CO + CH3OH = HCO2CH3

CO carbon monoxide + CH_3OH methanol ⟶ CH_3CO_2H acetic acid

Balance the chemical equation algebraically: CO + CH_3OH ⟶ CH_3CO_2H Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO + c_2 CH_3OH ⟶ c_3 CH_3CO_2H Set the number of atoms in the reactants equal to the number of atoms in the products for C, O and H: C: | c_1 + c_2 = 2 c_3 O: | c_1 + c_2 = 2 c_3 H: | 4 c_2 = 4 c_3 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: | | CO + CH_3OH ⟶ CH_3CO_2H

+ ⟶

carbon monoxide + methanol ⟶ acetic acid

| carbon monoxide | methanol | acetic acid molecular free energy | -137 kJ/mol | -166.3 kJ/mol | -389.9 kJ/mol total free energy | -137 kJ/mol | -166.3 kJ/mol | -389.9 kJ/mol | G_initial = -303.3 kJ/mol | | G_final = -389.9 kJ/mol ΔG_rxn^0 | -389.9 kJ/mol - -303.3 kJ/mol = -86.63 kJ/mol (exergonic) | |

| carbon monoxide | methanol | acetic acid molecular entropy | 198 J/(mol K) | 126.8 J/(mol K) | 160 J/(mol K) total entropy | 198 J/(mol K) | 126.8 J/(mol K) | 160 J/(mol K) | S_initial = 324.8 J/(mol K) | | S_final = 160 J/(mol K) ΔS_rxn^0 | 160 J/(mol K) - 324.8 J/(mol K) = -164.8 J/(mol K) (exoentropic) | |

Construct the equilibrium constant, K, expression for: CO + CH_3OH ⟶ CH_3CO_2H 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: CO + CH_3OH ⟶ CH_3CO_2H 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 CO | 1 | -1 CH_3OH | 1 | -1 CH_3CO_2H | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO | 1 | -1 | ([CO])^(-1) CH_3OH | 1 | -1 | ([CH3OH])^(-1) CH_3CO_2H | 1 | 1 | [CH3CO2H] 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 = ([CO])^(-1) ([CH3OH])^(-1) [CH3CO2H] = ([CH3CO2H])/([CO] [CH3OH])

Construct the rate of reaction expression for: CO + CH_3OH ⟶ CH_3CO_2H 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: CO + CH_3OH ⟶ CH_3CO_2H 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 CO | 1 | -1 CH_3OH | 1 | -1 CH_3CO_2H | 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 CO | 1 | -1 | -(Δ[CO])/(Δt) CH_3OH | 1 | -1 | -(Δ[CH3OH])/(Δt) CH_3CO_2H | 1 | 1 | (Δ[CH3CO2H])/(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[CO])/(Δt) = -(Δ[CH3OH])/(Δt) = (Δ[CH3CO2H])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon monoxide | methanol | acetic acid formula | CO | CH_3OH | CH_3CO_2H Hill formula | CO | CH_4O | C_2H_4O_2 name | carbon monoxide | methanol | acetic acid