HNO3 + C7H9 = H2O + C7H6(NO2)3

HNO_3 nitric acid + C7H9 ⟶ H_2O water + C7H6(NO2)3

Balance the chemical equation algebraically: HNO_3 + C7H9 ⟶ H_2O + C7H6(NO2)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 C7H9 ⟶ c_3 H_2O + c_4 C7H6(NO2)3 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 + 9 c_2 = 2 c_3 + 6 c_4 N: | c_1 = 3 c_4 O: | 3 c_1 = c_3 + 6 c_4 C: | 7 c_2 = 7 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 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 HNO_3 + C7H9 ⟶ 3 H_2O + C7H6(NO2)3

+ C7H9 ⟶ + C7H6(NO2)3

nitric acid + C7H9 ⟶ water + C7H6(NO2)3

Construct the equilibrium constant, K, expression for: HNO_3 + C7H9 ⟶ H_2O + C7H6(NO2)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: 3 HNO_3 + C7H9 ⟶ 3 H_2O + C7H6(NO2)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 HNO_3 | 3 | -3 C7H9 | 1 | -1 H_2O | 3 | 3 C7H6(NO2)3 | 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 | 3 | -3 | ([HNO3])^(-3) C7H9 | 1 | -1 | ([C7H9])^(-1) H_2O | 3 | 3 | ([H2O])^3 C7H6(NO2)3 | 1 | 1 | [C7H6(NO2)3] 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])^(-3) ([C7H9])^(-1) ([H2O])^3 [C7H6(NO2)3] = (([H2O])^3 [C7H6(NO2)3])/(([HNO3])^3 [C7H9])

Construct the rate of reaction expression for: HNO_3 + C7H9 ⟶ H_2O + C7H6(NO2)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: 3 HNO_3 + C7H9 ⟶ 3 H_2O + C7H6(NO2)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 HNO_3 | 3 | -3 C7H9 | 1 | -1 H_2O | 3 | 3 C7H6(NO2)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 HNO_3 | 3 | -3 | -1/3 (Δ[HNO3])/(Δt) C7H9 | 1 | -1 | -(Δ[C7H9])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) C7H6(NO2)3 | 1 | 1 | (Δ[C7H6(NO2)3])/(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 = -1/3 (Δ[HNO3])/(Δt) = -(Δ[C7H9])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[C7H6(NO2)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | C7H9 | water | C7H6(NO2)3 formula | HNO_3 | C7H9 | H_2O | C7H6(NO2)3 Hill formula | HNO_3 | C7H9 | H_2O | C7H6N3O6 name | nitric acid | | water |

| nitric acid | C7H9 | water | C7H6(NO2)3 molar mass | 63.012 g/mol | 93.15 g/mol | 18.015 g/mol | 228.14 g/mol phase | liquid (at STP) | | liquid (at STP) | melting point | -41.6 °C | | 0 °C | boiling point | 83 °C | | 99.9839 °C | density | 1.5129 g/cm^3 | | 1 g/cm^3 | solubility in water | miscible | | | surface tension | | | 0.0728 N/m | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |