H2O + NaOH + Al2O3 = NaAl(OH)4

H_2O (water) + NaOH (sodium hydroxide) + Al_2O_3 (aluminum oxide) ⟶ NaAl(OH)4

Balance the chemical equation algebraically: H_2O + NaOH + Al_2O_3 ⟶ NaAl(OH)4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NaOH + c_3 Al_2O_3 ⟶ c_4 NaAl(OH)4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na and Al: H: | 2 c_1 + c_2 = 4 c_4 O: | c_1 + c_2 + 3 c_3 = 4 c_4 Na: | c_2 = c_4 Al: | 2 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 NaOH + Al_2O_3 ⟶ 2 NaAl(OH)4

+ + ⟶ NaAl(OH)4

water + sodium hydroxide + aluminum oxide ⟶ NaAl(OH)4

Construct the equilibrium constant, K, expression for: H_2O + NaOH + Al_2O_3 ⟶ NaAl(OH)4 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: 3 H_2O + 2 NaOH + Al_2O_3 ⟶ 2 NaAl(OH)4 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 H_2O | 3 | -3 NaOH | 2 | -2 Al_2O_3 | 1 | -1 NaAl(OH)4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) NaOH | 2 | -2 | ([NaOH])^(-2) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) NaAl(OH)4 | 2 | 2 | ([NaAl(OH)4])^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 = ([H2O])^(-3) ([NaOH])^(-2) ([Al2O3])^(-1) ([NaAl(OH)4])^2 = ([NaAl(OH)4])^2/(([H2O])^3 ([NaOH])^2 [Al2O3])

Construct the rate of reaction expression for: H_2O + NaOH + Al_2O_3 ⟶ NaAl(OH)4 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: 3 H_2O + 2 NaOH + Al_2O_3 ⟶ 2 NaAl(OH)4 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 H_2O | 3 | -3 NaOH | 2 | -2 Al_2O_3 | 1 | -1 NaAl(OH)4 | 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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) NaAl(OH)4 | 2 | 2 | 1/2 (Δ[NaAl(OH)4])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[NaOH])/(Δt) = -(Δ[Al2O3])/(Δt) = 1/2 (Δ[NaAl(OH)4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium hydroxide | aluminum oxide | NaAl(OH)4 formula | H_2O | NaOH | Al_2O_3 | NaAl(OH)4 Hill formula | H_2O | HNaO | Al_2O_3 | H4AlNaO4 name | water | sodium hydroxide | aluminum oxide | IUPAC name | water | sodium hydroxide | dialuminum;oxygen(2-) |

| water | sodium hydroxide | aluminum oxide | NaAl(OH)4 molar mass | 18.015 g/mol | 39.997 g/mol | 101.96 g/mol | 118 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | 0 °C | 323 °C | 2040 °C | boiling point | 99.9839 °C | 1390 °C | | density | 1 g/cm^3 | 2.13 g/cm^3 | | solubility in water | | soluble | | surface tension | 0.0728 N/m | 0.07435 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.004 Pa s (at 350 °C) | | odor | odorless | | odorless |