H2O + CH4 = H2 + C3H7COH

H_2O water + CH_4 methane ⟶ H_2 hydrogen + CH_3CH_2CH_2CHO butyraldehyde

Balance the chemical equation algebraically: H_2O + CH_4 ⟶ H_2 + CH_3CH_2CH_2CHO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CH_4 ⟶ c_3 H_2 + c_4 CH_3CH_2CH_2CHO 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 + 4 c_2 = 2 c_3 + 8 c_4 O: | c_1 = c_4 C: | c_2 = 4 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 = 4 c_3 = 5 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 4 CH_4 ⟶ 5 H_2 + CH_3CH_2CH_2CHO

+ ⟶ +

water + methane ⟶ hydrogen + butyraldehyde

Construct the equilibrium constant, K, expression for: H_2O + CH_4 ⟶ H_2 + CH_3CH_2CH_2CHO 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 + 4 CH_4 ⟶ 5 H_2 + CH_3CH_2CH_2CHO 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 CH_4 | 4 | -4 H_2 | 5 | 5 CH_3CH_2CH_2CHO | 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) CH_4 | 4 | -4 | ([CH4])^(-4) H_2 | 5 | 5 | ([H2])^5 CH_3CH_2CH_2CHO | 1 | 1 | [CH3CH2CH2CHO] 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) ([CH4])^(-4) ([H2])^5 [CH3CH2CH2CHO] = (([H2])^5 [CH3CH2CH2CHO])/([H2O] ([CH4])^4)

Construct the rate of reaction expression for: H_2O + CH_4 ⟶ H_2 + CH_3CH_2CH_2CHO 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 + 4 CH_4 ⟶ 5 H_2 + CH_3CH_2CH_2CHO 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 CH_4 | 4 | -4 H_2 | 5 | 5 CH_3CH_2CH_2CHO | 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) CH_4 | 4 | -4 | -1/4 (Δ[CH4])/(Δt) H_2 | 5 | 5 | 1/5 (Δ[H2])/(Δt) CH_3CH_2CH_2CHO | 1 | 1 | (Δ[CH3CH2CH2CHO])/(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) = -1/4 (Δ[CH4])/(Δt) = 1/5 (Δ[H2])/(Δt) = (Δ[CH3CH2CH2CHO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | methane | hydrogen | butyraldehyde formula | H_2O | CH_4 | H_2 | CH_3CH_2CH_2CHO Hill formula | H_2O | CH_4 | H_2 | C_4H_8O name | water | methane | hydrogen | butyraldehyde IUPAC name | water | methane | molecular hydrogen | butanal