Question

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a 'k' value of $3.3 \times 10^{-4} s^{-1}$ at 153°C. The time in minutes it takes for the isomerization to proceed 40% to completion at this temperature is __________. (Rounded off to the nearest integer)

Hint:

Always check the units of the rate constant $k$. Here $s^{-1}$ implies a 1st order reaction. Don't forget to convert final seconds to minutes.

Answer 1

Correct Answer: 26

Step 1: For a 1st order reaction: $t = \frac{1}{k} \ln\left(\frac{[A]_0}{[A]}\right)$.
Step 2: $40%$ completion means $60%$ remains. $[A] = 0.6 [A]_0$.
Step 3: $t = \frac{1}{3.3 \times 10^{-4}} \ln\left(\frac{1}{0.6}\right) = \frac{1}{3.3 \times 10^{-4}} \ln(1.667) = \frac{0.5108}{3.3 \times 10^{-4}} \approx 1548$ seconds.
Step 4: Convert to minutes: $1548 / 60 \approx 25.8$ minutes.
Step 5: Nearest integer is 26.