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QJEEM22Chcac6: JEE Main 2022 Chemistry - Class 12 JEEM22Chcac6 Solution: At 345 K, the half life for the decomposition of a sample of a…

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 found to be 170 s. The order of the reaction is ____________. [integer answer]

Step-by-Step Verified Solution

t1/2∝1[P0]n−1t_{1 / 2} \propto \frac{1}{\left[P_{0}\right]^{n-1}}

amp;(t1/2)1(t1/2)2=[P0]2n−1[P0]1n−1amp;340170=(27.855.5)n−1amp;2=(12)n−1amp;2=(2)1−namp;1−n=1amp;n=0\begin{aligned}&\frac{\left(\mathrm{t}_{1 / 2}\right)_{1}}{\left(\mathrm{t}_{1 / 2}\right)_{2}}=\frac{\left[\mathrm{P}_{0}\right]_{2}^{\mathrm{n}-1}}{\left[\mathrm{P}_{0}\right]_{1}^{\mathrm{n}-1}} \\\\&\frac{340}{170}=\left(\frac{27.8}{55.5}\right)^{\mathrm{n}-1} \\\\&2=\left(\frac{1}{2}\right)^{\mathrm{n}-1} \\\\&2=(2)^{1-n} \\\\&1-\mathrm{n}=1 \\\\&\mathrm{n}=0\end{aligned}

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