Mg + Al2O3 = Al + MgO

Mg magnesium + Al_2O_3 aluminum oxide ⟶ Al aluminum + MgO magnesium oxide

Balance the chemical equation algebraically: Mg + Al_2O_3 ⟶ Al + MgO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 Al_2O_3 ⟶ c_3 Al + c_4 MgO Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Al and O: Mg: | c_1 = c_4 Al: | 2 c_2 = c_3 O: | 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 = 3 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Mg + Al_2O_3 ⟶ 2 Al + 3 MgO

+ ⟶ +

magnesium + aluminum oxide ⟶ aluminum + magnesium oxide

| magnesium | aluminum oxide | aluminum | magnesium oxide molecular enthalpy | 0 kJ/mol | -1676 kJ/mol | 0 kJ/mol | -601.6 kJ/mol total enthalpy | 0 kJ/mol | -1676 kJ/mol | 0 kJ/mol | -1805 kJ/mol | H_initial = -1676 kJ/mol | | H_final = -1805 kJ/mol | ΔH_rxn^0 | -1805 kJ/mol - -1676 kJ/mol = -128.8 kJ/mol (exothermic) | | |

| magnesium | aluminum oxide | aluminum | magnesium oxide molecular entropy | 33 J/(mol K) | 51 J/(mol K) | 28.3 J/(mol K) | 27 J/(mol K) total entropy | 99 J/(mol K) | 51 J/(mol K) | 56.6 J/(mol K) | 81 J/(mol K) | S_initial = 150 J/(mol K) | | S_final = 137.6 J/(mol K) | ΔS_rxn^0 | 137.6 J/(mol K) - 150 J/(mol K) = -12.4 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: Mg + Al_2O_3 ⟶ Al + 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: 3 Mg + Al_2O_3 ⟶ 2 Al + 3 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 | 3 | -3 Al_2O_3 | 1 | -1 Al | 2 | 2 MgO | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 3 | -3 | ([Mg])^(-3) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) Al | 2 | 2 | ([Al])^2 MgO | 3 | 3 | ([MgO])^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 = ([Mg])^(-3) ([Al2O3])^(-1) ([Al])^2 ([MgO])^3 = (([Al])^2 ([MgO])^3)/(([Mg])^3 [Al2O3])

Construct the rate of reaction expression for: Mg + Al_2O_3 ⟶ Al + 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: 3 Mg + Al_2O_3 ⟶ 2 Al + 3 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 | 3 | -3 Al_2O_3 | 1 | -1 Al | 2 | 2 MgO | 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 Mg | 3 | -3 | -1/3 (Δ[Mg])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) Al | 2 | 2 | 1/2 (Δ[Al])/(Δt) MgO | 3 | 3 | 1/3 (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 = -1/3 (Δ[Mg])/(Δt) = -(Δ[Al2O3])/(Δt) = 1/2 (Δ[Al])/(Δt) = 1/3 (Δ[MgO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | aluminum oxide | aluminum | magnesium oxide formula | Mg | Al_2O_3 | Al | MgO name | magnesium | aluminum oxide | aluminum | magnesium oxide IUPAC name | magnesium | dialuminum;oxygen(2-) | aluminum | oxomagnesium

| magnesium | aluminum oxide | aluminum | magnesium oxide molar mass | 24.305 g/mol | 101.96 g/mol | 26.9815385 g/mol | 40.304 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 648 °C | 2040 °C | 660.4 °C | 2852 °C boiling point | 1090 °C | | 2460 °C | 3600 °C density | 1.738 g/cm^3 | | 2.7 g/cm^3 | 3.58 g/cm^3 solubility in water | reacts | | insoluble | surface tension | | | 0.817 N/m | dynamic viscosity | | | 1.5×10^-4 Pa s (at 760 °C) | odor | | odorless | odorless | odorless