AsH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Zn and As: H: | 2 c_1 = 2 c_4 + 3 c_6 O: | 4 c_1 + 6 c_3 = c_4 + 4 c_5 S: | c_1 = c_5 Zn: | c_2 = c_5 As: | 4 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 12 c_2 = 12 c_3 = 1 c_4 = 6 c_5 = 12 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2SO_4 + 12 Zn + As4O6 ⟶ 6 H_2O + 12 ZnSO_4 + 4 AsH_3

+ + As4O6 ⟶ + +

Names

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sulfuric acid + zinc + As4O6 ⟶ water + zinc sulfate + arsine

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + Zn + As4O6 ⟶ H_2O + ZnSO_4 + 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 H_2SO_4 + 12 Zn + As4O6 ⟶ 6 H_2O + 12 ZnSO_4 + 4 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 H_2SO_4 | 12 | -12 Zn | 12 | -12 As4O6 | 1 | -1 H_2O | 6 | 6 ZnSO_4 | 12 | 12 AsH_3 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 12 | -12 | ([H2SO4])^(-12) Zn | 12 | -12 | ([Zn])^(-12) As4O6 | 1 | -1 | ([As4O6])^(-1) H_2O | 6 | 6 | ([H2O])^6 ZnSO_4 | 12 | 12 | ([ZnSO4])^12 AsH_3 | 4 | 4 | ([AsH3])^4 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 = ([H2SO4])^(-12) ([Zn])^(-12) ([As4O6])^(-1) ([H2O])^6 ([ZnSO4])^12 ([AsH3])^4 = (([H2O])^6 ([ZnSO4])^12 ([AsH3])^4)/(([H2SO4])^12 ([Zn])^12 [As4O6])

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + Zn + As4O6 ⟶ H_2O + ZnSO_4 + 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 H_2SO_4 + 12 Zn + As4O6 ⟶ 6 H_2O + 12 ZnSO_4 + 4 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 H_2SO_4 | 12 | -12 Zn | 12 | -12 As4O6 | 1 | -1 H_2O | 6 | 6 ZnSO_4 | 12 | 12 AsH_3 | 4 | 4 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_2SO_4 | 12 | -12 | -1/12 (Δ[H2SO4])/(Δt) Zn | 12 | -12 | -1/12 (Δ[Zn])/(Δt) As4O6 | 1 | -1 | -(Δ[As4O6])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) ZnSO_4 | 12 | 12 | 1/12 (Δ[ZnSO4])/(Δt) AsH_3 | 4 | 4 | 1/4 (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[H2SO4])/(Δt) = -1/12 (Δ[Zn])/(Δt) = -(Δ[As4O6])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/12 (Δ[ZnSO4])/(Δt) = 1/4 (Δ[AsH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)