H2O + C = H2 + CO2 + CO

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

Balance the chemical equation algebraically: H_2O + C ⟶ H_2 + CO_2 + CO 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 + c_5 CO 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_5 C: | c_2 = c_4 + c_5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1 - 1 c_3 = c_1 c_4 = 1 c_5 = c_1 - 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 C ⟶ 3 H_2 + CO_2 + CO

+ ⟶ + +

water + activated charcoal ⟶ hydrogen + carbon dioxide + carbon monoxide

Construct the equilibrium constant, K, expression for: H_2O + C ⟶ H_2 + CO_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: 3 H_2O + 2 C ⟶ 3 H_2 + CO_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 H_2O | 3 | -3 C | 2 | -2 H_2 | 3 | 3 CO_2 | 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_2O | 3 | -3 | ([H2O])^(-3) C | 2 | -2 | ([C])^(-2) H_2 | 3 | 3 | ([H2])^3 CO_2 | 1 | 1 | [CO2] 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 = ([H2O])^(-3) ([C])^(-2) ([H2])^3 [CO2] [CO] = (([H2])^3 [CO2] [CO])/(([H2O])^3 ([C])^2)

Construct the rate of reaction expression for: H_2O + C ⟶ H_2 + CO_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: 3 H_2O + 2 C ⟶ 3 H_2 + CO_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 H_2O | 3 | -3 C | 2 | -2 H_2 | 3 | 3 CO_2 | 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_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) C | 2 | -2 | -1/2 (Δ[C])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[C])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[CO2])/(Δt) = (Δ[CO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

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