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  4. The half life for the decomposition of gaseous compound A is 240 s when the gaseous pressure was 500 Torr initially. When the pressure was 250 Torr, the half life was found to be 4.0 min. The order of the reaction is....... (Nearest integer)

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Q. The half life for the decomposition of gaseous compound $A$ is $240\, s$ when the gaseous pressure was $500$ Torr initially. When the pressure was $250$ Torr, the half life was found to be $4.0\, \min$. The order of the reaction is....... (Nearest integer)

JEE MainJEE Main 2022Chemical Kinetics

Solution:

$\left( t _{1 / 2}\right)_{500 \text { torr }}=240 \,\sec =4\,\min$.
$\left( t _{1 / 2}\right)_{250 \text { torr }}=4 \,\min$.
$t _{1 / 2} \propto a ^{1- n }$
As $t_{1 / 2}$ is independent of initial pressure. Hence, order is $1 st$ order.