NaOH + Al2O3 = H2O + Na3AlO3

NaOH sodium hydroxide + Al_2O_3 aluminum oxide ⟶ H_2O water + Na3AlO3

Balance the chemical equation algebraically: NaOH + Al_2O_3 ⟶ H_2O + Na3AlO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Al_2O_3 ⟶ c_3 H_2O + c_4 Na3AlO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O and Al: H: | c_1 = 2 c_3 Na: | c_1 = 3 c_4 O: | c_1 + 3 c_2 = c_3 + 3 c_4 Al: | 2 c_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_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 NaOH + Al_2O_3 ⟶ 3 H_2O + 2 Na3AlO3

+ ⟶ + Na3AlO3

sodium hydroxide + aluminum oxide ⟶ water + Na3AlO3

Construct the equilibrium constant, K, expression for: NaOH + Al_2O_3 ⟶ H_2O + Na3AlO3 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 NaOH + Al_2O_3 ⟶ 3 H_2O + 2 Na3AlO3 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 NaOH | 6 | -6 Al_2O_3 | 1 | -1 H_2O | 3 | 3 Na3AlO3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 6 | -6 | ([NaOH])^(-6) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) H_2O | 3 | 3 | ([H2O])^3 Na3AlO3 | 2 | 2 | ([Na3AlO3])^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 = ([NaOH])^(-6) ([Al2O3])^(-1) ([H2O])^3 ([Na3AlO3])^2 = (([H2O])^3 ([Na3AlO3])^2)/(([NaOH])^6 [Al2O3])

Construct the rate of reaction expression for: NaOH + Al_2O_3 ⟶ H_2O + Na3AlO3 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 NaOH + Al_2O_3 ⟶ 3 H_2O + 2 Na3AlO3 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 NaOH | 6 | -6 Al_2O_3 | 1 | -1 H_2O | 3 | 3 Na3AlO3 | 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 NaOH | 6 | -6 | -1/6 (Δ[NaOH])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Na3AlO3 | 2 | 2 | 1/2 (Δ[Na3AlO3])/(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[NaOH])/(Δt) = -(Δ[Al2O3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[Na3AlO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | aluminum oxide | water | Na3AlO3 formula | NaOH | Al_2O_3 | H_2O | Na3AlO3 Hill formula | HNaO | Al_2O_3 | H_2O | AlNa3O3 name | sodium hydroxide | aluminum oxide | water | IUPAC name | sodium hydroxide | dialuminum;oxygen(2-) | water |

| sodium hydroxide | aluminum oxide | water | Na3AlO3 molar mass | 39.997 g/mol | 101.96 g/mol | 18.015 g/mol | 143.95 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | melting point | 323 °C | 2040 °C | 0 °C | boiling point | 1390 °C | | 99.9839 °C | density | 2.13 g/cm^3 | | 1 g/cm^3 | solubility in water | soluble | | | surface tension | 0.07435 N/m | | 0.0728 N/m | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | | odorless | odorless |