NO2 = O2 + N2

NO_2 nitrogen dioxide ⟶ O_2 oxygen + N_2 nitrogen

Balance the chemical equation algebraically: NO_2 ⟶ O_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NO_2 ⟶ c_2 O_2 + c_3 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for N and O: N: | c_1 = 2 c_3 O: | 2 c_1 = 2 c_2 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NO_2 ⟶ 2 O_2 + N_2

⟶ +

nitrogen dioxide ⟶ oxygen + nitrogen

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

| nitrogen dioxide | oxygen | nitrogen molecular free energy | 51.3 kJ/mol | 231.7 kJ/mol | 0 kJ/mol total free energy | 102.6 kJ/mol | 463.4 kJ/mol | 0 kJ/mol | G_initial = 102.6 kJ/mol | G_final = 463.4 kJ/mol | ΔG_rxn^0 | 463.4 kJ/mol - 102.6 kJ/mol = 360.8 kJ/mol (endergonic) | |

| nitrogen dioxide | oxygen | nitrogen molecular entropy | 240 J/(mol K) | 205 J/(mol K) | 192 J/(mol K) total entropy | 480 J/(mol K) | 410 J/(mol K) | 192 J/(mol K) | S_initial = 480 J/(mol K) | S_final = 602 J/(mol K) | ΔS_rxn^0 | 602 J/(mol K) - 480 J/(mol K) = 122 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: NO_2 ⟶ O_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: 2 NO_2 ⟶ 2 O_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 NO_2 | 2 | -2 O_2 | 2 | 2 N_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NO_2 | 2 | -2 | ([NO2])^(-2) O_2 | 2 | 2 | ([O2])^2 N_2 | 1 | 1 | [N2] 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 = ([NO2])^(-2) ([O2])^2 [N2] = (([O2])^2 [N2])/([NO2])^2

Construct the rate of reaction expression for: NO_2 ⟶ O_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: 2 NO_2 ⟶ 2 O_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 NO_2 | 2 | -2 O_2 | 2 | 2 N_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 NO_2 | 2 | -2 | -1/2 (Δ[NO2])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) N_2 | 1 | 1 | (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 = -1/2 (Δ[NO2])/(Δt) = 1/2 (Δ[O2])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitrogen dioxide | oxygen | nitrogen formula | NO_2 | O_2 | N_2 name | nitrogen dioxide | oxygen | nitrogen IUPAC name | Nitrogen dioxide | molecular oxygen | molecular nitrogen

| nitrogen dioxide | oxygen | nitrogen molar mass | 46.005 g/mol | 31.998 g/mol | 28.014 g/mol phase | gas (at STP) | gas (at STP) | gas (at STP) melting point | -11 °C | -218 °C | -210 °C boiling point | 21 °C | -183 °C | -195.79 °C density | 0.00188 g/cm^3 (at 25 °C) | 0.001429 g/cm^3 (at 0 °C) | 0.001251 g/cm^3 (at 0 °C) solubility in water | reacts | | insoluble surface tension | | 0.01347 N/m | 0.0066 N/m dynamic viscosity | 4.02×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) odor | | odorless | odorless