QJEEM21Ch236f: JEE Main 2021 Chemistry - Class 12 JEEM21Ch236f Solution: Gaseous cyclobutene isomerises to butadiene in a first order…

It is a first order isomerisation reaction. Integrated rate law for 1st order reaction is

$$kt=\ln \frac{{[A]}_0}{{[A]}_t}$$ ...(i)

Here,

k = rate constant

$$[A{]}_0$$ = initial concentration

$$[A{]}_t$$ = concentration at time 't'

Given, k = 3.3 $$\times$$ 10^$$-$$4 s^$$-$$1

$$[A{]}_0=100\Rightarrow [A{]}_t=100-40=60$$

Put values in Eq. (i), we get

$$3.3\times {10}^{-4}{s}^{-1}\times t=\ln \frac{100}{60}$$

t = 1547.95 s = 25.79 min (1 min = 60 s or 1s = $$\frac{1}{60}$$ min) = 26 minutes