O2 + CH3NO2 = H2O + CO2 + N2

O_2 oxygen + CH_3NO_2 nitromethane ⟶ H_2O water + CO_2 carbon dioxide + N_2 nitrogen

Balance the chemical equation algebraically: O_2 + CH_3NO_2 ⟶ H_2O + CO_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 CH_3NO_2 ⟶ c_3 H_2O + c_4 CO_2 + c_5 N_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 + 2 c_2 = c_3 + 2 c_4 C: | c_2 = c_4 H: | 3 c_2 = 2 c_3 N: | c_2 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 2 c_3 = 3 c_4 = 2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 4 c_3 = 6 c_4 = 4 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 4 CH_3NO_2 ⟶ 6 H_2O + 4 CO_2 + 2 N_2

+ ⟶ + +

oxygen + nitromethane ⟶ water + carbon dioxide + nitrogen

| oxygen | nitromethane | water | carbon dioxide | nitrogen molecular free energy | 231.7 kJ/mol | -14.4 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | 0 kJ/mol total free energy | 695.1 kJ/mol | -57.6 kJ/mol | -1423 kJ/mol | -1578 kJ/mol | 0 kJ/mol | G_initial = 637.5 kJ/mol | | G_final = -3000 kJ/mol | | ΔG_rxn^0 | -3000 kJ/mol - 637.5 kJ/mol = -3638 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: O_2 + CH_3NO_2 ⟶ H_2O + CO_2 + N_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: 3 O_2 + 4 CH_3NO_2 ⟶ 6 H_2O + 4 CO_2 + 2 N_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 | 3 | -3 CH_3NO_2 | 4 | -4 H_2O | 6 | 6 CO_2 | 4 | 4 N_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 | 3 | -3 | ([O2])^(-3) CH_3NO_2 | 4 | -4 | ([CH3NO2])^(-4) H_2O | 6 | 6 | ([H2O])^6 CO_2 | 4 | 4 | ([CO2])^4 N_2 | 2 | 2 | ([N2])^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])^(-3) ([CH3NO2])^(-4) ([H2O])^6 ([CO2])^4 ([N2])^2 = (([H2O])^6 ([CO2])^4 ([N2])^2)/(([O2])^3 ([CH3NO2])^4)

Construct the rate of reaction expression for: O_2 + CH_3NO_2 ⟶ H_2O + CO_2 + N_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: 3 O_2 + 4 CH_3NO_2 ⟶ 6 H_2O + 4 CO_2 + 2 N_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 | 3 | -3 CH_3NO_2 | 4 | -4 H_2O | 6 | 6 CO_2 | 4 | 4 N_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 | 3 | -3 | -1/3 (Δ[O2])/(Δt) CH_3NO_2 | 4 | -4 | -1/4 (Δ[CH3NO2])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) CO_2 | 4 | 4 | 1/4 (Δ[CO2])/(Δt) N_2 | 2 | 2 | 1/2 (Δ[N2])/(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[O2])/(Δt) = -1/4 (Δ[CH3NO2])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/4 (Δ[CO2])/(Δt) = 1/2 (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | nitromethane | water | carbon dioxide | nitrogen formula | O_2 | CH_3NO_2 | H_2O | CO_2 | N_2 name | oxygen | nitromethane | water | carbon dioxide | nitrogen IUPAC name | molecular oxygen | nitromethane | water | carbon dioxide | molecular nitrogen