H2SO4 + HNO3 + Zn = H2O + N2 + ZnSO4

Input interpretation

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H_2SO_4 sulfuric acid + HNO_3 nitric acid + Zn zinc ⟶ H_2O water + N_2 nitrogen + ZnSO_4 zinc sulfate

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + HNO_3 + Zn ⟶ H_2O + N_2 + ZnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 HNO_3 + c_3 Zn ⟶ c_4 H_2O + c_5 N_2 + c_6 ZnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, N and Zn: H: | 2 c_1 + c_2 = 2 c_4 O: | 4 c_1 + 3 c_2 = c_4 + 4 c_6 S: | c_1 = c_6 N: | c_2 = 2 c_5 Zn: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5 c_2 = 2 c_3 = 5 c_4 = 6 c_5 = 1 c_6 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2SO_4 + 2 HNO_3 + 5 Zn ⟶ 6 H_2O + N_2 + 5 ZnSO_4

+ + ⟶ + +

Names

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sulfuric acid + nitric acid + zinc ⟶ water + nitrogen + zinc sulfate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + HNO_3 + Zn ⟶ H_2O + N_2 + ZnSO_4 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: 5 H_2SO_4 + 2 HNO_3 + 5 Zn ⟶ 6 H_2O + N_2 + 5 ZnSO_4 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 | 5 | -5 HNO_3 | 2 | -2 Zn | 5 | -5 H_2O | 6 | 6 N_2 | 1 | 1 ZnSO_4 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 5 | -5 | ([H2SO4])^(-5) HNO_3 | 2 | -2 | ([HNO3])^(-2) Zn | 5 | -5 | ([Zn])^(-5) H_2O | 6 | 6 | ([H2O])^6 N_2 | 1 | 1 | [N2] ZnSO_4 | 5 | 5 | ([ZnSO4])^5 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])^(-5) ([HNO3])^(-2) ([Zn])^(-5) ([H2O])^6 [N2] ([ZnSO4])^5 = (([H2O])^6 [N2] ([ZnSO4])^5)/(([H2SO4])^5 ([HNO3])^2 ([Zn])^5)

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + HNO_3 + Zn ⟶ H_2O + N_2 + ZnSO_4 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: 5 H_2SO_4 + 2 HNO_3 + 5 Zn ⟶ 6 H_2O + N_2 + 5 ZnSO_4 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 | 5 | -5 HNO_3 | 2 | -2 Zn | 5 | -5 H_2O | 6 | 6 N_2 | 1 | 1 ZnSO_4 | 5 | 5 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 | 5 | -5 | -1/5 (Δ[H2SO4])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) Zn | 5 | -5 | -1/5 (Δ[Zn])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) ZnSO_4 | 5 | 5 | 1/5 (Δ[ZnSO4])/(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 = -1/5 (Δ[H2SO4])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = -1/5 (Δ[Zn])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[N2])/(Δt) = 1/5 (Δ[ZnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)