CH3COOH + NaHCO3 = H2O + CO2 + C2H3NaO2

CH_3CO_2H acetic acid + NaHCO_3 sodium bicarbonate ⟶ H_2O water + CO_2 carbon dioxide + CH_3COONa sodium acetate

Balance the chemical equation algebraically: CH_3CO_2H + NaHCO_3 ⟶ H_2O + CO_2 + CH_3COONa Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CH_3CO_2H + c_2 NaHCO_3 ⟶ 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, H, O and Na: C: | 2 c_1 + c_2 = c_4 + 2 c_5 H: | 4 c_1 + c_2 = 2 c_3 + 3 c_5 O: | 2 c_1 + 3 c_2 = c_3 + 2 c_4 + 2 c_5 Na: | c_2 = 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: | | CH_3CO_2H + NaHCO_3 ⟶ H_2O + CO_2 + CH_3COONa

+ ⟶ + +

acetic acid + sodium bicarbonate ⟶ water + carbon dioxide + sodium acetate

| acetic acid | sodium bicarbonate | water | carbon dioxide | sodium acetate molecular free energy | -389.9 kJ/mol | -851 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -607.2 kJ/mol total free energy | -389.9 kJ/mol | -851 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -607.2 kJ/mol | G_initial = -1241 kJ/mol | | G_final = -1239 kJ/mol | | ΔG_rxn^0 | -1239 kJ/mol - -1241 kJ/mol = 2.2 kJ/mol (endergonic) | | | |

Construct the equilibrium constant, K, expression for: CH_3CO_2H + NaHCO_3 ⟶ 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: CH_3CO_2H + NaHCO_3 ⟶ H_2O + CO_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 CH_3CO_2H | 1 | -1 NaHCO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 CH_3COONa | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CH_3CO_2H | 1 | -1 | ([CH3CO2H])^(-1) NaHCO_3 | 1 | -1 | ([NaHCO3])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] CH_3COONa | 1 | 1 | [CH3COONa] 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 = ([CH3CO2H])^(-1) ([NaHCO3])^(-1) [H2O] [CO2] [CH3COONa] = ([H2O] [CO2] [CH3COONa])/([CH3CO2H] [NaHCO3])

Construct the rate of reaction expression for: CH_3CO_2H + NaHCO_3 ⟶ 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: CH_3CO_2H + NaHCO_3 ⟶ H_2O + CO_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 CH_3CO_2H | 1 | -1 NaHCO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 CH_3COONa | 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 CH_3CO_2H | 1 | -1 | -(Δ[CH3CO2H])/(Δt) NaHCO_3 | 1 | -1 | -(Δ[NaHCO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) CH_3COONa | 1 | 1 | (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[CH3CO2H])/(Δt) = -(Δ[NaHCO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[CH3COONa])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| acetic acid | sodium bicarbonate | water | carbon dioxide | sodium acetate formula | CH_3CO_2H | NaHCO_3 | H_2O | CO_2 | CH_3COONa Hill formula | C_2H_4O_2 | CHNaO_3 | H_2O | CO_2 | C_2H_3NaO_2 name | acetic acid | sodium bicarbonate | water | carbon dioxide | sodium acetate IUPAC name | acetic acid | sodium hydrogen carbonate | water | carbon dioxide | sodium acetate