C + Fe2O3 = Fe + C2O3

C activated charcoal + Fe_2O_3 iron(III) oxide ⟶ Fe iron + C2O3

Balance the chemical equation algebraically: C + Fe_2O_3 ⟶ Fe + C2O3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Fe_2O_3 ⟶ c_3 Fe + c_4 C2O3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Fe and O: C: | c_1 = 2 c_4 Fe: | 2 c_2 = c_3 O: | 3 c_2 = 3 c_4 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 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 C + Fe_2O_3 ⟶ 2 Fe + C2O3

+ ⟶ + C2O3

activated charcoal + iron(III) oxide ⟶ iron + C2O3

Construct the equilibrium constant, K, expression for: C + Fe_2O_3 ⟶ Fe + C2O3 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: 2 C + Fe_2O_3 ⟶ 2 Fe + C2O3 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 C | 2 | -2 Fe_2O_3 | 1 | -1 Fe | 2 | 2 C2O3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 2 | -2 | ([C])^(-2) Fe_2O_3 | 1 | -1 | ([Fe2O3])^(-1) Fe | 2 | 2 | ([Fe])^2 C2O3 | 1 | 1 | [C2O3] 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 = ([C])^(-2) ([Fe2O3])^(-1) ([Fe])^2 [C2O3] = (([Fe])^2 [C2O3])/(([C])^2 [Fe2O3])

Construct the rate of reaction expression for: C + Fe_2O_3 ⟶ Fe + C2O3 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: 2 C + Fe_2O_3 ⟶ 2 Fe + C2O3 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 C | 2 | -2 Fe_2O_3 | 1 | -1 Fe | 2 | 2 C2O3 | 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 C | 2 | -2 | -1/2 (Δ[C])/(Δt) Fe_2O_3 | 1 | -1 | -(Δ[Fe2O3])/(Δt) Fe | 2 | 2 | 1/2 (Δ[Fe])/(Δt) C2O3 | 1 | 1 | (Δ[C2O3])/(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 = -1/2 (Δ[C])/(Δt) = -(Δ[Fe2O3])/(Δt) = 1/2 (Δ[Fe])/(Δt) = (Δ[C2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | iron(III) oxide | iron | C2O3 formula | C | Fe_2O_3 | Fe | C2O3 name | activated charcoal | iron(III) oxide | iron | IUPAC name | carbon | | iron |

| activated charcoal | iron(III) oxide | iron | C2O3 molar mass | 12.011 g/mol | 159.69 g/mol | 55.845 g/mol | 72.019 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 3550 °C | 1565 °C | 1535 °C | boiling point | 4027 °C | | 2750 °C | density | 2.26 g/cm^3 | 5.26 g/cm^3 | 7.874 g/cm^3 | solubility in water | insoluble | insoluble | insoluble | odor | | odorless | |