Al2O3 + Na2CO3 = CO2 + NaAlO2

Al_2O_3 aluminum oxide + Na_2CO_3 soda ash ⟶ CO_2 carbon dioxide + AlNaO_2 sodium aluminate

Balance the chemical equation algebraically: Al_2O_3 + Na_2CO_3 ⟶ CO_2 + AlNaO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al_2O_3 + c_2 Na_2CO_3 ⟶ c_3 CO_2 + c_4 AlNaO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, O, C and Na: Al: | 2 c_1 = c_4 O: | 3 c_1 + 3 c_2 = 2 c_3 + 2 c_4 C: | c_2 = c_3 Na: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al_2O_3 + Na_2CO_3 ⟶ CO_2 + 2 AlNaO_2

+ ⟶ +

aluminum oxide + soda ash ⟶ carbon dioxide + sodium aluminate

Construct the equilibrium constant, K, expression for: Al_2O_3 + Na_2CO_3 ⟶ CO_2 + 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: Al_2O_3 + Na_2CO_3 ⟶ CO_2 + 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 Al_2O_3 | 1 | -1 Na_2CO_3 | 1 | -1 CO_2 | 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 Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) Na_2CO_3 | 1 | -1 | ([Na2CO3])^(-1) CO_2 | 1 | 1 | [CO2] 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 = ([Al2O3])^(-1) ([Na2CO3])^(-1) [CO2] ([AlNaO2])^2 = ([CO2] ([AlNaO2])^2)/([Al2O3] [Na2CO3])

Construct the rate of reaction expression for: Al_2O_3 + Na_2CO_3 ⟶ CO_2 + 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: Al_2O_3 + Na_2CO_3 ⟶ CO_2 + 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 Al_2O_3 | 1 | -1 Na_2CO_3 | 1 | -1 CO_2 | 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 Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) Na_2CO_3 | 1 | -1 | -(Δ[Na2CO3])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(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 = -(Δ[Al2O3])/(Δt) = -(Δ[Na2CO3])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[AlNaO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum oxide | soda ash | carbon dioxide | sodium aluminate formula | Al_2O_3 | Na_2CO_3 | CO_2 | AlNaO_2 Hill formula | Al_2O_3 | CNa_2O_3 | CO_2 | AlNaO_2 name | aluminum oxide | soda ash | carbon dioxide | sodium aluminate IUPAC name | dialuminum;oxygen(2-) | disodium carbonate | carbon dioxide | sodium oxido-oxo-alumane

| aluminum oxide | soda ash | carbon dioxide | sodium aluminate molar mass | 101.96 g/mol | 105.99 g/mol | 44.009 g/mol | 81.969 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 2040 °C | 851 °C | -56.56 °C (at triple point) | 1800 °C boiling point | | 1600 °C | -78.5 °C (at sublimation point) | density | | | 0.00184212 g/cm^3 (at 20 °C) | 1.5 g/cm^3 solubility in water | | soluble | | soluble dynamic viscosity | | 0.00355 Pa s (at 900 °C) | 1.491×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless |