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

JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Chemical Kinetics

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

3.3 \times 1 0^{- 4} s^{- 1}

15 3^{\circ} 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)

Answer: 26

For a first-order reaction, the time required for x% completion is given by:

t = \frac{2.303}{k} lo g (\frac{100}{100 - x})

Given:

Calculation:

t = \frac{2.303}{3.3 \times 1 0 ^{- 4}} lo g (\frac{100}{60})

= \frac{2.303}{3.3 \times 1 0 ^{- 4}} lo g (1.667)

= \frac{2.303}{3.3 \times 1 0 ^{- 4}} \times 0.222

= \frac{2.303 \times 0.222}{3.3 \times 1 0 ^{- 4}}

= \frac{0.511}{3.3 \times 1 0 ^{- 4}} = 1548 seconds

Converting to minutes:

t = \frac{1548}{60} = 25.8 \approx 26 minutes

Answer: 26

JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Integer answer