Question

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a ${}^{{}^{\prime }}{k}_{}^{{}^{\prime }}$ value of $3.3\times 10^{-4}{s}^{-1}$ at $153^{\circ }C$ . 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 1

Answer: 26

For first order Reaction :-
$t=\frac{2.303}{k}log\left[\frac{100}{100-x}\right]$
$x=40,k=3.3\times 10^{-4}$
$t=\frac{2.303}{3.3\times 10^{-4}}log\left[\frac{100}{60}\right]$
$t=\frac{2.303}{3.3\times 10^{-4}}\times 0.22$
$t=0.15353\times 10^4$
$t=1535\sec =25.6Min\simeq 26\min$ .