O2 + C7H10N = H2O + CO2 + NO2

O_2 oxygen + C7H10N ⟶ H_2O water + CO_2 carbon dioxide + NO_2 nitrogen dioxide

Balance the chemical equation algebraically: O_2 + C7H10N ⟶ H_2O + CO_2 + NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 C7H10N ⟶ c_3 H_2O + c_4 CO_2 + c_5 NO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, C, H and N: O: | 2 c_1 = c_3 + 2 c_4 + 2 c_5 C: | 7 c_2 = c_4 H: | 10 c_2 = 2 c_3 N: | c_2 = 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_1 = 21/2 c_2 = 1 c_3 = 5 c_4 = 7 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 21 c_2 = 2 c_3 = 10 c_4 = 14 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 21 O_2 + 2 C7H10N ⟶ 10 H_2O + 14 CO_2 + 2 NO_2

+ C7H10N ⟶ + +

oxygen + C7H10N ⟶ water + carbon dioxide + nitrogen dioxide

Construct the equilibrium constant, K, expression for: O_2 + C7H10N ⟶ H_2O + CO_2 + NO_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: 21 O_2 + 2 C7H10N ⟶ 10 H_2O + 14 CO_2 + 2 NO_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 O_2 | 21 | -21 C7H10N | 2 | -2 H_2O | 10 | 10 CO_2 | 14 | 14 NO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 21 | -21 | ([O2])^(-21) C7H10N | 2 | -2 | ([C7H10N])^(-2) H_2O | 10 | 10 | ([H2O])^10 CO_2 | 14 | 14 | ([CO2])^14 NO_2 | 2 | 2 | ([NO2])^2 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])^(-21) ([C7H10N])^(-2) ([H2O])^10 ([CO2])^14 ([NO2])^2 = (([H2O])^10 ([CO2])^14 ([NO2])^2)/(([O2])^21 ([C7H10N])^2)

Construct the rate of reaction expression for: O_2 + C7H10N ⟶ H_2O + CO_2 + NO_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: 21 O_2 + 2 C7H10N ⟶ 10 H_2O + 14 CO_2 + 2 NO_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 O_2 | 21 | -21 C7H10N | 2 | -2 H_2O | 10 | 10 CO_2 | 14 | 14 NO_2 | 2 | 2 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 | 21 | -21 | -1/21 (Δ[O2])/(Δt) C7H10N | 2 | -2 | -1/2 (Δ[C7H10N])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) CO_2 | 14 | 14 | 1/14 (Δ[CO2])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(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 = -1/21 (Δ[O2])/(Δt) = -1/2 (Δ[C7H10N])/(Δt) = 1/10 (Δ[H2O])/(Δt) = 1/14 (Δ[CO2])/(Δt) = 1/2 (Δ[NO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | C7H10N | water | carbon dioxide | nitrogen dioxide formula | O_2 | C7H10N | H_2O | CO_2 | NO_2 name | oxygen | | water | carbon dioxide | nitrogen dioxide IUPAC name | molecular oxygen | | water | carbon dioxide | Nitrogen dioxide

| oxygen | C7H10N | water | carbon dioxide | nitrogen dioxide molar mass | 31.998 g/mol | 108.16 g/mol | 18.015 g/mol | 44.009 g/mol | 46.005 g/mol phase | gas (at STP) | | liquid (at STP) | gas (at STP) | gas (at STP) melting point | -218 °C | | 0 °C | -56.56 °C (at triple point) | -11 °C boiling point | -183 °C | | 99.9839 °C | -78.5 °C (at sublimation point) | 21 °C density | 0.001429 g/cm^3 (at 0 °C) | | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 0.00188 g/cm^3 (at 25 °C) solubility in water | | | | | reacts surface tension | 0.01347 N/m | | 0.0728 N/m | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) odor | odorless | | odorless | odorless |