HNO3 + Zn = H2O + Zn(NO3)2 + HN4NO3

Input interpretation

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HNO_3 nitric acid + Zn zinc ⟶ H_2O water + Zn(NO3)2 + HN4NO3

Balanced equation

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Balance the chemical equation algebraically: HNO_3 + Zn ⟶ H_2O + Zn(NO3)2 + HN4NO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Zn ⟶ c_3 H_2O + c_4 Zn(NO3)2 + c_5 HN4NO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Zn: H: | c_1 = 2 c_3 + c_5 N: | c_1 = 2 c_4 + 5 c_5 O: | 3 c_1 = c_3 + 6 c_4 + 3 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 = 25 c_2 = 10 c_3 = 12 c_4 = 10 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 25 HNO_3 + 10 Zn ⟶ 12 H_2O + 10 Zn(NO3)2 + HN4NO3

+ ⟶ + Zn(NO3)2 + HN4NO3

Names

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nitric acid + zinc ⟶ water + Zn(NO3)2 + HN4NO3

Equilibrium constant

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Construct the equilibrium constant, K, expression for: HNO_3 + Zn ⟶ H_2O + Zn(NO3)2 + HN4NO3 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: 25 HNO_3 + 10 Zn ⟶ 12 H_2O + 10 Zn(NO3)2 + HN4NO3 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 HNO_3 | 25 | -25 Zn | 10 | -10 H_2O | 12 | 12 Zn(NO3)2 | 10 | 10 HN4NO3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 25 | -25 | ([HNO3])^(-25) Zn | 10 | -10 | ([Zn])^(-10) H_2O | 12 | 12 | ([H2O])^12 Zn(NO3)2 | 10 | 10 | ([Zn(NO3)2])^10 HN4NO3 | 1 | 1 | [HN4NO3] 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 = ([HNO3])^(-25) ([Zn])^(-10) ([H2O])^12 ([Zn(NO3)2])^10 [HN4NO3] = (([H2O])^12 ([Zn(NO3)2])^10 [HN4NO3])/(([HNO3])^25 ([Zn])^10)

Rate of reaction

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Construct the rate of reaction expression for: HNO_3 + Zn ⟶ H_2O + Zn(NO3)2 + HN4NO3 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: 25 HNO_3 + 10 Zn ⟶ 12 H_2O + 10 Zn(NO3)2 + HN4NO3 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 HNO_3 | 25 | -25 Zn | 10 | -10 H_2O | 12 | 12 Zn(NO3)2 | 10 | 10 HN4NO3 | 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 HNO_3 | 25 | -25 | -1/25 (Δ[HNO3])/(Δt) Zn | 10 | -10 | -1/10 (Δ[Zn])/(Δt) H_2O | 12 | 12 | 1/12 (Δ[H2O])/(Δt) Zn(NO3)2 | 10 | 10 | 1/10 (Δ[Zn(NO3)2])/(Δt) HN4NO3 | 1 | 1 | (Δ[HN4NO3])/(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 = -1/25 (Δ[HNO3])/(Δt) = -1/10 (Δ[Zn])/(Δt) = 1/12 (Δ[H2O])/(Δt) = 1/10 (Δ[Zn(NO3)2])/(Δt) = (Δ[HN4NO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)