H2 + CO2 = H2O + CO

H_2 hydrogen + CO_2 carbon dioxide ⟶ H_2O water + CO carbon monoxide

Balance the chemical equation algebraically: H_2 + CO_2 ⟶ H_2O + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 CO_2 ⟶ c_3 H_2O + c_4 CO Set the number of atoms in the reactants equal to the number of atoms in the products for H, C and O: H: | 2 c_1 = 2 c_3 C: | c_2 = c_4 O: | 2 c_2 = c_3 + 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: | | H_2 + CO_2 ⟶ H_2O + CO

+ ⟶ +

hydrogen + carbon dioxide ⟶ water + carbon monoxide

| hydrogen | carbon dioxide | water | carbon monoxide molecular enthalpy | 0 kJ/mol | -393.5 kJ/mol | -285.8 kJ/mol | -110.5 kJ/mol total enthalpy | 0 kJ/mol | -393.5 kJ/mol | -285.8 kJ/mol | -110.5 kJ/mol | H_initial = -393.5 kJ/mol | | H_final = -396.3 kJ/mol | ΔH_rxn^0 | -396.3 kJ/mol - -393.5 kJ/mol = -2.83 kJ/mol (exothermic) | | |

| hydrogen | carbon dioxide | water | carbon monoxide molecular free energy | 0 kJ/mol | -394.4 kJ/mol | -237.1 kJ/mol | -137 kJ/mol total free energy | 0 kJ/mol | -394.4 kJ/mol | -237.1 kJ/mol | -137 kJ/mol | G_initial = -394.4 kJ/mol | | G_final = -374.1 kJ/mol | ΔG_rxn^0 | -374.1 kJ/mol - -394.4 kJ/mol = 20.3 kJ/mol (endergonic) | | |

| hydrogen | carbon dioxide | water | carbon monoxide molecular entropy | 115 J/(mol K) | 214 J/(mol K) | 69.91 J/(mol K) | 198 J/(mol K) total entropy | 115 J/(mol K) | 214 J/(mol K) | 69.91 J/(mol K) | 198 J/(mol K) | S_initial = 329 J/(mol K) | | S_final = 267.9 J/(mol K) | ΔS_rxn^0 | 267.9 J/(mol K) - 329 J/(mol K) = -61.09 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: H_2 + CO_2 ⟶ H_2O + 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: H_2 + CO_2 ⟶ H_2O + 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 H_2 | 1 | -1 CO_2 | 1 | -1 H_2O | 1 | 1 CO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 1 | -1 | ([H2])^(-1) CO_2 | 1 | -1 | ([CO2])^(-1) H_2O | 1 | 1 | [H2O] CO | 1 | 1 | [CO] 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 = ([H2])^(-1) ([CO2])^(-1) [H2O] [CO] = ([H2O] [CO])/([H2] [CO2])

Construct the rate of reaction expression for: H_2 + CO_2 ⟶ H_2O + 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: H_2 + CO_2 ⟶ H_2O + 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 H_2 | 1 | -1 CO_2 | 1 | -1 H_2O | 1 | 1 CO | 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 H_2 | 1 | -1 | -(Δ[H2])/(Δt) CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO | 1 | 1 | (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[H2])/(Δt) = -(Δ[CO2])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | carbon dioxide | water | carbon monoxide formula | H_2 | CO_2 | H_2O | CO name | hydrogen | carbon dioxide | water | carbon monoxide IUPAC name | molecular hydrogen | carbon dioxide | water | carbon monoxide