O2 + Al4C3 = CO2 + Al2O3

O_2 oxygen + Al4C3 ⟶ CO_2 carbon dioxide + Al_2O_3 aluminum oxide

Balance the chemical equation algebraically: O_2 + Al4C3 ⟶ CO_2 + Al_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 Al4C3 ⟶ c_3 CO_2 + c_4 Al_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Al and C: O: | 2 c_1 = 2 c_3 + 3 c_4 Al: | 4 c_2 = 2 c_4 C: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 O_2 + Al4C3 ⟶ 3 CO_2 + 2 Al_2O_3

+ Al4C3 ⟶ +

oxygen + Al4C3 ⟶ carbon dioxide + aluminum oxide

Construct the equilibrium constant, K, expression for: O_2 + Al4C3 ⟶ CO_2 + Al_2O_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: 6 O_2 + Al4C3 ⟶ 3 CO_2 + 2 Al_2O_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 O_2 | 6 | -6 Al4C3 | 1 | -1 CO_2 | 3 | 3 Al_2O_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 6 | -6 | ([O2])^(-6) Al4C3 | 1 | -1 | ([Al4C3])^(-1) CO_2 | 3 | 3 | ([CO2])^3 Al_2O_3 | 2 | 2 | ([Al2O3])^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 = ([O2])^(-6) ([Al4C3])^(-1) ([CO2])^3 ([Al2O3])^2 = (([CO2])^3 ([Al2O3])^2)/(([O2])^6 [Al4C3])

Construct the rate of reaction expression for: O_2 + Al4C3 ⟶ CO_2 + Al_2O_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: 6 O_2 + Al4C3 ⟶ 3 CO_2 + 2 Al_2O_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 O_2 | 6 | -6 Al4C3 | 1 | -1 CO_2 | 3 | 3 Al_2O_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 O_2 | 6 | -6 | -1/6 (Δ[O2])/(Δt) Al4C3 | 1 | -1 | -(Δ[Al4C3])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) Al_2O_3 | 2 | 2 | 1/2 (Δ[Al2O3])/(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 = -1/6 (Δ[O2])/(Δt) = -(Δ[Al4C3])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/2 (Δ[Al2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | Al4C3 | carbon dioxide | aluminum oxide formula | O_2 | Al4C3 | CO_2 | Al_2O_3 Hill formula | O_2 | C3Al4 | CO_2 | Al_2O_3 name | oxygen | | carbon dioxide | aluminum oxide IUPAC name | molecular oxygen | | carbon dioxide | dialuminum;oxygen(2-)

| oxygen | Al4C3 | carbon dioxide | aluminum oxide molar mass | 31.998 g/mol | 143.959 g/mol | 44.009 g/mol | 101.96 g/mol phase | gas (at STP) | | gas (at STP) | solid (at STP) melting point | -218 °C | | -56.56 °C (at triple point) | 2040 °C boiling point | -183 °C | | -78.5 °C (at sublimation point) | density | 0.001429 g/cm^3 (at 0 °C) | | 0.00184212 g/cm^3 (at 20 °C) | surface tension | 0.01347 N/m | | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | 1.491×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless