HNO3 + C6H6 = H2O + C6H5NO2

HNO_3 nitric acid + C_6H_6 benzene ⟶ H_2O water + C_6H_5NO_2 nitrobenzene

Balance the chemical equation algebraically: HNO_3 + C_6H_6 ⟶ H_2O + C_6H_5NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 C_6H_6 ⟶ c_3 H_2O + c_4 C_6H_5NO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and C: H: | c_1 + 6 c_2 = 2 c_3 + 5 c_4 N: | c_1 = c_4 O: | 3 c_1 = c_3 + 2 c_4 C: | 6 c_2 = 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: | | HNO_3 + C_6H_6 ⟶ H_2O + C_6H_5NO_2

+ ⟶ +

nitric acid + benzene ⟶ water + nitrobenzene

Construct the equilibrium constant, K, expression for: HNO_3 + C_6H_6 ⟶ H_2O + C_6H_5NO_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: HNO_3 + C_6H_6 ⟶ H_2O + C_6H_5NO_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 HNO_3 | 1 | -1 C_6H_6 | 1 | -1 H_2O | 1 | 1 C_6H_5NO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 1 | -1 | ([HNO3])^(-1) C_6H_6 | 1 | -1 | ([C6H6])^(-1) H_2O | 1 | 1 | [H2O] C_6H_5NO_2 | 1 | 1 | [C6H5NO2] 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 = ([HNO3])^(-1) ([C6H6])^(-1) [H2O] [C6H5NO2] = ([H2O] [C6H5NO2])/([HNO3] [C6H6])

Construct the rate of reaction expression for: HNO_3 + C_6H_6 ⟶ H_2O + C_6H_5NO_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: HNO_3 + C_6H_6 ⟶ H_2O + C_6H_5NO_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 HNO_3 | 1 | -1 C_6H_6 | 1 | -1 H_2O | 1 | 1 C_6H_5NO_2 | 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 HNO_3 | 1 | -1 | -(Δ[HNO3])/(Δt) C_6H_6 | 1 | -1 | -(Δ[C6H6])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) C_6H_5NO_2 | 1 | 1 | (Δ[C6H5NO2])/(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[HNO3])/(Δt) = -(Δ[C6H6])/(Δt) = (Δ[H2O])/(Δt) = (Δ[C6H5NO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | benzene | water | nitrobenzene formula | HNO_3 | C_6H_6 | H_2O | C_6H_5NO_2 name | nitric acid | benzene | water | nitrobenzene