CO2 + CH4 = H2 + CO

CO_2 carbon dioxide + CH_4 methane ⟶ H_2 hydrogen + CO carbon monoxide

Balance the chemical equation algebraically: CO_2 + CH_4 ⟶ H_2 + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 + c_2 CH_4 ⟶ c_3 H_2 + c_4 CO 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 = c_4 O: | 2 c_1 = c_4 H: | 4 c_2 = 2 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 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CO_2 + CH_4 ⟶ 2 H_2 + 2 CO

+ ⟶ +

carbon dioxide + methane ⟶ hydrogen + carbon monoxide

| carbon dioxide | methane | hydrogen | carbon monoxide molecular enthalpy | -393.5 kJ/mol | -74.6 kJ/mol | 0 kJ/mol | -110.5 kJ/mol total enthalpy | -393.5 kJ/mol | -74.6 kJ/mol | 0 kJ/mol | -221 kJ/mol | H_initial = -468.1 kJ/mol | | H_final = -221 kJ/mol | ΔH_rxn^0 | -221 kJ/mol - -468.1 kJ/mol = 247.1 kJ/mol (endothermic) | | |

| carbon dioxide | methane | hydrogen | carbon monoxide molecular free energy | -394.4 kJ/mol | -51 kJ/mol | 0 kJ/mol | -137 kJ/mol total free energy | -394.4 kJ/mol | -51 kJ/mol | 0 kJ/mol | -274 kJ/mol | G_initial = -445.4 kJ/mol | | G_final = -274 kJ/mol | ΔG_rxn^0 | -274 kJ/mol - -445.4 kJ/mol = 171.4 kJ/mol (endergonic) | | |

| carbon dioxide | methane | hydrogen | carbon monoxide molecular entropy | 214 J/(mol K) | 186 J/(mol K) | 115 J/(mol K) | 198 J/(mol K) total entropy | 214 J/(mol K) | 186 J/(mol K) | 230 J/(mol K) | 396 J/(mol K) | S_initial = 400 J/(mol K) | | S_final = 626 J/(mol K) | ΔS_rxn^0 | 626 J/(mol K) - 400 J/(mol K) = 226 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: CO_2 + CH_4 ⟶ H_2 + CO 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_2 + CH_4 ⟶ 2 H_2 + 2 CO 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_2 | 1 | -1 CH_4 | 1 | -1 H_2 | 2 | 2 CO | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO_2 | 1 | -1 | ([CO2])^(-1) CH_4 | 1 | -1 | ([CH4])^(-1) H_2 | 2 | 2 | ([H2])^2 CO | 2 | 2 | ([CO])^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 = ([CO2])^(-1) ([CH4])^(-1) ([H2])^2 ([CO])^2 = (([H2])^2 ([CO])^2)/([CO2] [CH4])

Construct the rate of reaction expression for: CO_2 + CH_4 ⟶ H_2 + CO 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_2 + CH_4 ⟶ 2 H_2 + 2 CO 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_2 | 1 | -1 CH_4 | 1 | -1 H_2 | 2 | 2 CO | 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 CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) CH_4 | 1 | -1 | -(Δ[CH4])/(Δt) H_2 | 2 | 2 | 1/2 (Δ[H2])/(Δt) CO | 2 | 2 | 1/2 (Δ[CO])/(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[CO2])/(Δt) = -(Δ[CH4])/(Δt) = 1/2 (Δ[H2])/(Δt) = 1/2 (Δ[CO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon dioxide | methane | hydrogen | carbon monoxide formula | CO_2 | CH_4 | H_2 | CO name | carbon dioxide | methane | hydrogen | carbon monoxide IUPAC name | carbon dioxide | methane | molecular hydrogen | carbon monoxide