The half-life periods of decomposition of PH_ | vedclass

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(A) The order of a reaction can be determined from the relationship between half-life $(t_{1/2})$ and initial pressure $(p_0)$: $t_{1/2} \propto (p_0)

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(A) The order of a reaction can be determined from the relationship between half-life $(t_{1/2})$ and initial pressure $(p_0)$: $t_{1/2} \propto (p_0)^{1-n}$,where $n$ is the order of the reaction. Given that the half-life $(t_{1/2} = 84 	ext{ min})$ remains constant despite changes in the initial pressure $(707, 79, 37.5 	ext{ torr})$,it implies that $t_{1/2}$ is independent of the initial pressure. For a first-order reaction,$t_{1/2} = \frac{0.693}{k}$,which is independent of the initial concentration or pressure. Therefore,the reaction is of the first order $(n = 1)$.

Initial Pressure $p$ (torr)	$707$	$79$	$37.5$
Half-life $t_{1/2}$ (min)	$84$	$84$	$84$

Initial Conc. $(A)$	Initial Conc. $(B)$	Initial rate of formation of $C \ (mol \ L^{-1} \ s^{-1})$
$0.1 \ M$	$0.1 \ M$	$1.2 \times 10^{-3}$
$0.1 \ M$	$0.2 \ M$	$1.2 \times 10^{-3}$
$0.2 \ M$	$0.1 \ M$	$2.4 \times 10^{-3}$

$[A] \ (mol \ L^{-1})$	$[B] \ (mol \ L^{-1})$	Initial Rate $(mol \ L^{-1} \ s^{-1})$
$0.05$	$0.05$	$0.045$
$0.10$	$0.05$	$0.090$
$0.20$	$0.10$	$0.72$

The half-life periods of decomposition of $PH_3$ for different initial pressures are given below $:$
Initial Pressure $p$ (torr) $707$ $79$ $37.5$
Half-life $t_{1/2}$ (min) $84$ $84$ $84$
Determine the order of the reaction.

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The half-life periods of decomposition of $PH_3$ for different initial pressures are given below $:$ Initial Pressure $p$ (torr)$707$$79$$37.5$Half-life $t_{1/2}$ (min)$84$$84$$84$ Determine the order of the reaction.