Question

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?

Answer 1

Answer:

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