H2SO4 + HNO3 + FeSO4 = H2O + NO2 + Fe2(SO4)3

H_2SO_4 sulfuric acid + HNO_3 nitric acid + FeSO_4 duretter ⟶ H_2O water + NO_2 nitrogen dioxide + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: H_2SO_4 + HNO_3 + FeSO_4 ⟶ H_2O + NO_2 + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 HNO_3 + c_3 FeSO_4 ⟶ c_4 H_2O + c_5 NO_2 + c_6 Fe_2(SO_4)_3·xH_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, N and Fe: H: | 2 c_1 + c_2 = 2 c_4 O: | 4 c_1 + 3 c_2 + 4 c_3 = c_4 + 2 c_5 + 12 c_6 S: | c_1 + c_3 = 3 c_6 N: | c_2 = c_5 Fe: | c_3 = 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + 2 HNO_3 + 2 FeSO_4 ⟶ 2 H_2O + 2 NO_2 + Fe_2(SO_4)_3·xH_2O

+ + ⟶ + +

sulfuric acid + nitric acid + duretter ⟶ water + nitrogen dioxide + iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: H_2SO_4 + HNO_3 + FeSO_4 ⟶ H_2O + NO_2 + Fe_2(SO_4)_3·xH_2O 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: H_2SO_4 + 2 HNO_3 + 2 FeSO_4 ⟶ 2 H_2O + 2 NO_2 + Fe_2(SO_4)_3·xH_2O 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 | 1 | -1 HNO_3 | 2 | -2 FeSO_4 | 2 | -2 H_2O | 2 | 2 NO_2 | 2 | 2 Fe_2(SO_4)_3·xH_2O | 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 | 1 | -1 | ([H2SO4])^(-1) HNO_3 | 2 | -2 | ([HNO3])^(-2) FeSO_4 | 2 | -2 | ([FeSO4])^(-2) H_2O | 2 | 2 | ([H2O])^2 NO_2 | 2 | 2 | ([NO2])^2 Fe_2(SO_4)_3·xH_2O | 1 | 1 | [Fe2(SO4)3·xH2O] 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])^(-1) ([HNO3])^(-2) ([FeSO4])^(-2) ([H2O])^2 ([NO2])^2 [Fe2(SO4)3·xH2O] = (([H2O])^2 ([NO2])^2 [Fe2(SO4)3·xH2O])/([H2SO4] ([HNO3])^2 ([FeSO4])^2)

Construct the rate of reaction expression for: H_2SO_4 + HNO_3 + FeSO_4 ⟶ H_2O + NO_2 + Fe_2(SO_4)_3·xH_2O 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: H_2SO_4 + 2 HNO_3 + 2 FeSO_4 ⟶ 2 H_2O + 2 NO_2 + Fe_2(SO_4)_3·xH_2O 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 | 1 | -1 HNO_3 | 2 | -2 FeSO_4 | 2 | -2 H_2O | 2 | 2 NO_2 | 2 | 2 Fe_2(SO_4)_3·xH_2O | 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 | 1 | -1 | -(Δ[H2SO4])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) FeSO_4 | 2 | -2 | -1/2 (Δ[FeSO4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | 1 | (Δ[Fe2(SO4)3·xH2O])/(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 = -(Δ[H2SO4])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = -1/2 (Δ[FeSO4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[NO2])/(Δt) = (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | nitric acid | duretter | water | nitrogen dioxide | iron(III) sulfate hydrate formula | H_2SO_4 | HNO_3 | FeSO_4 | H_2O | NO_2 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | HNO_3 | FeO_4S | H_2O | NO_2 | Fe_2O_12S_3 name | sulfuric acid | nitric acid | duretter | water | nitrogen dioxide | iron(III) sulfate hydrate IUPAC name | sulfuric acid | nitric acid | iron(+2) cation sulfate | water | Nitrogen dioxide | diferric trisulfate