Na2CO3 + SiO2 = CO2 + Na4SiO4

Na_2CO_3 soda ash + SiO_2 silicon dioxide ⟶ CO_2 carbon dioxide + Na_4O_4Si sodium silicate

Balance the chemical equation algebraically: Na_2CO_3 + SiO_2 ⟶ CO_2 + Na_4O_4Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2CO_3 + c_2 SiO_2 ⟶ c_3 CO_2 + c_4 Na_4O_4Si Set the number of atoms in the reactants equal to the number of atoms in the products for C, Na, O and Si: C: | c_1 = c_3 Na: | 2 c_1 = 4 c_4 O: | 3 c_1 + 2 c_2 = 2 c_3 + 4 c_4 Si: | 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 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Na_2CO_3 + SiO_2 ⟶ 2 CO_2 + Na_4O_4Si

+ ⟶ +

soda ash + silicon dioxide ⟶ carbon dioxide + sodium silicate

Construct the equilibrium constant, K, expression for: Na_2CO_3 + SiO_2 ⟶ CO_2 + Na_4O_4Si 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 Na_2CO_3 + SiO_2 ⟶ 2 CO_2 + Na_4O_4Si 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 | 2 | -2 SiO_2 | 1 | -1 CO_2 | 2 | 2 Na_4O_4Si | 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 | 2 | -2 | ([Na2CO3])^(-2) SiO_2 | 1 | -1 | ([SiO2])^(-1) CO_2 | 2 | 2 | ([CO2])^2 Na_4O_4Si | 1 | 1 | [Na4O4Si] 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])^(-2) ([SiO2])^(-1) ([CO2])^2 [Na4O4Si] = (([CO2])^2 [Na4O4Si])/(([Na2CO3])^2 [SiO2])

Construct the rate of reaction expression for: Na_2CO_3 + SiO_2 ⟶ CO_2 + Na_4O_4Si 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 Na_2CO_3 + SiO_2 ⟶ 2 CO_2 + Na_4O_4Si 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 | 2 | -2 SiO_2 | 1 | -1 CO_2 | 2 | 2 Na_4O_4Si | 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 | 2 | -2 | -1/2 (Δ[Na2CO3])/(Δt) SiO_2 | 1 | -1 | -(Δ[SiO2])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) Na_4O_4Si | 1 | 1 | (Δ[Na4O4Si])/(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[Na2CO3])/(Δt) = -(Δ[SiO2])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[Na4O4Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| soda ash | silicon dioxide | carbon dioxide | sodium silicate formula | Na_2CO_3 | SiO_2 | CO_2 | Na_4O_4Si Hill formula | CNa_2O_3 | O_2Si | CO_2 | Na_4O_4Si_1 name | soda ash | silicon dioxide | carbon dioxide | sodium silicate IUPAC name | disodium carbonate | dioxosilane | carbon dioxide |

| soda ash | silicon dioxide | carbon dioxide | sodium silicate molar mass | 105.99 g/mol | 60.083 g/mol | 44.009 g/mol | 184.04 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 851 °C | 1713 °C | -56.56 °C (at triple point) | boiling point | 1600 °C | 2950 °C | -78.5 °C (at sublimation point) | density | | 2.196 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 1.37 g/cm^3 solubility in water | soluble | insoluble | | slightly 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 | odorless |