Al2O3 + K = Al + K2O

Al_2O_3 aluminum oxide + K potassium ⟶ Al aluminum + K_2O potassium oxide

Balance the chemical equation algebraically: Al_2O_3 + K ⟶ Al + K_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al_2O_3 + c_2 K ⟶ c_3 Al + c_4 K_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Al, O and K: Al: | 2 c_1 = c_3 O: | 3 c_1 = c_4 K: | c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 6 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al_2O_3 + 6 K ⟶ 2 Al + 3 K_2O

+ ⟶ +

aluminum oxide + potassium ⟶ aluminum + potassium oxide

Construct the equilibrium constant, K, expression for: Al_2O_3 + K ⟶ Al + K_2O 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: Al_2O_3 + 6 K ⟶ 2 Al + 3 K_2O 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 Al_2O_3 | 1 | -1 K | 6 | -6 Al | 2 | 2 K_2O | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) K | 6 | -6 | ([K])^(-6) Al | 2 | 2 | ([Al])^2 K_2O | 3 | 3 | ([K2O])^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 = ([Al2O3])^(-1) ([K])^(-6) ([Al])^2 ([K2O])^3 = (([Al])^2 ([K2O])^3)/([Al2O3] ([K])^6)

Construct the rate of reaction expression for: Al_2O_3 + K ⟶ Al + K_2O 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: Al_2O_3 + 6 K ⟶ 2 Al + 3 K_2O 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 Al_2O_3 | 1 | -1 K | 6 | -6 Al | 2 | 2 K_2O | 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 Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) K | 6 | -6 | -1/6 (Δ[K])/(Δt) Al | 2 | 2 | 1/2 (Δ[Al])/(Δt) K_2O | 3 | 3 | 1/3 (Δ[K2O])/(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 = -(Δ[Al2O3])/(Δt) = -1/6 (Δ[K])/(Δt) = 1/2 (Δ[Al])/(Δt) = 1/3 (Δ[K2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum oxide | potassium | aluminum | potassium oxide formula | Al_2O_3 | K | Al | K_2O name | aluminum oxide | potassium | aluminum | potassium oxide IUPAC name | dialuminum;oxygen(2-) | potassium | aluminum | dipotassium oxygen(2-)

| aluminum oxide | potassium | aluminum | potassium oxide molar mass | 101.96 g/mol | 39.0983 g/mol | 26.9815385 g/mol | 94.196 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 2040 °C | 64 °C | 660.4 °C | boiling point | | 760 °C | 2460 °C | density | | 0.86 g/cm^3 | 2.7 g/cm^3 | solubility in water | | reacts | insoluble | surface tension | | | 0.817 N/m | dynamic viscosity | | | 1.5×10^-4 Pa s (at 760 °C) | odor | odorless | | odorless |