O2 + C6H5CH3 = H2O + CO2 + C6H5OH

O_2 oxygen + C_6H_5CH_3 toluene ⟶ H_2O water + CO_2 carbon dioxide + C_6H_5OH phenol

Balance the chemical equation algebraically: O_2 + C_6H_5CH_3 ⟶ H_2O + CO_2 + C_6H_5OH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 C_6H_5CH_3 ⟶ c_3 H_2O + c_4 CO_2 + c_5 C_6H_5OH Set the number of atoms in the reactants equal to the number of atoms in the products for O, C and H: O: | 2 c_1 = c_3 + 2 c_4 + c_5 C: | 7 c_2 = c_4 + 6 c_5 H: | 8 c_2 = 2 c_3 + 6 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_2 = 1 and solve the system of equations for the remaining coefficients: c_2 = 1 c_3 = (3 c_1)/7 + 1/7 c_4 = (6 c_1)/7 - 5/7 c_5 = 9/7 - c_1/7 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 O_2 + C_6H_5CH_3 ⟶ H_2O + CO_2 + C_6H_5OH

+ ⟶ + +

oxygen + toluene ⟶ water + carbon dioxide + phenol

Construct the equilibrium constant, K, expression for: O_2 + C_6H_5CH_3 ⟶ H_2O + CO_2 + C_6H_5OH 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 O_2 + C_6H_5CH_3 ⟶ H_2O + CO_2 + C_6H_5OH 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 O_2 | 2 | -2 C_6H_5CH_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 C_6H_5OH | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 2 | -2 | ([O2])^(-2) C_6H_5CH_3 | 1 | -1 | ([C6H5CH3])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] C_6H_5OH | 1 | 1 | [C6H5OH] 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 = ([O2])^(-2) ([C6H5CH3])^(-1) [H2O] [CO2] [C6H5OH] = ([H2O] [CO2] [C6H5OH])/(([O2])^2 [C6H5CH3])

Construct the rate of reaction expression for: O_2 + C_6H_5CH_3 ⟶ H_2O + CO_2 + C_6H_5OH 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 O_2 + C_6H_5CH_3 ⟶ H_2O + CO_2 + C_6H_5OH 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 O_2 | 2 | -2 C_6H_5CH_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 C_6H_5OH | 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 O_2 | 2 | -2 | -1/2 (Δ[O2])/(Δt) C_6H_5CH_3 | 1 | -1 | -(Δ[C6H5CH3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) C_6H_5OH | 1 | 1 | (Δ[C6H5OH])/(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[O2])/(Δt) = -(Δ[C6H5CH3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[C6H5OH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | toluene | water | carbon dioxide | phenol formula | O_2 | C_6H_5CH_3 | H_2O | CO_2 | C_6H_5OH Hill formula | O_2 | C_7H_8 | H_2O | CO_2 | C_6H_6O name | oxygen | toluene | water | carbon dioxide | phenol IUPAC name | molecular oxygen | methylbenzene | water | carbon dioxide | phenol