Nitrogen forms many oxides, some of which are significant in the formation of photochemical smog. Th — Thermodynamics / Equilibrium Chemistry Question
Problem Context
Nitrogen forms many oxides, some of which are significant in the formation of photochemical smog. The ∆Hf° and ∆Gf° values for several of these nitrogen oxides are given in the table below.
Calculate the enthalpy and free energy changes at 25.0 °C for the
i. formation of NO2(g) from NO(g) and O2(g).
Model Answer
NO (g) + ½ O2 (g) → NO2 (g)
∆Hºrxn = 33.85 kJ/mol – 90.37 kJ/mol = –56.52 kJ/mol
∆Gºrxn = 51.84 kJ/mol – 86.71 kJ/mol = –34.87 kJ/mol
ii. dimerization of NO2(g) to form N2O4(g).
Model Answer
2 NO2 (g) → N2O4 (g)
∆Hºrxn = 9.66 kJ/mol – 2(33.85 kJ/mol) = –58.04 kJ/mol
∆Gºrxn = 98.29 kJ/mol – 2(51.84 kJ/mol) = –5.39 kJ/mol
Calculate the equilibrium constant for the dimerization of NO2(g) at 25.0 °C.
Model Answer
∆Gº = –RT ln Keq Since the standard state for gases is 1 atm pressure, Keq = Kp
–5390 J/mol = –(8.314 J/mol•K)(298 K) ln Kp
2.176 = ln Kp
Kp = 8.81
For an atmospheric concentration of NO2 equal to 30. ppb (1.2 x 10–9 M) at 298 K, calculate the equilibrium concentration of N2O4.
Model Answer
Kp = p(N2O4) / p(NO2)^2 = 8.81. If there is 30 ppb NO2, p(NO2) = (30 × 10^-9) × (1 atm) = 3.0 × 10^-8 atm
p(N2O4) = 8.81 × (3.0 × 10^-8)^2 = 7.9 × 10^-15 atm = 7.9 × 10^-6 ppb
[N2O4] = n/V = P/(RT) = 7.9 × 10^-15 atm / (0.0821 L atm mol^-1 K^-1)(298 K) = 3.2 × 10^-16 mol/L
If the atmospheric temperature increases to 43.0 °C and equilibrium is established, does the new concentration of nitrogen dioxide formed from conversion of N2O4 exceed the EPA limit of 53 ppb (2.2 × 10–9 M)? Explain.
Model Answer
No. There is so little N2O4 (about 10 parts per billion of the total NO2!) that even if it all dissociates, it will have a negligible effect on the [NO2], which will remain 30 ppb (all the gases in the atmosphere change volume with temperature to approximately the same extent).
The positive ∆Gf° for NO2 indicates that its decomposition to form the elements N2 and O2 is spontaneous. Suggest a reason that this process does not occur to a significant extent in the atmosphere once NO2 has been formed.
Model Answer
While the decomposition may be thermodynamically favorable, the reaction may be kinetically limited. That is, the reaction could lack a sufficient pathway (mechanism) to allow it to proceed.