Cl2 + C + Al2O3 = CO + AlCl3

Cl_2 (chlorine) + C (activated charcoal) + Al_2O_3 (aluminum oxide) ⟶ CO (carbon monoxide) + AlCl_3 (aluminum chloride)

Balance the chemical equation algebraically: Cl_2 + C + Al_2O_3 ⟶ CO + AlCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 C + c_3 Al_2O_3 ⟶ c_4 CO + c_5 AlCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, C, Al and O: Cl: | 2 c_1 = 3 c_5 C: | c_2 = c_4 Al: | 2 c_3 = c_5 O: | 3 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3 c_3 = 1 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cl_2 + 3 C + Al_2O_3 ⟶ 3 CO + 2 AlCl_3

+ + ⟶ +

chlorine + activated charcoal + aluminum oxide ⟶ carbon monoxide + aluminum chloride

Construct the equilibrium constant, K, expression for: Cl_2 + C + Al_2O_3 ⟶ CO + AlCl_3 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 Cl_2 + 3 C + Al_2O_3 ⟶ 3 CO + 2 AlCl_3 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 Cl_2 | 3 | -3 C | 3 | -3 Al_2O_3 | 1 | -1 CO | 3 | 3 AlCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 3 | -3 | ([Cl2])^(-3) C | 3 | -3 | ([C])^(-3) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) CO | 3 | 3 | ([CO])^3 AlCl_3 | 2 | 2 | ([AlCl3])^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 = ([Cl2])^(-3) ([C])^(-3) ([Al2O3])^(-1) ([CO])^3 ([AlCl3])^2 = (([CO])^3 ([AlCl3])^2)/(([Cl2])^3 ([C])^3 [Al2O3])

Construct the rate of reaction expression for: Cl_2 + C + Al_2O_3 ⟶ CO + AlCl_3 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 Cl_2 + 3 C + Al_2O_3 ⟶ 3 CO + 2 AlCl_3 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 Cl_2 | 3 | -3 C | 3 | -3 Al_2O_3 | 1 | -1 CO | 3 | 3 AlCl_3 | 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 Cl_2 | 3 | -3 | -1/3 (Δ[Cl2])/(Δt) C | 3 | -3 | -1/3 (Δ[C])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) CO | 3 | 3 | 1/3 (Δ[CO])/(Δt) AlCl_3 | 2 | 2 | 1/2 (Δ[AlCl3])/(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[Cl2])/(Δt) = -1/3 (Δ[C])/(Δt) = -(Δ[Al2O3])/(Δt) = 1/3 (Δ[CO])/(Δt) = 1/2 (Δ[AlCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | activated charcoal | aluminum oxide | carbon monoxide | aluminum chloride formula | Cl_2 | C | Al_2O_3 | CO | AlCl_3 name | chlorine | activated charcoal | aluminum oxide | carbon monoxide | aluminum chloride IUPAC name | molecular chlorine | carbon | dialuminum;oxygen(2-) | carbon monoxide | trichloroalumane