O2 + NO = NO2

O_2 (oxygen) + NO (nitric oxide) ⟶ NO_2 (nitrogen dioxide)

Balance the chemical equation algebraically: O_2 + NO ⟶ NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 NO ⟶ c_3 NO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O and N: O: | 2 c_1 + c_2 = 2 c_3 N: | c_2 = c_3 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 = 2 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + 2 NO ⟶ 2 NO_2

+ ⟶

oxygen + nitric oxide ⟶ nitrogen dioxide

| oxygen | nitric oxide | nitrogen dioxide molecular enthalpy | 0 kJ/mol | 91.3 kJ/mol | 33.2 kJ/mol total enthalpy | 0 kJ/mol | 182.6 kJ/mol | 66.4 kJ/mol | H_initial = 182.6 kJ/mol | | H_final = 66.4 kJ/mol ΔH_rxn^0 | 66.4 kJ/mol - 182.6 kJ/mol = -116.2 kJ/mol (exothermic) | |

| oxygen | nitric oxide | nitrogen dioxide molecular free energy | 231.7 kJ/mol | 87.6 kJ/mol | 51.3 kJ/mol total free energy | 231.7 kJ/mol | 175.2 kJ/mol | 102.6 kJ/mol | G_initial = 406.9 kJ/mol | | G_final = 102.6 kJ/mol ΔG_rxn^0 | 102.6 kJ/mol - 406.9 kJ/mol = -304.3 kJ/mol (exergonic) | |

| oxygen | nitric oxide | nitrogen dioxide molecular entropy | 205 J/(mol K) | 211 J/(mol K) | 240 J/(mol K) total entropy | 205 J/(mol K) | 422 J/(mol K) | 480 J/(mol K) | S_initial = 627 J/(mol K) | | S_final = 480 J/(mol K) ΔS_rxn^0 | 480 J/(mol K) - 627 J/(mol K) = -147 J/(mol K) (exoentropic) | |

Construct the equilibrium constant, K, expression for: O_2 + NO ⟶ 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: O_2 + 2 NO ⟶ 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 | 1 | -1 NO | 2 | -2 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 | 1 | -1 | ([O2])^(-1) NO | 2 | -2 | ([NO])^(-2) 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])^(-1) ([NO])^(-2) ([NO2])^2 = ([NO2])^2/([O2] ([NO])^2)

Construct the rate of reaction expression for: O_2 + NO ⟶ 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: O_2 + 2 NO ⟶ 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 | 1 | -1 NO | 2 | -2 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 | 1 | -1 | -(Δ[O2])/(Δt) NO | 2 | -2 | -1/2 (Δ[NO])/(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 = -(Δ[O2])/(Δt) = -1/2 (Δ[NO])/(Δt) = 1/2 (Δ[NO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | nitric oxide | nitrogen dioxide formula | O_2 | NO | NO_2 name | oxygen | nitric oxide | nitrogen dioxide IUPAC name | molecular oxygen | nitric oxide | Nitrogen dioxide

| oxygen | nitric oxide | nitrogen dioxide molar mass | 31.998 g/mol | 30.006 g/mol | 46.005 g/mol phase | gas (at STP) | gas (at STP) | gas (at STP) melting point | -218 °C | -163.6 °C | -11 °C boiling point | -183 °C | -151.7 °C | 21 °C density | 0.001429 g/cm^3 (at 0 °C) | 0.001226 g/cm^3 (at 25 °C) | 0.00188 g/cm^3 (at 25 °C) solubility in water | | | reacts surface tension | 0.01347 N/m | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | 1.911×10^-5 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) odor | odorless | |