H2SO4 + FeSO4 + K2CrO4 = H2O + K2SO4 + Cr2(SO4)3 + Fe2(SO4)3

H_2SO_4 sulfuric acid + FeSO_4 duretter + K_2CrO_4 potassium chromate ⟶ H_2O water + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balance the chemical equation algebraically: H_2SO_4 + FeSO_4 + K_2CrO_4 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 FeSO_4 + c_3 K_2CrO_4 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Cr_2(SO_4)_3 + c_7 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, Fe, Cr and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 4 c_3 = c_4 + 4 c_5 + 12 c_6 + 12 c_7 S: | c_1 + c_2 = c_5 + 3 c_6 + 3 c_7 Fe: | c_2 = 2 c_7 Cr: | c_3 = 2 c_6 K: | 2 c_3 = 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 6 c_3 = 2 c_4 = 8 c_5 = 2 c_6 = 1 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2SO_4 + 6 FeSO_4 + 2 K_2CrO_4 ⟶ 8 H_2O + 2 K_2SO_4 + Cr_2(SO_4)_3 + 3 Fe_2(SO_4)_3·xH_2O

+ + ⟶ + + +

sulfuric acid + duretter + potassium chromate ⟶ water + potassium sulfate + chromium sulfate + iron(III) sulfate hydrate

Construct the equilibrium constant, K, expression for: H_2SO_4 + FeSO_4 + K_2CrO_4 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + 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: 8 H_2SO_4 + 6 FeSO_4 + 2 K_2CrO_4 ⟶ 8 H_2O + 2 K_2SO_4 + Cr_2(SO_4)_3 + 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 | 8 | -8 FeSO_4 | 6 | -6 K_2CrO_4 | 2 | -2 H_2O | 8 | 8 K_2SO_4 | 2 | 2 Cr_2(SO_4)_3 | 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 | 8 | -8 | ([H2SO4])^(-8) FeSO_4 | 6 | -6 | ([FeSO4])^(-6) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) H_2O | 8 | 8 | ([H2O])^8 K_2SO_4 | 2 | 2 | ([K2SO4])^2 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] 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])^(-8) ([FeSO4])^(-6) ([K2CrO4])^(-2) ([H2O])^8 ([K2SO4])^2 [Cr2(SO4)3] ([Fe2(SO4)3·xH2O])^3 = (([H2O])^8 ([K2SO4])^2 [Cr2(SO4)3] ([Fe2(SO4)3·xH2O])^3)/(([H2SO4])^8 ([FeSO4])^6 ([K2CrO4])^2)

Construct the rate of reaction expression for: H_2SO_4 + FeSO_4 + K_2CrO_4 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + 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: 8 H_2SO_4 + 6 FeSO_4 + 2 K_2CrO_4 ⟶ 8 H_2O + 2 K_2SO_4 + Cr_2(SO_4)_3 + 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 | 8 | -8 FeSO_4 | 6 | -6 K_2CrO_4 | 2 | -2 H_2O | 8 | 8 K_2SO_4 | 2 | 2 Cr_2(SO_4)_3 | 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 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) FeSO_4 | 6 | -6 | -1/6 (Δ[FeSO4])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(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 = -1/8 (Δ[H2SO4])/(Δt) = -1/6 (Δ[FeSO4])/(Δt) = -1/2 (Δ[K2CrO4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | duretter | potassium chromate | water | potassium sulfate | chromium sulfate | iron(III) sulfate hydrate formula | H_2SO_4 | FeSO_4 | K_2CrO_4 | H_2O | K_2SO_4 | Cr_2(SO_4)_3 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | FeO_4S | CrK_2O_4 | H_2O | K_2O_4S | Cr_2O_12S_3 | Fe_2O_12S_3 name | sulfuric acid | duretter | potassium chromate | water | potassium sulfate | chromium sulfate | iron(III) sulfate hydrate IUPAC name | sulfuric acid | iron(+2) cation sulfate | dipotassium dioxido-dioxochromium | water | dipotassium sulfate | chromium(+3) cation trisulfate | diferric trisulfate