Na2CO3 + CH3COOH = H2O + CO2 + CH3COONa

Na_2CO_3 soda ash + CH_3CO_2H acetic acid ⟶ H_2O water + CO_2 carbon dioxide + CH_3COONa sodium acetate

Balance the chemical equation algebraically: Na_2CO_3 + CH_3CO_2H ⟶ H_2O + CO_2 + CH_3COONa Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2CO_3 + c_2 CH_3CO_2H ⟶ c_3 H_2O + c_4 CO_2 + c_5 CH_3COONa Set the number of atoms in the reactants equal to the number of atoms in the products for C, Na, O and H: C: | c_1 + 2 c_2 = c_4 + 2 c_5 Na: | 2 c_1 = c_5 O: | 3 c_1 + 2 c_2 = c_3 + 2 c_4 + 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: | | Na_2CO_3 + 2 CH_3CO_2H ⟶ H_2O + CO_2 + 2 CH_3COONa

+ ⟶ + +

soda ash + acetic acid ⟶ water + carbon dioxide + sodium acetate

| soda ash | acetic acid | water | carbon dioxide | sodium acetate molecular free energy | -1044 kJ/mol | -389.9 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -607.2 kJ/mol total free energy | -1044 kJ/mol | -779.8 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -1214 kJ/mol | G_initial = -1824 kJ/mol | | G_final = -1846 kJ/mol | | ΔG_rxn^0 | -1846 kJ/mol - -1824 kJ/mol = -21.7 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: Na_2CO_3 + CH_3CO_2H ⟶ H_2O + CO_2 + CH_3COONa 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: Na_2CO_3 + 2 CH_3CO_2H ⟶ H_2O + CO_2 + 2 CH_3COONa 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 | 1 | -1 CH_3CO_2H | 2 | -2 H_2O | 1 | 1 CO_2 | 1 | 1 CH_3COONa | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2CO_3 | 1 | -1 | ([Na2CO3])^(-1) CH_3CO_2H | 2 | -2 | ([CH3CO2H])^(-2) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] CH_3COONa | 2 | 2 | ([CH3COONa])^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 = ([Na2CO3])^(-1) ([CH3CO2H])^(-2) [H2O] [CO2] ([CH3COONa])^2 = ([H2O] [CO2] ([CH3COONa])^2)/([Na2CO3] ([CH3CO2H])^2)

Construct the rate of reaction expression for: Na_2CO_3 + CH_3CO_2H ⟶ H_2O + CO_2 + CH_3COONa 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: Na_2CO_3 + 2 CH_3CO_2H ⟶ H_2O + CO_2 + 2 CH_3COONa 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 | 1 | -1 CH_3CO_2H | 2 | -2 H_2O | 1 | 1 CO_2 | 1 | 1 CH_3COONa | 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 Na_2CO_3 | 1 | -1 | -(Δ[Na2CO3])/(Δt) CH_3CO_2H | 2 | -2 | -1/2 (Δ[CH3CO2H])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) CH_3COONa | 2 | 2 | 1/2 (Δ[CH3COONa])/(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[Na2CO3])/(Δt) = -1/2 (Δ[CH3CO2H])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[CH3COONa])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| soda ash | acetic acid | water | carbon dioxide | sodium acetate formula | Na_2CO_3 | CH_3CO_2H | H_2O | CO_2 | CH_3COONa Hill formula | CNa_2O_3 | C_2H_4O_2 | H_2O | CO_2 | C_2H_3NaO_2 name | soda ash | acetic acid | water | carbon dioxide | sodium acetate IUPAC name | disodium carbonate | acetic acid | water | carbon dioxide | sodium acetate

| soda ash | acetic acid | water | carbon dioxide | sodium acetate molar mass | 105.99 g/mol | 60.052 g/mol | 18.015 g/mol | 44.009 g/mol | 82.034 g/mol phase | solid (at STP) | liquid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 851 °C | 16.2 °C | 0 °C | -56.56 °C (at triple point) | 300 °C boiling point | 1600 °C | 117.5 °C | 99.9839 °C | -78.5 °C (at sublimation point) | 881.4 °C density | | 1.049 g/cm^3 | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 1.528 g/cm^3 solubility in water | soluble | miscible | | | soluble surface tension | | 0.0288 N/m | 0.0728 N/m | | dynamic viscosity | 0.00355 Pa s (at 900 °C) | 0.001056 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | odor | | vinegar-like | odorless | odorless | odorless