CO + CH4 = H2O + C2H2

CO carbon monoxide + CH_4 methane ⟶ H_2O water + C_2H_2 acetylene

Balance the chemical equation algebraically: CO + CH_4 ⟶ H_2O + C_2H_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO + c_2 CH_4 ⟶ c_3 H_2O + c_4 C_2H_2 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_4 O: | c_1 = c_3 H: | 4 c_2 = 2 c_3 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CO + CH_4 ⟶ H_2O + C_2H_2

+ ⟶ +

carbon monoxide + methane ⟶ water + acetylene

| carbon monoxide | methane | water | acetylene molecular enthalpy | -110.5 kJ/mol | -74.6 kJ/mol | -285.8 kJ/mol | 227.4 kJ/mol total enthalpy | -110.5 kJ/mol | -74.6 kJ/mol | -285.8 kJ/mol | 227.4 kJ/mol | H_initial = -185.1 kJ/mol | | H_final = -58.43 kJ/mol | ΔH_rxn^0 | -58.43 kJ/mol - -185.1 kJ/mol = 126.7 kJ/mol (endothermic) | | |

| carbon monoxide | methane | water | acetylene molecular free energy | -137 kJ/mol | -51 kJ/mol | -237.1 kJ/mol | 209.9 kJ/mol total free energy | -137 kJ/mol | -51 kJ/mol | -237.1 kJ/mol | 209.9 kJ/mol | G_initial = -188 kJ/mol | | G_final = -27.2 kJ/mol | ΔG_rxn^0 | -27.2 kJ/mol - -188 kJ/mol = 160.8 kJ/mol (endergonic) | | |

| carbon monoxide | methane | water | acetylene molecular entropy | 198 J/(mol K) | 186 J/(mol K) | 69.91 J/(mol K) | 201 J/(mol K) total entropy | 198 J/(mol K) | 186 J/(mol K) | 69.91 J/(mol K) | 201 J/(mol K) | S_initial = 384 J/(mol K) | | S_final = 270.9 J/(mol K) | ΔS_rxn^0 | 270.9 J/(mol K) - 384 J/(mol K) = -113.1 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: CO + CH_4 ⟶ H_2O + C_2H_2 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_4 ⟶ H_2O + C_2H_2 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_4 | 1 | -1 H_2O | 1 | 1 C_2H_2 | 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_4 | 1 | -1 | ([CH4])^(-1) H_2O | 1 | 1 | [H2O] C_2H_2 | 1 | 1 | [C2H2] 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) ([CH4])^(-1) [H2O] [C2H2] = ([H2O] [C2H2])/([CO] [CH4])

Construct the rate of reaction expression for: CO + CH_4 ⟶ H_2O + C_2H_2 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_4 ⟶ H_2O + C_2H_2 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_4 | 1 | -1 H_2O | 1 | 1 C_2H_2 | 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_4 | 1 | -1 | -(Δ[CH4])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) C_2H_2 | 1 | 1 | (Δ[C2H2])/(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[CH4])/(Δt) = (Δ[H2O])/(Δt) = (Δ[C2H2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon monoxide | methane | water | acetylene formula | CO | CH_4 | H_2O | C_2H_2 name | carbon monoxide | methane | water | acetylene