H2O + ZnSO4 = H2SO4 + (ZnOH)2SO4

Input interpretation

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H_2O water + ZnSO_4 zinc sulfate ⟶ H_2SO_4 sulfuric acid + (ZnOH)2SO4

Balanced equation

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Balance the chemical equation algebraically: H_2O + ZnSO_4 ⟶ H_2SO_4 + (ZnOH)2SO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 ZnSO_4 ⟶ c_3 H_2SO_4 + c_4 (ZnOH)2SO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Zn: H: | 2 c_1 = 2 c_3 + 2 c_4 O: | c_1 + 4 c_2 = 4 c_3 + 6 c_4 S: | c_2 = c_3 + c_4 Zn: | c_2 = 2 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 = 2 c_2 = 2 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 ZnSO_4 ⟶ H_2SO_4 + (ZnOH)2SO4

+ ⟶ + (ZnOH)2SO4

Names

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water + zinc sulfate ⟶ sulfuric acid + (ZnOH)2SO4

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2O + ZnSO_4 ⟶ H_2SO_4 + (ZnOH)2SO4 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: 2 H_2O + 2 ZnSO_4 ⟶ H_2SO_4 + (ZnOH)2SO4 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_2O | 2 | -2 ZnSO_4 | 2 | -2 H_2SO_4 | 1 | 1 (ZnOH)2SO4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) ZnSO_4 | 2 | -2 | ([ZnSO4])^(-2) H_2SO_4 | 1 | 1 | [H2SO4] (ZnOH)2SO4 | 1 | 1 | [(ZnOH)2SO4] 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 = ([H2O])^(-2) ([ZnSO4])^(-2) [H2SO4] [(ZnOH)2SO4] = ([H2SO4] [(ZnOH)2SO4])/(([H2O])^2 ([ZnSO4])^2)

Rate of reaction

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Construct the rate of reaction expression for: H_2O + ZnSO_4 ⟶ H_2SO_4 + (ZnOH)2SO4 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: 2 H_2O + 2 ZnSO_4 ⟶ H_2SO_4 + (ZnOH)2SO4 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_2O | 2 | -2 ZnSO_4 | 2 | -2 H_2SO_4 | 1 | 1 (ZnOH)2SO4 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) ZnSO_4 | 2 | -2 | -1/2 (Δ[ZnSO4])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) (ZnOH)2SO4 | 1 | 1 | (Δ[(ZnOH)2SO4])/(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 = -1/2 (Δ[H2O])/(Δt) = -1/2 (Δ[ZnSO4])/(Δt) = (Δ[H2SO4])/(Δt) = (Δ[(ZnOH)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)