Question Detail
Question
At 25°C, the second-order reaction NOCl(g) → NO(g) + ½Cl₂(g) is 50% complete after 5.82 hours when the initial concentration of NOCl is 4.46 mol/L. How long will it take for the reaction to be 75% complete?
Correct Answer
Option D is the correct answer.
Detailed Explanation
For second-order, t₁/₂ = 1/(k[A]₀). First, find k: 5.82 hr = 1/(k × 4.46) → k = 1/(5.82×4.46) = 1/25.96 = 0.0385 M⁻¹hr⁻¹. For 75% complete, 25% remains, so [A] = 0.25[A]₀. Integrated rate law: 1/[A] - 1/[A]₀ = kt. 1/(0.25×4.46) - 1/4.46 = 0.0385 t. 1/1.115 - 0.224 = 0.897 - 0.224 = 0.673 = 0.0385 t. t = 0.673/0.0385 = 17.48 hr ≈ 17.5 hr.
Hint
Use second-order integrated rate law.