Al2O3 = Al + AlO2

Al_2O_3 aluminum oxide ⟶ Al aluminum + AlO2

Balance the chemical equation algebraically: Al_2O_3 ⟶ Al + AlO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al_2O_3 ⟶ c_2 Al + c_3 AlO2 Set the number of atoms in the reactants equal to the number of atoms in the products for Al and O: Al: | 2 c_1 = c_2 + c_3 O: | 3 c_1 = 2 c_3 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 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al_2O_3 ⟶ Al + 3 AlO2

⟶ + AlO2

aluminum oxide ⟶ aluminum + AlO2

Construct the equilibrium constant, K, expression for: Al_2O_3 ⟶ Al + AlO2 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 Al_2O_3 ⟶ Al + 3 AlO2 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 Al_2O_3 | 2 | -2 Al | 1 | 1 AlO2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al_2O_3 | 2 | -2 | ([Al2O3])^(-2) Al | 1 | 1 | [Al] AlO2 | 3 | 3 | ([AlO2])^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 = ([Al2O3])^(-2) [Al] ([AlO2])^3 = ([Al] ([AlO2])^3)/([Al2O3])^2

Construct the rate of reaction expression for: Al_2O_3 ⟶ Al + AlO2 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 Al_2O_3 ⟶ Al + 3 AlO2 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 Al_2O_3 | 2 | -2 Al | 1 | 1 AlO2 | 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 Al_2O_3 | 2 | -2 | -1/2 (Δ[Al2O3])/(Δt) Al | 1 | 1 | (Δ[Al])/(Δt) AlO2 | 3 | 3 | 1/3 (Δ[AlO2])/(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[Al2O3])/(Δt) = (Δ[Al])/(Δt) = 1/3 (Δ[AlO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum oxide | aluminum | AlO2 formula | Al_2O_3 | Al | AlO2 name | aluminum oxide | aluminum | IUPAC name | dialuminum;oxygen(2-) | aluminum |

| aluminum oxide | aluminum | AlO2 molar mass | 101.96 g/mol | 26.9815385 g/mol | 58.98 g/mol phase | solid (at STP) | solid (at STP) | melting point | 2040 °C | 660.4 °C | boiling point | | 2460 °C | density | | 2.7 g/cm^3 | solubility in water | | insoluble | surface tension | | 0.817 N/m | dynamic viscosity | | 1.5×10^-4 Pa s (at 760 °C) | odor | odorless | odorless |