Mg + Fe2O = Fe + MgO

Mg magnesium + Fe2O ⟶ Fe iron + MgO magnesium oxide

Balance the chemical equation algebraically: Mg + Fe2O ⟶ Fe + MgO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 Fe2O ⟶ 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: | 2 c_2 = c_3 O: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Mg + Fe2O ⟶ 2 Fe + MgO

+ Fe2O ⟶ +

magnesium + Fe2O ⟶ iron + magnesium oxide

Construct the equilibrium constant, K, expression for: Mg + Fe2O ⟶ 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: Mg + Fe2O ⟶ 2 Fe + 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 | 1 | -1 Fe2O | 1 | -1 Fe | 2 | 2 MgO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 1 | -1 | ([Mg])^(-1) Fe2O | 1 | -1 | ([Fe2O])^(-1) Fe | 2 | 2 | ([Fe])^2 MgO | 1 | 1 | [MgO] 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])^(-1) ([Fe2O])^(-1) ([Fe])^2 [MgO] = (([Fe])^2 [MgO])/([Mg] [Fe2O])

Construct the rate of reaction expression for: Mg + Fe2O ⟶ 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: Mg + Fe2O ⟶ 2 Fe + 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 | 1 | -1 Fe2O | 1 | -1 Fe | 2 | 2 MgO | 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 Mg | 1 | -1 | -(Δ[Mg])/(Δt) Fe2O | 1 | -1 | -(Δ[Fe2O])/(Δt) Fe | 2 | 2 | 1/2 (Δ[Fe])/(Δt) MgO | 1 | 1 | (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 = -(Δ[Mg])/(Δt) = -(Δ[Fe2O])/(Δt) = 1/2 (Δ[Fe])/(Δt) = (Δ[MgO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | Fe2O | iron | magnesium oxide formula | Mg | Fe2O | Fe | MgO name | magnesium | | iron | magnesium oxide IUPAC name | magnesium | | iron | oxomagnesium

| magnesium | Fe2O | iron | magnesium oxide molar mass | 24.305 g/mol | 127.69 g/mol | 55.845 g/mol | 40.304 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 648 °C | | 1535 °C | 2852 °C boiling point | 1090 °C | | 2750 °C | 3600 °C density | 1.738 g/cm^3 | | 7.874 g/cm^3 | 3.58 g/cm^3 solubility in water | reacts | | insoluble | odor | | | | odorless