Question

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a 'k' value of 3.3 × 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)

Options

• 25

• 26

• 27

• 28

Answer 1

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a 'k' value of 3.3 × 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 26.

Explanation:

For first order reaction,

K = ${\displaystyle \frac{2.303}{\text{t}}\log \frac{\text{a}}{\text{a}-\text{x}}}$

⇒ t = ${\displaystyle \frac{2.303}{3.3\times {10}^{-4}}\log \frac{1}{0.6}}$

= ${\displaystyle \frac{2.303\times 0.22}{3.3\times {10}^{-4}}}$

= 0.1554 × 10⁴

= 1554 sec

= ${\displaystyle \frac{1554}{60}}$

= 25.9 minutes

= 26 minutes