H2O + Fe2(SO4)3 = H2SO4 + Fe(OH)3

H_2O water + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate ⟶ H_2SO_4 sulfuric acid + Fe(OH)_3 iron(III) hydroxide

Balance the chemical equation algebraically: H_2O + Fe_2(SO_4)_3·xH_2O ⟶ H_2SO_4 + Fe(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Fe_2(SO_4)_3·xH_2O ⟶ c_3 H_2SO_4 + c_4 Fe(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Fe and S: H: | 2 c_1 = 2 c_3 + 3 c_4 O: | c_1 + 12 c_2 = 4 c_3 + 3 c_4 Fe: | 2 c_2 = c_4 S: | 3 c_2 = c_3 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 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + Fe_2(SO_4)_3·xH_2O ⟶ 3 H_2SO_4 + 2 Fe(OH)_3

+ ⟶ +

water + iron(III) sulfate hydrate ⟶ sulfuric acid + iron(III) hydroxide

Construct the equilibrium constant, K, expression for: H_2O + Fe_2(SO_4)_3·xH_2O ⟶ H_2SO_4 + Fe(OH)_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: 6 H_2O + Fe_2(SO_4)_3·xH_2O ⟶ 3 H_2SO_4 + 2 Fe(OH)_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 H_2O | 6 | -6 Fe_2(SO_4)_3·xH_2O | 1 | -1 H_2SO_4 | 3 | 3 Fe(OH)_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) Fe_2(SO_4)_3·xH_2O | 1 | -1 | ([Fe2(SO4)3·xH2O])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 Fe(OH)_3 | 2 | 2 | ([Fe(OH)3])^2 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 = ([H2O])^(-6) ([Fe2(SO4)3·xH2O])^(-1) ([H2SO4])^3 ([Fe(OH)3])^2 = (([H2SO4])^3 ([Fe(OH)3])^2)/(([H2O])^6 [Fe2(SO4)3·xH2O])

Construct the rate of reaction expression for: H_2O + Fe_2(SO_4)_3·xH_2O ⟶ H_2SO_4 + Fe(OH)_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: 6 H_2O + Fe_2(SO_4)_3·xH_2O ⟶ 3 H_2SO_4 + 2 Fe(OH)_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 H_2O | 6 | -6 Fe_2(SO_4)_3·xH_2O | 1 | -1 H_2SO_4 | 3 | 3 Fe(OH)_3 | 2 | 2 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_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | -1 | -(Δ[Fe2(SO4)3·xH2O])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) Fe(OH)_3 | 2 | 2 | 1/2 (Δ[Fe(OH)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 = -1/6 (Δ[H2O])/(Δt) = -(Δ[Fe2(SO4)3·xH2O])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/2 (Δ[Fe(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | iron(III) sulfate hydrate | sulfuric acid | iron(III) hydroxide formula | H_2O | Fe_2(SO_4)_3·xH_2O | H_2SO_4 | Fe(OH)_3 Hill formula | H_2O | Fe_2O_12S_3 | H_2O_4S | FeH_3O_3 name | water | iron(III) sulfate hydrate | sulfuric acid | iron(III) hydroxide IUPAC name | water | diferric trisulfate | sulfuric acid | ferric trihydroxide