O2 + C6H5CH(CH3)2 = C6H5OH + (CH3)2CO

O_2 oxygen + C_6H_5CH(CH_3)_2 cumene ⟶ C_6H_5OH phenol + CH_3COCH_3 acetone

Balance the chemical equation algebraically: O_2 + C_6H_5CH(CH_3)_2 ⟶ C_6H_5OH + CH_3COCH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 C_6H_5CH(CH_3)_2 ⟶ c_3 C_6H_5OH + c_4 CH_3COCH_3 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 + c_4 C: | 9 c_2 = 6 c_3 + 3 c_4 H: | 12 c_2 = 6 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_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + C_6H_5CH(CH_3)_2 ⟶ C_6H_5OH + CH_3COCH_3

+ ⟶ +

oxygen + cumene ⟶ phenol + acetone

Construct the equilibrium constant, K, expression for: O_2 + C_6H_5CH(CH_3)_2 ⟶ C_6H_5OH + CH_3COCH_3 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: O_2 + C_6H_5CH(CH_3)_2 ⟶ C_6H_5OH + CH_3COCH_3 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 | 1 | -1 C_6H_5CH(CH_3)_2 | 1 | -1 C_6H_5OH | 1 | 1 CH_3COCH_3 | 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 | 1 | -1 | ([O2])^(-1) C_6H_5CH(CH_3)_2 | 1 | -1 | ([C6H5CH(CH3)2])^(-1) C_6H_5OH | 1 | 1 | [C6H5OH] CH_3COCH_3 | 1 | 1 | [CH3COCH3] 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])^(-1) ([C6H5CH(CH3)2])^(-1) [C6H5OH] [CH3COCH3] = ([C6H5OH] [CH3COCH3])/([O2] [C6H5CH(CH3)2])

Construct the rate of reaction expression for: O_2 + C_6H_5CH(CH_3)_2 ⟶ C_6H_5OH + CH_3COCH_3 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: O_2 + C_6H_5CH(CH_3)_2 ⟶ C_6H_5OH + CH_3COCH_3 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 | 1 | -1 C_6H_5CH(CH_3)_2 | 1 | -1 C_6H_5OH | 1 | 1 CH_3COCH_3 | 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 | 1 | -1 | -(Δ[O2])/(Δt) C_6H_5CH(CH_3)_2 | 1 | -1 | -(Δ[C6H5CH(CH3)2])/(Δt) C_6H_5OH | 1 | 1 | (Δ[C6H5OH])/(Δt) CH_3COCH_3 | 1 | 1 | (Δ[CH3COCH3])/(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[O2])/(Δt) = -(Δ[C6H5CH(CH3)2])/(Δt) = (Δ[C6H5OH])/(Δt) = (Δ[CH3COCH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | cumene | phenol | acetone formula | O_2 | C_6H_5CH(CH_3)_2 | C_6H_5OH | CH_3COCH_3 Hill formula | O_2 | C_9H_12 | C_6H_6O | C_3H_6O name | oxygen | cumene | phenol | acetone IUPAC name | molecular oxygen | isopropylbenzene | phenol | acetone