Na2CO3 + KAlSi3O8 = CO2 + Na2SiO3 + KAlO2

Na_2CO_3 soda ash + KAlSi3O8 ⟶ CO_2 carbon dioxide + Na_2SiO_3 sodium metasilicate + KAlO2

Balance the chemical equation algebraically: Na_2CO_3 + KAlSi3O8 ⟶ CO_2 + Na_2SiO_3 + KAlO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2CO_3 + c_2 KAlSi3O8 ⟶ c_3 CO_2 + c_4 Na_2SiO_3 + c_5 KAlO2 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Na, O, K, Al and Si: C: | c_1 = c_3 Na: | 2 c_1 = 2 c_4 O: | 3 c_1 + 8 c_2 = 2 c_3 + 3 c_4 + 2 c_5 K: | c_2 = c_5 Al: | c_2 = c_5 Si: | 3 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 = 3 c_2 = 1 c_3 = 3 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Na_2CO_3 + KAlSi3O8 ⟶ 3 CO_2 + 3 Na_2SiO_3 + KAlO2

+ KAlSi3O8 ⟶ + + KAlO2

soda ash + KAlSi3O8 ⟶ carbon dioxide + sodium metasilicate + KAlO2

Construct the equilibrium constant, K, expression for: Na_2CO_3 + KAlSi3O8 ⟶ CO_2 + Na_2SiO_3 + KAlO2 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 Na_2CO_3 + KAlSi3O8 ⟶ 3 CO_2 + 3 Na_2SiO_3 + KAlO2 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 Na_2CO_3 | 3 | -3 KAlSi3O8 | 1 | -1 CO_2 | 3 | 3 Na_2SiO_3 | 3 | 3 KAlO2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2CO_3 | 3 | -3 | ([Na2CO3])^(-3) KAlSi3O8 | 1 | -1 | ([KAlSi3O8])^(-1) CO_2 | 3 | 3 | ([CO2])^3 Na_2SiO_3 | 3 | 3 | ([Na2SiO3])^3 KAlO2 | 1 | 1 | [KAlO2] 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 = ([Na2CO3])^(-3) ([KAlSi3O8])^(-1) ([CO2])^3 ([Na2SiO3])^3 [KAlO2] = (([CO2])^3 ([Na2SiO3])^3 [KAlO2])/(([Na2CO3])^3 [KAlSi3O8])

Construct the rate of reaction expression for: Na_2CO_3 + KAlSi3O8 ⟶ CO_2 + Na_2SiO_3 + KAlO2 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 Na_2CO_3 + KAlSi3O8 ⟶ 3 CO_2 + 3 Na_2SiO_3 + KAlO2 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 Na_2CO_3 | 3 | -3 KAlSi3O8 | 1 | -1 CO_2 | 3 | 3 Na_2SiO_3 | 3 | 3 KAlO2 | 1 | 1 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 Na_2CO_3 | 3 | -3 | -1/3 (Δ[Na2CO3])/(Δt) KAlSi3O8 | 1 | -1 | -(Δ[KAlSi3O8])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) Na_2SiO_3 | 3 | 3 | 1/3 (Δ[Na2SiO3])/(Δt) KAlO2 | 1 | 1 | (Δ[KAlO2])/(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[Na2CO3])/(Δt) = -(Δ[KAlSi3O8])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/3 (Δ[Na2SiO3])/(Δt) = (Δ[KAlO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| soda ash | KAlSi3O8 | carbon dioxide | sodium metasilicate | KAlO2 formula | Na_2CO_3 | KAlSi3O8 | CO_2 | Na_2SiO_3 | KAlO2 Hill formula | CNa_2O_3 | AlKO8Si3 | CO_2 | Na_2O_3Si | AlKO2 name | soda ash | | carbon dioxide | sodium metasilicate | IUPAC name | disodium carbonate | | carbon dioxide | disodium dioxido-oxosilane |

| soda ash | KAlSi3O8 | carbon dioxide | sodium metasilicate | KAlO2 molar mass | 105.99 g/mol | 278.33 g/mol | 44.009 g/mol | 122.06 g/mol | 98.078 g/mol phase | solid (at STP) | | gas (at STP) | solid (at STP) | melting point | 851 °C | | -56.56 °C (at triple point) | 72.2 °C | boiling point | 1600 °C | | -78.5 °C (at sublimation point) | | density | | | 0.00184212 g/cm^3 (at 20 °C) | 1.749 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) | 1 Pa s (at 1088 °C) | odor | | | odorless | |