O2 + K2CO3 + FeCr2O4 = CO2 + Fe2O3 + K2CrO4

O_2 oxygen + K_2CO_3 pearl ash + FeCr_2O_4 iron(II) chromite ⟶ CO_2 carbon dioxide + Fe_2O_3 iron(III) oxide + K_2CrO_4 potassium chromate

Balance the chemical equation algebraically: O_2 + K_2CO_3 + FeCr_2O_4 ⟶ CO_2 + Fe_2O_3 + K_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 K_2CO_3 + c_3 FeCr_2O_4 ⟶ c_4 CO_2 + c_5 Fe_2O_3 + c_6 K_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, C, K, Cr and Fe: O: | 2 c_1 + 3 c_2 + 3 c_3 = 2 c_4 + 3 c_5 + 4 c_6 C: | c_2 = c_4 K: | 2 c_2 = 2 c_6 Cr: | c_3 = c_6 Fe: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 4 c_3 = 4 c_4 = 4 c_5 = 2 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 4 K_2CO_3 + 4 FeCr_2O_4 ⟶ 4 CO_2 + 2 Fe_2O_3 + 4 K_2CrO_4

+ + ⟶ + +

oxygen + pearl ash + iron(II) chromite ⟶ carbon dioxide + iron(III) oxide + potassium chromate

Construct the equilibrium constant, K, expression for: O_2 + K_2CO_3 + FeCr_2O_4 ⟶ CO_2 + Fe_2O_3 + K_2CrO_4 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: 3 O_2 + 4 K_2CO_3 + 4 FeCr_2O_4 ⟶ 4 CO_2 + 2 Fe_2O_3 + 4 K_2CrO_4 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 O_2 | 3 | -3 K_2CO_3 | 4 | -4 FeCr_2O_4 | 4 | -4 CO_2 | 4 | 4 Fe_2O_3 | 2 | 2 K_2CrO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 3 | -3 | ([O2])^(-3) K_2CO_3 | 4 | -4 | ([K2CO3])^(-4) FeCr_2O_4 | 4 | -4 | ([FeCr2O4])^(-4) CO_2 | 4 | 4 | ([CO2])^4 Fe_2O_3 | 2 | 2 | ([Fe2O3])^2 K_2CrO_4 | 4 | 4 | ([K2CrO4])^4 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 = ([O2])^(-3) ([K2CO3])^(-4) ([FeCr2O4])^(-4) ([CO2])^4 ([Fe2O3])^2 ([K2CrO4])^4 = (([CO2])^4 ([Fe2O3])^2 ([K2CrO4])^4)/(([O2])^3 ([K2CO3])^4 ([FeCr2O4])^4)

Construct the rate of reaction expression for: O_2 + K_2CO_3 + FeCr_2O_4 ⟶ CO_2 + Fe_2O_3 + K_2CrO_4 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: 3 O_2 + 4 K_2CO_3 + 4 FeCr_2O_4 ⟶ 4 CO_2 + 2 Fe_2O_3 + 4 K_2CrO_4 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 O_2 | 3 | -3 K_2CO_3 | 4 | -4 FeCr_2O_4 | 4 | -4 CO_2 | 4 | 4 Fe_2O_3 | 2 | 2 K_2CrO_4 | 4 | 4 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 O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) K_2CO_3 | 4 | -4 | -1/4 (Δ[K2CO3])/(Δt) FeCr_2O_4 | 4 | -4 | -1/4 (Δ[FeCr2O4])/(Δt) CO_2 | 4 | 4 | 1/4 (Δ[CO2])/(Δt) Fe_2O_3 | 2 | 2 | 1/2 (Δ[Fe2O3])/(Δt) K_2CrO_4 | 4 | 4 | 1/4 (Δ[K2CrO4])/(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 = -1/3 (Δ[O2])/(Δt) = -1/4 (Δ[K2CO3])/(Δt) = -1/4 (Δ[FeCr2O4])/(Δt) = 1/4 (Δ[CO2])/(Δt) = 1/2 (Δ[Fe2O3])/(Δt) = 1/4 (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | pearl ash | iron(II) chromite | carbon dioxide | iron(III) oxide | potassium chromate formula | O_2 | K_2CO_3 | FeCr_2O_4 | CO_2 | Fe_2O_3 | K_2CrO_4 Hill formula | O_2 | CK_2O_3 | Cr_2FeO_4 | CO_2 | Fe_2O_3 | CrK_2O_4 name | oxygen | pearl ash | iron(II) chromite | carbon dioxide | iron(III) oxide | potassium chromate IUPAC name | molecular oxygen | dipotassium carbonate | | carbon dioxide | | dipotassium dioxido-dioxochromium