Al + (OH)3 = H2O + Al2O3

Al aluminum + (OH)3 ⟶ H_2O water + Al_2O_3 aluminum oxide

Balance the chemical equation algebraically: Al + (OH)3 ⟶ H_2O + Al_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 (OH)3 ⟶ c_3 H_2O + c_4 Al_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, O and H: Al: | c_1 = 2 c_4 O: | 3 c_2 = c_3 + 3 c_4 H: | 3 c_2 = 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 = 2 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + 2 (OH)3 ⟶ 3 H_2O + Al_2O_3

+ (OH)3 ⟶ +

aluminum + (OH)3 ⟶ water + aluminum oxide

Construct the equilibrium constant, K, expression for: Al + (OH)3 ⟶ H_2O + 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: 2 Al + 2 (OH)3 ⟶ 3 H_2O + 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 Al | 2 | -2 (OH)3 | 2 | -2 H_2O | 3 | 3 Al_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 2 | -2 | ([Al])^(-2) (OH)3 | 2 | -2 | ([(OH)3])^(-2) H_2O | 3 | 3 | ([H2O])^3 Al_2O_3 | 1 | 1 | [Al2O3] 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 = ([Al])^(-2) ([(OH)3])^(-2) ([H2O])^3 [Al2O3] = (([H2O])^3 [Al2O3])/(([Al])^2 ([(OH)3])^2)

Construct the rate of reaction expression for: Al + (OH)3 ⟶ H_2O + 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: 2 Al + 2 (OH)3 ⟶ 3 H_2O + 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 Al | 2 | -2 (OH)3 | 2 | -2 H_2O | 3 | 3 Al_2O_3 | 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 Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) (OH)3 | 2 | -2 | -1/2 (Δ[(OH)3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Al_2O_3 | 1 | 1 | (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 = -1/2 (Δ[Al])/(Δt) = -1/2 (Δ[(OH)3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[Al2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | (OH)3 | water | aluminum oxide formula | Al | (OH)3 | H_2O | Al_2O_3 Hill formula | Al | H3O3 | H_2O | Al_2O_3 name | aluminum | | water | aluminum oxide IUPAC name | aluminum | | water | dialuminum;oxygen(2-)

| aluminum | (OH)3 | water | aluminum oxide molar mass | 26.9815385 g/mol | 51.021 g/mol | 18.015 g/mol | 101.96 g/mol phase | solid (at STP) | | liquid (at STP) | solid (at STP) melting point | 660.4 °C | | 0 °C | 2040 °C boiling point | 2460 °C | | 99.9839 °C | density | 2.7 g/cm^3 | | 1 g/cm^3 | solubility in water | insoluble | | | surface tension | 0.817 N/m | | 0.0728 N/m | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless | odorless