C + Al2O3 = Al + CO

C activated charcoal + Al_2O_3 aluminum oxide ⟶ Al aluminum + CO carbon monoxide

Balance the chemical equation algebraically: C + Al_2O_3 ⟶ Al + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Al_2O_3 ⟶ c_3 Al + c_4 CO Set the number of atoms in the reactants equal to the number of atoms in the products for C, Al and O: C: | 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 C + Al_2O_3 ⟶ 2 Al + 3 CO

+ ⟶ +

activated charcoal + aluminum oxide ⟶ aluminum + carbon monoxide

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

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

| activated charcoal | aluminum oxide | aluminum | carbon monoxide formula | C | Al_2O_3 | Al | CO name | activated charcoal | aluminum oxide | aluminum | carbon monoxide IUPAC name | carbon | dialuminum;oxygen(2-) | aluminum | carbon monoxide