CO2 + Fe2O3 = Fe2(CO3)3

CO_2 carbon dioxide + Fe_2O_3 iron(III) oxide ⟶ Fe2(CO3)3

Balance the chemical equation algebraically: CO_2 + Fe_2O_3 ⟶ Fe2(CO3)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 + c_2 Fe_2O_3 ⟶ c_3 Fe2(CO3)3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, O and Fe: C: | c_1 = 3 c_3 O: | 2 c_1 + 3 c_2 = 9 c_3 Fe: | 2 c_2 = 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 = 3 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CO_2 + Fe_2O_3 ⟶ Fe2(CO3)3

+ ⟶ Fe2(CO3)3

carbon dioxide + iron(III) oxide ⟶ Fe2(CO3)3

Construct the equilibrium constant, K, expression for: CO_2 + Fe_2O_3 ⟶ Fe2(CO3)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: 3 CO_2 + Fe_2O_3 ⟶ Fe2(CO3)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 CO_2 | 3 | -3 Fe_2O_3 | 1 | -1 Fe2(CO3)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO_2 | 3 | -3 | ([CO2])^(-3) Fe_2O_3 | 1 | -1 | ([Fe2O3])^(-1) Fe2(CO3)3 | 1 | 1 | [Fe2(CO3)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 = ([CO2])^(-3) ([Fe2O3])^(-1) [Fe2(CO3)3] = ([Fe2(CO3)3])/(([CO2])^3 [Fe2O3])

Construct the rate of reaction expression for: CO_2 + Fe_2O_3 ⟶ Fe2(CO3)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: 3 CO_2 + Fe_2O_3 ⟶ Fe2(CO3)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 CO_2 | 3 | -3 Fe_2O_3 | 1 | -1 Fe2(CO3)3 | 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 CO_2 | 3 | -3 | -1/3 (Δ[CO2])/(Δt) Fe_2O_3 | 1 | -1 | -(Δ[Fe2O3])/(Δt) Fe2(CO3)3 | 1 | 1 | (Δ[Fe2(CO3)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 = -1/3 (Δ[CO2])/(Δt) = -(Δ[Fe2O3])/(Δt) = (Δ[Fe2(CO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon dioxide | iron(III) oxide | Fe2(CO3)3 formula | CO_2 | Fe_2O_3 | Fe2(CO3)3 Hill formula | CO_2 | Fe_2O_3 | C3Fe2O9 name | carbon dioxide | iron(III) oxide |

| carbon dioxide | iron(III) oxide | Fe2(CO3)3 molar mass | 44.009 g/mol | 159.69 g/mol | 291.71 g/mol phase | gas (at STP) | solid (at STP) | melting point | -56.56 °C (at triple point) | 1565 °C | boiling point | -78.5 °C (at sublimation point) | | density | 0.00184212 g/cm^3 (at 20 °C) | 5.26 g/cm^3 | solubility in water | | insoluble | dynamic viscosity | 1.491×10^-5 Pa s (at 25 °C) | | odor | odorless | odorless |