At a certain temperature,the half-life period | vedclass

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(C) For a reaction of order $n$,the half-life period $(t_{1/2})$ is related to the initial pressure $(P)$ as $(t_{1/2}) \propto P^{1-n}$.Using the dat

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$70$

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(C) For a reaction of order $n$,the half-life period $(t_{1/2})$ is related to the initial pressure $(P)$ as $(t_{1/2}) \propto P^{1-n}$.Using the data: $\frac{(t_{1/2})_1}{(t_{1/2})_2} = (\frac{P_1}{P_2})^{1-n}$.Taking the first two values: $\frac{3.52}{1.76} = (\frac{50}{100})^{1-n} \implies 2 = (\frac{1}{2})^{1-n} = 2^{n-1}$.Comparing exponents: $n-1 = 1$,so $n = 2$.Now,for $t_{1/2} = 2.5 \ hrs$,we use the relation $(t_{1/2}) \propto P^{1-2} \implies (t_{1/2}) \propto P^{-1} \implies (t_{1/2}) 	imes P = 	ext{constant}$.Using the first data point: $3.52 	imes 50 = 2.5 	imes P_2$.$P_2 = \frac{3.52 	imes 50}{2.5} = \frac{176}{2.5} = 70.4 \ mm \ Hg$.Rounding to the nearest integer,the pressure is $70 \ mm \ Hg$.

Pressure $(mm \ Hg)$	$50, 100, 200$
Half-life period $(hrs)$	$3.52, 1.76, 0.88$

At a certain temperature,the half-life periods for the catalytic decomposition of $NH_3$ were found to be as follows:

Pressure $(mm \ Hg)$ $50, 100, 200$

Half-life period $(hrs)$ $3.52, 1.76, 0.88$

What will be the pressure when the half-life period is $2.5 \ hrs$?

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At a certain temperature,the half-life periods for the catalytic decomposition of $NH_3$ were found to be as follows: Pressure $(mm \ Hg)$ $50, 100, 200$ Half-life period $(hrs)$ $3.52, 1.76, 0.88$ What will be the pressure when the half-life period is $2.5 \ hrs$?