CH3COOH = CO2 + CH4

CH_3CO_2H acetic acid ⟶ CO_2 carbon dioxide + CH_4 methane

Balance the chemical equation algebraically: CH_3CO_2H ⟶ CO_2 + CH_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CH_3CO_2H ⟶ c_2 CO_2 + c_3 CH_4 Set the number of atoms in the reactants equal to the number of atoms in the products for C, H and O: C: | 2 c_1 = c_2 + c_3 H: | 4 c_1 = 4 c_3 O: | 2 c_1 = 2 c_2 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 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CH_3CO_2H ⟶ CO_2 + CH_4

⟶ +

acetic acid ⟶ carbon dioxide + methane

| acetic acid | carbon dioxide | methane molecular free energy | -389.9 kJ/mol | -394.4 kJ/mol | -51 kJ/mol total free energy | -389.9 kJ/mol | -394.4 kJ/mol | -51 kJ/mol | G_initial = -389.9 kJ/mol | G_final = -445.4 kJ/mol | ΔG_rxn^0 | -445.4 kJ/mol - -389.9 kJ/mol = -55.5 kJ/mol (exergonic) | |

| acetic acid | carbon dioxide | methane molecular entropy | 160 J/(mol K) | 214 J/(mol K) | 186 J/(mol K) total entropy | 160 J/(mol K) | 214 J/(mol K) | 186 J/(mol K) | S_initial = 160 J/(mol K) | S_final = 400 J/(mol K) | ΔS_rxn^0 | 400 J/(mol K) - 160 J/(mol K) = 240 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: CH_3CO_2H ⟶ CO_2 + CH_4 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 ⟶ CO_2 + CH_4 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 CO_2 | 1 | 1 CH_4 | 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) CO_2 | 1 | 1 | [CO2] CH_4 | 1 | 1 | [CH4] 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) [CO2] [CH4] = ([CO2] [CH4])/([CH3CO2H])

Construct the rate of reaction expression for: CH_3CO_2H ⟶ CO_2 + CH_4 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 ⟶ CO_2 + CH_4 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 CO_2 | 1 | 1 CH_4 | 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) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) CH_4 | 1 | 1 | (Δ[CH4])/(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[CO2])/(Δt) = (Δ[CH4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| acetic acid | carbon dioxide | methane formula | CH_3CO_2H | CO_2 | CH_4 Hill formula | C_2H_4O_2 | CO_2 | CH_4 name | acetic acid | carbon dioxide | methane