JEE MAIN - Chemistry (2021 - 24th February Morning Shift - No. 22)
Gaseous cyclobutene isomerises 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)
(Rounded off to the nearest integer)
Answer
26
Explanation
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It is a first order isomerisation reaction. Integrated rate law for 1st order reaction is
$$kt = \ln {{{{[A]}_0}} \over {{{[A]}_t}}}$$ ...(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
$$3.3 \times {10^{ - 4}}{s^{ - 1}} \times t = \ln {{100} \over {60}}$$
t = 1547.95 s = 25.79 min (1 min = 60 s or 1s = $${1 \over {60}}$$ min) = 26 minutes
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