NaOH + CO2 = H2O + Na2CO3

NaOH (sodium hydroxide) + CO_2 (carbon dioxide) ⟶ H_2O (water) + Na_2CO_3 (soda ash)

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

+ ⟶ +

sodium hydroxide + carbon dioxide ⟶ water + soda ash

| sodium hydroxide | carbon dioxide | water | soda ash molecular enthalpy | -425.8 kJ/mol | -393.5 kJ/mol | -285.8 kJ/mol | -1131 kJ/mol total enthalpy | -851.6 kJ/mol | -393.5 kJ/mol | -285.8 kJ/mol | -1131 kJ/mol | H_initial = -1245 kJ/mol | | H_final = -1417 kJ/mol | ΔH_rxn^0 | -1417 kJ/mol - -1245 kJ/mol = -171.4 kJ/mol (exothermic) | | |

| sodium hydroxide | carbon dioxide | water | soda ash molecular free energy | -379.7 kJ/mol | -394.4 kJ/mol | -237.1 kJ/mol | -1044 kJ/mol total free energy | -759.4 kJ/mol | -394.4 kJ/mol | -237.1 kJ/mol | -1044 kJ/mol | G_initial = -1154 kJ/mol | | G_final = -1282 kJ/mol | ΔG_rxn^0 | -1282 kJ/mol - -1154 kJ/mol = -127.7 kJ/mol (exergonic) | | |

| sodium hydroxide | carbon dioxide | water | soda ash molecular entropy | 64 J/(mol K) | 214 J/(mol K) | 69.91 J/(mol K) | 136 J/(mol K) total entropy | 128 J/(mol K) | 214 J/(mol K) | 69.91 J/(mol K) | 136 J/(mol K) | S_initial = 342 J/(mol K) | | S_final = 205.9 J/(mol K) | ΔS_rxn^0 | 205.9 J/(mol K) - 342 J/(mol K) = -136.1 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: NaOH + CO_2 ⟶ H_2O + Na_2CO_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: 2 NaOH + CO_2 ⟶ H_2O + Na_2CO_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 NaOH | 2 | -2 CO_2 | 1 | -1 H_2O | 1 | 1 Na_2CO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) CO_2 | 1 | -1 | ([CO2])^(-1) H_2O | 1 | 1 | [H2O] Na_2CO_3 | 1 | 1 | [Na2CO3] 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 = ([NaOH])^(-2) ([CO2])^(-1) [H2O] [Na2CO3] = ([H2O] [Na2CO3])/(([NaOH])^2 [CO2])

Construct the rate of reaction expression for: NaOH + CO_2 ⟶ H_2O + Na_2CO_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: 2 NaOH + CO_2 ⟶ H_2O + Na_2CO_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 NaOH | 2 | -2 CO_2 | 1 | -1 H_2O | 1 | 1 Na_2CO_3 | 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Na_2CO_3 | 1 | 1 | (Δ[Na2CO3])/(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[NaOH])/(Δt) = -(Δ[CO2])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Na2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | carbon dioxide | water | soda ash formula | NaOH | CO_2 | H_2O | Na_2CO_3 Hill formula | HNaO | CO_2 | H_2O | CNa_2O_3 name | sodium hydroxide | carbon dioxide | water | soda ash IUPAC name | sodium hydroxide | carbon dioxide | water | disodium carbonate