HNO3 + FeSO4 = H2O + H2SO4 + NO2 + Fe(NO3)3

Input interpretation

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HNO_3 nitric acid + FeSO_4 duretter ⟶ H_2O water + H_2SO_4 sulfuric acid + NO_2 nitrogen dioxide + Fe(NO_3)_3 ferric nitrate

Balanced equation

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Balance the chemical equation algebraically: HNO_3 + FeSO_4 ⟶ H_2O + H_2SO_4 + NO_2 + Fe(NO_3)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 FeSO_4 ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 NO_2 + c_6 Fe(NO_3)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Fe and S: H: | c_1 = 2 c_3 + 2 c_4 N: | c_1 = c_5 + 3 c_6 O: | 3 c_1 + 4 c_2 = c_3 + 4 c_4 + 2 c_5 + 9 c_6 Fe: | c_2 = c_6 S: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_3 + FeSO_4 ⟶ H_2O + H_2SO_4 + NO_2 + Fe(NO_3)_3

+ ⟶ + + +

Names

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nitric acid + duretter ⟶ water + sulfuric acid + nitrogen dioxide + ferric nitrate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: HNO_3 + FeSO_4 ⟶ H_2O + H_2SO_4 + NO_2 + Fe(NO_3)_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: 4 HNO_3 + FeSO_4 ⟶ H_2O + H_2SO_4 + NO_2 + Fe(NO_3)_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 HNO_3 | 4 | -4 FeSO_4 | 1 | -1 H_2O | 1 | 1 H_2SO_4 | 1 | 1 NO_2 | 1 | 1 Fe(NO_3)_3 | 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 | 4 | -4 | ([HNO3])^(-4) FeSO_4 | 1 | -1 | ([FeSO4])^(-1) H_2O | 1 | 1 | [H2O] H_2SO_4 | 1 | 1 | [H2SO4] NO_2 | 1 | 1 | [NO2] Fe(NO_3)_3 | 1 | 1 | [Fe(NO3)3] 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])^(-4) ([FeSO4])^(-1) [H2O] [H2SO4] [NO2] [Fe(NO3)3] = ([H2O] [H2SO4] [NO2] [Fe(NO3)3])/(([HNO3])^4 [FeSO4])

Rate of reaction

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Construct the rate of reaction expression for: HNO_3 + FeSO_4 ⟶ H_2O + H_2SO_4 + NO_2 + Fe(NO_3)_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: 4 HNO_3 + FeSO_4 ⟶ H_2O + H_2SO_4 + NO_2 + Fe(NO_3)_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 HNO_3 | 4 | -4 FeSO_4 | 1 | -1 H_2O | 1 | 1 H_2SO_4 | 1 | 1 NO_2 | 1 | 1 Fe(NO_3)_3 | 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 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) FeSO_4 | 1 | -1 | -(Δ[FeSO4])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) NO_2 | 1 | 1 | (Δ[NO2])/(Δt) Fe(NO_3)_3 | 1 | 1 | (Δ[Fe(NO3)3])/(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 = -1/4 (Δ[HNO3])/(Δt) = -(Δ[FeSO4])/(Δt) = (Δ[H2O])/(Δt) = (Δ[H2SO4])/(Δt) = (Δ[NO2])/(Δt) = (Δ[Fe(NO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)