H2O2 + C6H6 = H2O + CO2

H_2O_2 hydrogen peroxide + C_6H_6 benzene ⟶ H_2O water + CO_2 carbon dioxide

Balance the chemical equation algebraically: H_2O_2 + C_6H_6 ⟶ H_2O + CO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 C_6H_6 ⟶ c_3 H_2O + c_4 CO_2 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 + 6 c_2 = 2 c_3 O: | 2 c_1 = c_3 + 2 c_4 C: | 6 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 15 c_2 = 1 c_3 = 18 c_4 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 15 H_2O_2 + C_6H_6 ⟶ 18 H_2O + 6 CO_2

+ ⟶ +

hydrogen peroxide + benzene ⟶ water + carbon dioxide

| hydrogen peroxide | benzene | water | carbon dioxide molecular free energy | -120.4 kJ/mol | 124.5 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol total free energy | -1806 kJ/mol | 124.5 kJ/mol | -4268 kJ/mol | -2366 kJ/mol | G_initial = -1682 kJ/mol | | G_final = -6634 kJ/mol | ΔG_rxn^0 | -6634 kJ/mol - -1682 kJ/mol = -4953 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: H_2O_2 + C_6H_6 ⟶ H_2O + CO_2 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: 15 H_2O_2 + C_6H_6 ⟶ 18 H_2O + 6 CO_2 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_2 | 15 | -15 C_6H_6 | 1 | -1 H_2O | 18 | 18 CO_2 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O_2 | 15 | -15 | ([H2O2])^(-15) C_6H_6 | 1 | -1 | ([C6H6])^(-1) H_2O | 18 | 18 | ([H2O])^18 CO_2 | 6 | 6 | ([CO2])^6 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 = ([H2O2])^(-15) ([C6H6])^(-1) ([H2O])^18 ([CO2])^6 = (([H2O])^18 ([CO2])^6)/(([H2O2])^15 [C6H6])

Construct the rate of reaction expression for: H_2O_2 + C_6H_6 ⟶ H_2O + CO_2 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: 15 H_2O_2 + C_6H_6 ⟶ 18 H_2O + 6 CO_2 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_2 | 15 | -15 C_6H_6 | 1 | -1 H_2O | 18 | 18 CO_2 | 6 | 6 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_2 | 15 | -15 | -1/15 (Δ[H2O2])/(Δt) C_6H_6 | 1 | -1 | -(Δ[C6H6])/(Δt) H_2O | 18 | 18 | 1/18 (Δ[H2O])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(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 = -1/15 (Δ[H2O2])/(Δt) = -(Δ[C6H6])/(Δt) = 1/18 (Δ[H2O])/(Δt) = 1/6 (Δ[CO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen peroxide | benzene | water | carbon dioxide formula | H_2O_2 | C_6H_6 | H_2O | CO_2 name | hydrogen peroxide | benzene | water | carbon dioxide