CO2 + Na(Al(OH)4) = H2O + Na2CO3 + Al(OH)3

CO_2 carbon dioxide + NaAl(OH)4 ⟶ H_2O water + Na_2CO_3 soda ash + Al(OH)_3 aluminum hydroxide

Balance the chemical equation algebraically: CO_2 + NaAl(OH)4 ⟶ H_2O + Na_2CO_3 + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 + c_2 NaAl(OH)4 ⟶ c_3 H_2O + c_4 Na_2CO_3 + c_5 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, O, Na, Al and H: C: | c_1 = c_4 O: | 2 c_1 + 4 c_2 = c_3 + 3 c_4 + 3 c_5 Na: | c_2 = 2 c_4 Al: | c_2 = c_5 H: | 4 c_2 = 2 c_3 + 3 c_5 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 = 2 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CO_2 + 2 NaAl(OH)4 ⟶ H_2O + Na_2CO_3 + 2 Al(OH)_3

+ NaAl(OH)4 ⟶ + +

carbon dioxide + NaAl(OH)4 ⟶ water + soda ash + aluminum hydroxide

Construct the equilibrium constant, K, expression for: CO_2 + NaAl(OH)4 ⟶ H_2O + Na_2CO_3 + Al(OH)_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: CO_2 + 2 NaAl(OH)4 ⟶ H_2O + Na_2CO_3 + 2 Al(OH)_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 CO_2 | 1 | -1 NaAl(OH)4 | 2 | -2 H_2O | 1 | 1 Na_2CO_3 | 1 | 1 Al(OH)_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO_2 | 1 | -1 | ([CO2])^(-1) NaAl(OH)4 | 2 | -2 | ([NaAl(OH)4])^(-2) H_2O | 1 | 1 | [H2O] Na_2CO_3 | 1 | 1 | [Na2CO3] Al(OH)_3 | 2 | 2 | ([Al(OH)3])^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 = ([CO2])^(-1) ([NaAl(OH)4])^(-2) [H2O] [Na2CO3] ([Al(OH)3])^2 = ([H2O] [Na2CO3] ([Al(OH)3])^2)/([CO2] ([NaAl(OH)4])^2)

Construct the rate of reaction expression for: CO_2 + NaAl(OH)4 ⟶ H_2O + Na_2CO_3 + Al(OH)_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: CO_2 + 2 NaAl(OH)4 ⟶ H_2O + Na_2CO_3 + 2 Al(OH)_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 CO_2 | 1 | -1 NaAl(OH)4 | 2 | -2 H_2O | 1 | 1 Na_2CO_3 | 1 | 1 Al(OH)_3 | 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 CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) NaAl(OH)4 | 2 | -2 | -1/2 (Δ[NaAl(OH)4])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Na_2CO_3 | 1 | 1 | (Δ[Na2CO3])/(Δt) Al(OH)_3 | 2 | 2 | 1/2 (Δ[Al(OH)3])/(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[CO2])/(Δt) = -1/2 (Δ[NaAl(OH)4])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Na2CO3])/(Δt) = 1/2 (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon dioxide | NaAl(OH)4 | water | soda ash | aluminum hydroxide formula | CO_2 | NaAl(OH)4 | H_2O | Na_2CO_3 | Al(OH)_3 Hill formula | CO_2 | H4AlNaO4 | H_2O | CNa_2O_3 | AlH_3O_3 name | carbon dioxide | | water | soda ash | aluminum hydroxide IUPAC name | carbon dioxide | | water | disodium carbonate | aluminum hydroxide

| carbon dioxide | NaAl(OH)4 | water | soda ash | aluminum hydroxide molar mass | 44.009 g/mol | 118 g/mol | 18.015 g/mol | 105.99 g/mol | 78.003 g/mol phase | gas (at STP) | | liquid (at STP) | solid (at STP) | melting point | -56.56 °C (at triple point) | | 0 °C | 851 °C | boiling point | -78.5 °C (at sublimation point) | | 99.9839 °C | 1600 °C | density | 0.00184212 g/cm^3 (at 20 °C) | | 1 g/cm^3 | | solubility in water | | | | soluble | surface tension | | | 0.0728 N/m | | dynamic viscosity | 1.491×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 0.00355 Pa s (at 900 °C) | odor | odorless | | odorless | |