H2O + CO = H2 + CO2

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

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

+ ⟶ +

water + carbon monoxide ⟶ hydrogen + carbon dioxide

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

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

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

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

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

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