H2 + C6H5CH3 = CH4 + C6H6

H_2 hydrogen + C_6H_5CH_3 toluene ⟶ CH_4 methane + C_6H_6 benzene

Balance the chemical equation algebraically: H_2 + C_6H_5CH_3 ⟶ CH_4 + C_6H_6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 C_6H_5CH_3 ⟶ c_3 CH_4 + c_4 C_6H_6 Set the number of atoms in the reactants equal to the number of atoms in the products for H and C: H: | 2 c_1 + 8 c_2 = 4 c_3 + 6 c_4 C: | 7 c_2 = c_3 + 6 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_3 = c_2/3 + 2/3 c_4 = (10 c_2)/9 - 1/9 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 1 and solve 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 + C_6H_5CH_3 ⟶ CH_4 + C_6H_6

+ ⟶ +

hydrogen + toluene ⟶ methane + benzene

Construct the equilibrium constant, K, expression for: H_2 + C_6H_5CH_3 ⟶ CH_4 + C_6H_6 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 + C_6H_5CH_3 ⟶ CH_4 + C_6H_6 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 C_6H_5CH_3 | 1 | -1 CH_4 | 1 | 1 C_6H_6 | 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) C_6H_5CH_3 | 1 | -1 | ([C6H5CH3])^(-1) CH_4 | 1 | 1 | [CH4] C_6H_6 | 1 | 1 | [C6H6] 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) ([C6H5CH3])^(-1) [CH4] [C6H6] = ([CH4] [C6H6])/([H2] [C6H5CH3])

Construct the rate of reaction expression for: H_2 + C_6H_5CH_3 ⟶ CH_4 + C_6H_6 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 + C_6H_5CH_3 ⟶ CH_4 + C_6H_6 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 C_6H_5CH_3 | 1 | -1 CH_4 | 1 | 1 C_6H_6 | 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) C_6H_5CH_3 | 1 | -1 | -(Δ[C6H5CH3])/(Δt) CH_4 | 1 | 1 | (Δ[CH4])/(Δt) C_6H_6 | 1 | 1 | (Δ[C6H6])/(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[C6H5CH3])/(Δt) = (Δ[CH4])/(Δt) = (Δ[C6H6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | toluene | methane | benzene formula | H_2 | C_6H_5CH_3 | CH_4 | C_6H_6 Hill formula | H_2 | C_7H_8 | CH_4 | C_6H_6 name | hydrogen | toluene | methane | benzene IUPAC name | molecular hydrogen | methylbenzene | methane | benzene