The half-life for the decomposition of gaseou | vedclass

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(D) The half-life for a reaction of order $n$ is given by the relation $t_{1/2} \propto \frac{1}{P_0^{n-1}}$,where $P_0$ is the initial pressure.Given

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$1$

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(D) The half-life for a reaction of order $n$ is given by the relation $t_{1/2} \propto \frac{1}{P_0^{n-1}}$,where $P_0$ is the initial pressure.Given: $(t_{1/2})_1 = 240 \ s = 4 \ min$ at $P_1 = 500 \ Torr$.Given: $(t_{1/2})_2 = 4 \ min$ at $P_2 = 250 \ Torr$.Since the half-life remains constant $(4 \ min)$ despite the change in initial pressure,the half-life is independent of the initial pressure.For $t_{1/2}$ to be independent of $P_0$,the exponent $(n-1)$ must be $0$.Therefore,$n-1 = 0$,which implies $n = 1$.The reaction is of the $1^{st}$ order.

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

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