H2SO4 + Fe3O4 = H2O + SO2 + Fe2(SO4)3

H_2SO_4 sulfuric acid + FeO·Fe_2O_3 iron(II, III) oxide ⟶ H_2O water + SO_2 sulfur dioxide + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: H_2SO_4 + FeO·Fe_2O_3 ⟶ H_2O + SO_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 FeO·Fe_2O_3 ⟶ c_3 H_2O + c_4 SO_2 + c_5 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 and Fe: H: | 2 c_1 = 2 c_3 O: | 4 c_1 + 4 c_2 = c_3 + 2 c_4 + 12 c_5 S: | c_1 = c_4 + 3 c_5 Fe: | 3 c_2 = 2 c_5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 2 c_3 = 10 c_4 = 1 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 H_2SO_4 + 2 FeO·Fe_2O_3 ⟶ 10 H_2O + SO_2 + 3 Fe_2(SO_4)_3·xH_2O

+ ⟶ + +

sulfuric acid + iron(II, III) oxide ⟶ water + sulfur dioxide + iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: H_2SO_4 + FeO·Fe_2O_3 ⟶ H_2O + SO_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: 10 H_2SO_4 + 2 FeO·Fe_2O_3 ⟶ 10 H_2O + SO_2 + 3 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 | 10 | -10 FeO·Fe_2O_3 | 2 | -2 H_2O | 10 | 10 SO_2 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 10 | -10 | ([H2SO4])^(-10) FeO·Fe_2O_3 | 2 | -2 | ([FeO·Fe2O3])^(-2) H_2O | 10 | 10 | ([H2O])^10 SO_2 | 1 | 1 | [SO2] Fe_2(SO_4)_3·xH_2O | 3 | 3 | ([Fe2(SO4)3·xH2O])^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 = ([H2SO4])^(-10) ([FeO·Fe2O3])^(-2) ([H2O])^10 [SO2] ([Fe2(SO4)3·xH2O])^3 = (([H2O])^10 [SO2] ([Fe2(SO4)3·xH2O])^3)/(([H2SO4])^10 ([FeO·Fe2O3])^2)

Construct the rate of reaction expression for: H_2SO_4 + FeO·Fe_2O_3 ⟶ H_2O + SO_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: 10 H_2SO_4 + 2 FeO·Fe_2O_3 ⟶ 10 H_2O + SO_2 + 3 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 | 10 | -10 FeO·Fe_2O_3 | 2 | -2 H_2O | 10 | 10 SO_2 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 3 | 3 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 | 10 | -10 | -1/10 (Δ[H2SO4])/(Δt) FeO·Fe_2O_3 | 2 | -2 | -1/2 (Δ[FeO·Fe2O3])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) Fe_2(SO_4)_3·xH_2O | 3 | 3 | 1/3 (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 = -1/10 (Δ[H2SO4])/(Δt) = -1/2 (Δ[FeO·Fe2O3])/(Δt) = 1/10 (Δ[H2O])/(Δt) = (Δ[SO2])/(Δt) = 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | iron(II, III) oxide | water | sulfur dioxide | iron(III) sulfate hydrate formula | H_2SO_4 | FeO·Fe_2O_3 | H_2O | SO_2 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | Fe_3O_4 | H_2O | O_2S | Fe_2O_12S_3 name | sulfuric acid | iron(II, III) oxide | water | sulfur dioxide | iron(III) sulfate hydrate IUPAC name | sulfuric acid | | water | sulfur dioxide | diferric trisulfate