C + Al2O3 = CO + Al4C3

C activated charcoal + Al_2O_3 aluminum oxide ⟶ CO carbon monoxide + Al4C3

Balance the chemical equation algebraically: C + Al_2O_3 ⟶ CO + Al4C3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Al_2O_3 ⟶ c_3 CO + c_4 Al4C3 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_3 + 3 c_4 Al: | 2 c_2 = 4 c_4 O: | 3 c_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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 9 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 C + 2 Al_2O_3 ⟶ 6 CO + Al4C3

+ ⟶ + Al4C3

activated charcoal + aluminum oxide ⟶ carbon monoxide + Al4C3

Construct the equilibrium constant, K, expression for: C + Al_2O_3 ⟶ CO + Al4C3 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: 9 C + 2 Al_2O_3 ⟶ 6 CO + Al4C3 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 | 9 | -9 Al_2O_3 | 2 | -2 CO | 6 | 6 Al4C3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 9 | -9 | ([C])^(-9) Al_2O_3 | 2 | -2 | ([Al2O3])^(-2) CO | 6 | 6 | ([CO])^6 Al4C3 | 1 | 1 | [Al4C3] 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])^(-9) ([Al2O3])^(-2) ([CO])^6 [Al4C3] = (([CO])^6 [Al4C3])/(([C])^9 ([Al2O3])^2)

Construct the rate of reaction expression for: C + Al_2O_3 ⟶ CO + Al4C3 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: 9 C + 2 Al_2O_3 ⟶ 6 CO + Al4C3 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 | 9 | -9 Al_2O_3 | 2 | -2 CO | 6 | 6 Al4C3 | 1 | 1 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 | 9 | -9 | -1/9 (Δ[C])/(Δt) Al_2O_3 | 2 | -2 | -1/2 (Δ[Al2O3])/(Δt) CO | 6 | 6 | 1/6 (Δ[CO])/(Δt) Al4C3 | 1 | 1 | (Δ[Al4C3])/(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 = -1/9 (Δ[C])/(Δt) = -1/2 (Δ[Al2O3])/(Δt) = 1/6 (Δ[CO])/(Δt) = (Δ[Al4C3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | aluminum oxide | carbon monoxide | Al4C3 formula | C | Al_2O_3 | CO | Al4C3 Hill formula | C | Al_2O_3 | CO | C3Al4 name | activated charcoal | aluminum oxide | carbon monoxide | IUPAC name | carbon | dialuminum;oxygen(2-) | carbon monoxide |

| activated charcoal | aluminum oxide | carbon monoxide | Al4C3 molar mass | 12.011 g/mol | 101.96 g/mol | 28.01 g/mol | 143.959 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 3550 °C | 2040 °C | -205 °C | boiling point | 4027 °C | | -191.5 °C | density | 2.26 g/cm^3 | | 0.001145 g/cm^3 (at 25 °C) | solubility in water | insoluble | | | dynamic viscosity | | | 1.772×10^-5 Pa s (at 25 °C) | odor | | odorless | odorless |