H2O + CO2 + Na2SiO3 = Na2CO3 + H2SiO3

H_2O water + CO_2 carbon dioxide + Na_2SiO_3 sodium metasilicate ⟶ Na_2CO_3 soda ash + H_2O_3Si metasilicic acid

Balance the chemical equation algebraically: H_2O + CO_2 + Na_2SiO_3 ⟶ Na_2CO_3 + H_2O_3Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CO_2 + c_3 Na_2SiO_3 ⟶ c_4 Na_2CO_3 + c_5 H_2O_3Si Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, C, Na and Si: H: | 2 c_1 = 2 c_5 O: | c_1 + 2 c_2 + 3 c_3 = 3 c_4 + 3 c_5 C: | c_2 = c_4 Na: | 2 c_3 = 2 c_4 Si: | c_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 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + CO_2 + Na_2SiO_3 ⟶ Na_2CO_3 + H_2O_3Si

+ + ⟶ +

water + carbon dioxide + sodium metasilicate ⟶ soda ash + metasilicic acid

| water | carbon dioxide | sodium metasilicate | soda ash | metasilicic acid molecular enthalpy | -285.8 kJ/mol | -393.5 kJ/mol | -1555 kJ/mol | -1131 kJ/mol | -1189 kJ/mol total enthalpy | -285.8 kJ/mol | -393.5 kJ/mol | -1555 kJ/mol | -1131 kJ/mol | -1189 kJ/mol | H_initial = -2234 kJ/mol | | | H_final = -2319 kJ/mol | ΔH_rxn^0 | -2319 kJ/mol - -2234 kJ/mol = -85.17 kJ/mol (exothermic) | | | |

| water | carbon dioxide | sodium metasilicate | soda ash | metasilicic acid molecular free energy | -237.1 kJ/mol | -394.4 kJ/mol | -14628 kJ/mol | -1044 kJ/mol | -1092 kJ/mol total free energy | -237.1 kJ/mol | -394.4 kJ/mol | -14628 kJ/mol | -1044 kJ/mol | -1092 kJ/mol | G_initial = -15260 kJ/mol | | | G_final = -2137 kJ/mol | ΔG_rxn^0 | -2137 kJ/mol - -15260 kJ/mol = 13123 kJ/mol (endergonic) | | | |

Construct the equilibrium constant, K, expression for: H_2O + CO_2 + Na_2SiO_3 ⟶ Na_2CO_3 + H_2O_3Si 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: H_2O + CO_2 + Na_2SiO_3 ⟶ Na_2CO_3 + H_2O_3Si 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 H_2O | 1 | -1 CO_2 | 1 | -1 Na_2SiO_3 | 1 | -1 Na_2CO_3 | 1 | 1 H_2O_3Si | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) CO_2 | 1 | -1 | ([CO2])^(-1) Na_2SiO_3 | 1 | -1 | ([Na2SiO3])^(-1) Na_2CO_3 | 1 | 1 | [Na2CO3] H_2O_3Si | 1 | 1 | [H2O3Si] 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 = ([H2O])^(-1) ([CO2])^(-1) ([Na2SiO3])^(-1) [Na2CO3] [H2O3Si] = ([Na2CO3] [H2O3Si])/([H2O] [CO2] [Na2SiO3])

Construct the rate of reaction expression for: H_2O + CO_2 + Na_2SiO_3 ⟶ Na_2CO_3 + H_2O_3Si 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: H_2O + CO_2 + Na_2SiO_3 ⟶ Na_2CO_3 + H_2O_3Si 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 H_2O | 1 | -1 CO_2 | 1 | -1 Na_2SiO_3 | 1 | -1 Na_2CO_3 | 1 | 1 H_2O_3Si | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) Na_2SiO_3 | 1 | -1 | -(Δ[Na2SiO3])/(Δt) Na_2CO_3 | 1 | 1 | (Δ[Na2CO3])/(Δt) H_2O_3Si | 1 | 1 | (Δ[H2O3Si])/(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[H2O])/(Δt) = -(Δ[CO2])/(Δt) = -(Δ[Na2SiO3])/(Δt) = (Δ[Na2CO3])/(Δt) = (Δ[H2O3Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | carbon dioxide | sodium metasilicate | soda ash | metasilicic acid formula | H_2O | CO_2 | Na_2SiO_3 | Na_2CO_3 | H_2O_3Si Hill formula | H_2O | CO_2 | Na_2O_3Si | CNa_2O_3 | H_2O_3Si name | water | carbon dioxide | sodium metasilicate | soda ash | metasilicic acid IUPAC name | water | carbon dioxide | disodium dioxido-oxosilane | disodium carbonate | dihydroxy-oxo-silane

| water | carbon dioxide | sodium metasilicate | soda ash | metasilicic acid molar mass | 18.015 g/mol | 44.009 g/mol | 122.06 g/mol | 105.99 g/mol | 78.098 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | -56.56 °C (at triple point) | 72.2 °C | 851 °C | 1704 °C boiling point | 99.9839 °C | -78.5 °C (at sublimation point) | | 1600 °C | density | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 1.749 g/cm^3 | | 1 g/cm^3 solubility in water | | | soluble | soluble | surface tension | 0.0728 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | 1 Pa s (at 1088 °C) | 0.00355 Pa s (at 900 °C) | odor | odorless | odorless | | |