CO + Al2O2 = CO2 + Al

CO carbon monoxide + Al2O2 ⟶ CO_2 carbon dioxide + Al aluminum

Balance the chemical equation algebraically: CO + Al2O2 ⟶ CO_2 + Al Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO + c_2 Al2O2 ⟶ c_3 CO_2 + c_4 Al Set the number of atoms in the reactants equal to the number of atoms in the products for C, O and Al: C: | c_1 = c_3 O: | c_1 + 2 c_2 = 2 c_3 Al: | 2 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 = 2 c_2 = 1 c_3 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 CO + Al2O2 ⟶ 2 CO_2 + 2 Al

+ Al2O2 ⟶ +

carbon monoxide + Al2O2 ⟶ carbon dioxide + aluminum

Construct the equilibrium constant, K, expression for: CO + Al2O2 ⟶ CO_2 + Al 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 CO + Al2O2 ⟶ 2 CO_2 + 2 Al 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 | 2 | -2 Al2O2 | 1 | -1 CO_2 | 2 | 2 Al | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO | 2 | -2 | ([CO])^(-2) Al2O2 | 1 | -1 | ([Al2O2])^(-1) CO_2 | 2 | 2 | ([CO2])^2 Al | 2 | 2 | ([Al])^2 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])^(-2) ([Al2O2])^(-1) ([CO2])^2 ([Al])^2 = (([CO2])^2 ([Al])^2)/(([CO])^2 [Al2O2])

Construct the rate of reaction expression for: CO + Al2O2 ⟶ CO_2 + Al 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 CO + Al2O2 ⟶ 2 CO_2 + 2 Al 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 | 2 | -2 Al2O2 | 1 | -1 CO_2 | 2 | 2 Al | 2 | 2 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 | 2 | -2 | -1/2 (Δ[CO])/(Δt) Al2O2 | 1 | -1 | -(Δ[Al2O2])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) Al | 2 | 2 | 1/2 (Δ[Al])/(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[CO])/(Δt) = -(Δ[Al2O2])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[Al])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon monoxide | Al2O2 | carbon dioxide | aluminum formula | CO | Al2O2 | CO_2 | Al name | carbon monoxide | | carbon dioxide | aluminum