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  4. At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was fund to be 170 s. The order of the reaction is . [integer answer]

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Q. At $345\, K$, the half life for the decomposition of a sample of a gaseous compound initially at $55.5\, kPa$ was $340\, s$. When the pressure was $27.8 \,kPa$, the half life was fund to be $170\, s$. The order of the reaction is ____. [integer answer]

JEE MainJEE Main 2022Chemical Kinetics

Solution:

$t _{1 / 2} \times \frac{1}{\left[ P _{0}\right]^{ n -1}}$
$\frac{ t _{1}}{ t _{2}}=\frac{\left( P _{2}\right)^{ n -1}}{\left( P _{1}\right)^{ n -1}}$
$\frac{340}{170}=\left(\frac{27.8}{55.5}\right)^{ n -1}$
$\Rightarrow 2=\frac{1}{(2)^{ n -1}}$
$n =0$