Mg + Fe3O4 = Fe + MgO

Mg magnesium + FeO·Fe_2O_3 iron(II, III) oxide ⟶ Fe iron + MgO magnesium oxide

Balance the chemical equation algebraically: Mg + FeO·Fe_2O_3 ⟶ Fe + MgO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 FeO·Fe_2O_3 ⟶ c_3 Fe + c_4 MgO Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Fe and O: Mg: | c_1 = c_4 Fe: | 3 c_2 = c_3 O: | 4 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 = 3 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Mg + FeO·Fe_2O_3 ⟶ 3 Fe + 4 MgO

+ ⟶ +

magnesium + iron(II, III) oxide ⟶ iron + magnesium oxide

| magnesium | iron(II, III) oxide | iron | magnesium oxide molecular enthalpy | 0 kJ/mol | -1118 kJ/mol | 0 kJ/mol | -601.6 kJ/mol total enthalpy | 0 kJ/mol | -1118 kJ/mol | 0 kJ/mol | -2406 kJ/mol | H_initial = -1118 kJ/mol | | H_final = -2406 kJ/mol | ΔH_rxn^0 | -2406 kJ/mol - -1118 kJ/mol = -1288 kJ/mol (exothermic) | | |

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

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

| magnesium | iron(II, III) oxide | iron | magnesium oxide formula | Mg | FeO·Fe_2O_3 | Fe | MgO Hill formula | Mg | Fe_3O_4 | Fe | MgO name | magnesium | iron(II, III) oxide | iron | magnesium oxide IUPAC name | magnesium | | iron | oxomagnesium

| magnesium | iron(II, III) oxide | iron | magnesium oxide molar mass | 24.305 g/mol | 231.53 g/mol | 55.845 g/mol | 40.304 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 648 °C | 1538 °C | 1535 °C | 2852 °C boiling point | 1090 °C | | 2750 °C | 3600 °C density | 1.738 g/cm^3 | 5 g/cm^3 | 7.874 g/cm^3 | 3.58 g/cm^3 solubility in water | reacts | | insoluble | odor | | | | odorless