CO + Fe3O4 = CO2 + Fe

CO (carbon monoxide) + FeO·Fe_2O_3 (iron(II, III) oxide) ⟶ CO_2 (carbon dioxide) + Fe (iron)

Balance the chemical equation algebraically: CO + FeO·Fe_2O_3 ⟶ CO_2 + Fe Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO + c_2 FeO·Fe_2O_3 ⟶ c_3 CO_2 + c_4 Fe 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 = c_3 O: | c_1 + 4 c_2 = 2 c_3 Fe: | 3 c_2 = 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 = 4 c_2 = 1 c_3 = 4 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 CO + FeO·Fe_2O_3 ⟶ 4 CO_2 + 3 Fe

+ ⟶ +

carbon monoxide + iron(II, III) oxide ⟶ carbon dioxide + iron

| carbon monoxide | iron(II, III) oxide | carbon dioxide | iron molecular enthalpy | -110.5 kJ/mol | -1118 kJ/mol | -393.5 kJ/mol | 0 kJ/mol total enthalpy | -442 kJ/mol | -1118 kJ/mol | -1574 kJ/mol | 0 kJ/mol | H_initial = -1560 kJ/mol | | H_final = -1574 kJ/mol | ΔH_rxn^0 | -1574 kJ/mol - -1560 kJ/mol = -13.6 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: CO + FeO·Fe_2O_3 ⟶ CO_2 + Fe 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: 4 CO + FeO·Fe_2O_3 ⟶ 4 CO_2 + 3 Fe 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 | 4 | -4 FeO·Fe_2O_3 | 1 | -1 CO_2 | 4 | 4 Fe | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO | 4 | -4 | ([CO])^(-4) FeO·Fe_2O_3 | 1 | -1 | ([FeO·Fe2O3])^(-1) CO_2 | 4 | 4 | ([CO2])^4 Fe | 3 | 3 | ([Fe])^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 = ([CO])^(-4) ([FeO·Fe2O3])^(-1) ([CO2])^4 ([Fe])^3 = (([CO2])^4 ([Fe])^3)/(([CO])^4 [FeO·Fe2O3])

Construct the rate of reaction expression for: CO + FeO·Fe_2O_3 ⟶ CO_2 + Fe 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: 4 CO + FeO·Fe_2O_3 ⟶ 4 CO_2 + 3 Fe 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 | 4 | -4 FeO·Fe_2O_3 | 1 | -1 CO_2 | 4 | 4 Fe | 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 CO | 4 | -4 | -1/4 (Δ[CO])/(Δt) FeO·Fe_2O_3 | 1 | -1 | -(Δ[FeO·Fe2O3])/(Δt) CO_2 | 4 | 4 | 1/4 (Δ[CO2])/(Δt) Fe | 3 | 3 | 1/3 (Δ[Fe])/(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 = -1/4 (Δ[CO])/(Δt) = -(Δ[FeO·Fe2O3])/(Δt) = 1/4 (Δ[CO2])/(Δt) = 1/3 (Δ[Fe])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon monoxide | iron(II, III) oxide | carbon dioxide | iron formula | CO | FeO·Fe_2O_3 | CO_2 | Fe Hill formula | CO | Fe_3O_4 | CO_2 | Fe name | carbon monoxide | iron(II, III) oxide | carbon dioxide | iron

| carbon monoxide | iron(II, III) oxide | carbon dioxide | iron molar mass | 28.01 g/mol | 231.53 g/mol | 44.009 g/mol | 55.845 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -205 °C | 1538 °C | -56.56 °C (at triple point) | 1535 °C boiling point | -191.5 °C | | -78.5 °C (at sublimation point) | 2750 °C density | 0.001145 g/cm^3 (at 25 °C) | 5 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 7.874 g/cm^3 solubility in water | | | | insoluble dynamic viscosity | 1.772×10^-5 Pa s (at 25 °C) | | 1.491×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless |