NaOH + Al2O3 = H2O + NaAlO2

NaOH (sodium hydroxide) + Al_2O_3 (aluminum oxide) ⟶ H_2O (water) + AlNaO_2 (sodium aluminate)

Balance the chemical equation algebraically: NaOH + Al_2O_3 ⟶ H_2O + AlNaO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Al_2O_3 ⟶ c_3 H_2O + c_4 AlNaO_2 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 = c_4 O: | c_1 + 3 c_2 = c_3 + 2 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 = 2 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + Al_2O_3 ⟶ H_2O + 2 AlNaO_2

+ ⟶ +

sodium hydroxide + aluminum oxide ⟶ water + sodium aluminate

Construct the equilibrium constant, K, expression for: NaOH + Al_2O_3 ⟶ H_2O + AlNaO_2 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 NaOH + Al_2O_3 ⟶ H_2O + 2 AlNaO_2 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 | 2 | -2 Al_2O_3 | 1 | -1 H_2O | 1 | 1 AlNaO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) H_2O | 1 | 1 | [H2O] AlNaO_2 | 2 | 2 | ([AlNaO2])^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])^(-2) ([Al2O3])^(-1) [H2O] ([AlNaO2])^2 = ([H2O] ([AlNaO2])^2)/(([NaOH])^2 [Al2O3])

Construct the rate of reaction expression for: NaOH + Al_2O_3 ⟶ H_2O + AlNaO_2 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 NaOH + Al_2O_3 ⟶ H_2O + 2 AlNaO_2 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 | 2 | -2 Al_2O_3 | 1 | -1 H_2O | 1 | 1 AlNaO_2 | 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 | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) AlNaO_2 | 2 | 2 | 1/2 (Δ[AlNaO2])/(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[NaOH])/(Δt) = -(Δ[Al2O3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[AlNaO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | aluminum oxide | water | sodium aluminate formula | NaOH | Al_2O_3 | H_2O | AlNaO_2 Hill formula | HNaO | Al_2O_3 | H_2O | AlNaO_2 name | sodium hydroxide | aluminum oxide | water | sodium aluminate IUPAC name | sodium hydroxide | dialuminum;oxygen(2-) | water | sodium oxido-oxo-alumane

| sodium hydroxide | aluminum oxide | water | sodium aluminate molar mass | 39.997 g/mol | 101.96 g/mol | 18.015 g/mol | 81.969 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | 323 °C | 2040 °C | 0 °C | 1800 °C boiling point | 1390 °C | | 99.9839 °C | density | 2.13 g/cm^3 | | 1 g/cm^3 | 1.5 g/cm^3 solubility in water | soluble | | | 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 |