Our atmosphere is composed primarily of nitrogen and oxygen, which coexist at 25°C without reacting to any significant extent. However, the two gases can react to form nitrogen monoxide according to the reaction: N2 (g) + O2 (g) = 2 NO (g)

a. Calculate AGⓇ and K, for this reaction at 298 K. Is the reaction spontaneous?

b. Estimate AGⓇ at 2000 K. Does the reaction become more spontaneous as temperature increases?

a) T = 298 K

⇒ ΔG° = 173.1 KJ/mol

∴ ΔG° > 0 ... the reaction occurs spontaneously in the reverse direction as given.

⇒ K = 4.542 E-31

b) T = 2000 K:

⇒ ΔG° = 1161.745 KJ/mol

ΔG° (2000K) > 0; We confirm that the reaction becomes more spontaneous as the temperature increases.

Explanation:

N2 (g) + O2 (g) → 2 NO (g)

a) ΔG° (298K) = 2 ΔG°fNO = 2 (86.55 KJ/mol)

⇒ ΔG° (298K) = 173.1 KJ/mol

∴ ΔG° > 0 ... the reaction is spontaneous

K = e∧ (-ΔG°/RT)

∴ R = 8.314 E-3 KJ/mol. K

⇒ K = e∧ (-173.1 / (8.314E-3) (298)) = 4.542 E-31

b) T = 2000 K

ΔG° = - (LnK) (RT)

⇒ ΔG° (2000K) = - (Ln (4.542 E-31)) (8.314 E-3 KJ/mol. K) (2000K)

⇒ ΔG° (2000K) = 1161.745 KJ/mol

∴ ΔG° (2000K) > 0; We confirm that the reaction becomes more spontaneous as the temperature increases