H2O + C = H2 + CO2

H_2O water + C activated charcoal ⟶ H_2 hydrogen + CO_2 carbon dioxide

Balance the chemical equation algebraically: H_2O + C ⟶ H_2 + CO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 C ⟶ 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 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + C ⟶ 2 H_2 + CO_2

+ ⟶ +

water + activated charcoal ⟶ hydrogen + carbon dioxide

Construct the equilibrium constant, K, expression for: H_2O + C ⟶ 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: 2 H_2O + C ⟶ 2 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 | 2 | -2 C | 1 | -1 H_2 | 2 | 2 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 | 2 | -2 | ([H2O])^(-2) C | 1 | -1 | ([C])^(-1) H_2 | 2 | 2 | ([H2])^2 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])^(-2) ([C])^(-1) ([H2])^2 [CO2] = (([H2])^2 [CO2])/(([H2O])^2 [C])

Construct the rate of reaction expression for: H_2O + C ⟶ 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: 2 H_2O + C ⟶ 2 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 | 2 | -2 C | 1 | -1 H_2 | 2 | 2 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) H_2 | 2 | 2 | 1/2 (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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[C])/(Δt) = 1/2 (Δ[H2])/(Δt) = (Δ[CO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | activated charcoal | hydrogen | carbon dioxide formula | H_2O | C | H_2 | CO_2 name | water | activated charcoal | hydrogen | carbon dioxide IUPAC name | water | carbon | molecular hydrogen | carbon dioxide