H2SO4 + Zn = H2O + ZnSO4 + H2S2

Input interpretation

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H_2SO_4 sulfuric acid + Zn zinc ⟶ H_2O water + ZnSO_4 zinc sulfate + H2S2

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + Zn ⟶ H_2O + ZnSO_4 + H2S2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Zn ⟶ c_3 H_2O + c_4 ZnSO_4 + c_5 H2S2 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_5 O: | 4 c_1 = c_3 + 4 c_4 S: | c_1 = c_4 + 2 c_5 Zn: | c_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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 9 c_2 = 7 c_3 = 8 c_4 = 7 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 H_2SO_4 + 7 Zn ⟶ 8 H_2O + 7 ZnSO_4 + H2S2

+ ⟶ + + H2S2

Names

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sulfuric acid + zinc ⟶ water + zinc sulfate + H2S2

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + Zn ⟶ H_2O + ZnSO_4 + H2S2 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: 9 H_2SO_4 + 7 Zn ⟶ 8 H_2O + 7 ZnSO_4 + H2S2 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 | 9 | -9 Zn | 7 | -7 H_2O | 8 | 8 ZnSO_4 | 7 | 7 H2S2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 9 | -9 | ([H2SO4])^(-9) Zn | 7 | -7 | ([Zn])^(-7) H_2O | 8 | 8 | ([H2O])^8 ZnSO_4 | 7 | 7 | ([ZnSO4])^7 H2S2 | 1 | 1 | [H2S2] 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])^(-9) ([Zn])^(-7) ([H2O])^8 ([ZnSO4])^7 [H2S2] = (([H2O])^8 ([ZnSO4])^7 [H2S2])/(([H2SO4])^9 ([Zn])^7)

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + Zn ⟶ H_2O + ZnSO_4 + H2S2 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: 9 H_2SO_4 + 7 Zn ⟶ 8 H_2O + 7 ZnSO_4 + H2S2 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 | 9 | -9 Zn | 7 | -7 H_2O | 8 | 8 ZnSO_4 | 7 | 7 H2S2 | 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_2SO_4 | 9 | -9 | -1/9 (Δ[H2SO4])/(Δt) Zn | 7 | -7 | -1/7 (Δ[Zn])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) ZnSO_4 | 7 | 7 | 1/7 (Δ[ZnSO4])/(Δt) H2S2 | 1 | 1 | (Δ[H2S2])/(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 = -1/9 (Δ[H2SO4])/(Δt) = -1/7 (Δ[Zn])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/7 (Δ[ZnSO4])/(Δt) = (Δ[H2S2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)