For a reaction A longrightarrow P,a plot betw | vedclass

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(B) For a reaction of order $n$,the half-life is given by $t_{1/2} \propto \frac{1}{[A]_0^{n-1}}$.Given that the plot of $[A]_0$ $Vs$ $\frac{1}{t_{1/2

Vedclass · Accepted Answer

$10$

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(B) For a reaction of order $n$,the half-life is given by $t_{1/2} \propto \frac{1}{[A]_0^{n-1}}$.Given that the plot of $[A]_0$ $Vs$ $\frac{1}{t_{1/2}}$ is a straight line with a positive slope,we have $\frac{1}{t_{1/2}} = k[A]_0$,which implies $t_{1/2} \propto \frac{1}{[A]_0}$.This corresponds to a reaction of order $n = 2$.Since $t_{1/2} 	imes [A]_0 = 	ext{constant}$,we can write: $(t_{1/2})_1 	imes [A]_1 = (t_{1/2})_2 	imes [A]_2$.Substituting the given values: $20 \ min 	imes 1 	imes 10^{-2} \ M = (t_{1/2})_2 	imes 2 	imes 10^{-2} \ M$.Solving for $(t_{1/2})_2$,we get $(t_{1/2})_2 = \frac{20 	imes 1 	imes 10^{-2}}{2 	imes 10^{-2}} \ min = 10 \ min$.

$Observation$	$[A] \ (mol \ L^{-1})$	$[B] \ (mol \ L^{-1})$	$Rate \ (mol \ L^{-1} \ sec^{-1})$
$1$	$0.1$	$0.1$	$2 \times 10^{-3}$
$2$	$0.2$	$0.1$	$4 \times 10^{-3}$
$3$	$0.1$	$0.2$	$8 \times 10^{-3}$

$[HI] \ (M)$	Rate $(M \ s^{-1})$
$0.0500$	$8.80 \times 10^{-10}$
$0.1000$	$3.52 \times 10^{-9}$
$0.1500$	$7.92 \times 10^{-9}$

Similar Questions

The rate law for the reaction between substances $A$ and $B$ is given by $\text{Rate} = k[A]^n[B]^m$. If the concentration of $A$ is doubled and the concentration of $B$ is halved,what is the ratio of the new rate to the initial rate?

The hypothetical reaction : $2A + B \to C + D$ is catalyzed by $E$ as indicated in the possible mechanism below -
Step-$1$ : $A + E \rightleftharpoons AE$ (fast)
Step-$2$ : $AE + A \to A_2 + E$ (slow)
Step-$3$ : $A_2 + B \to C + D$ (fast)
What rate law best agrees with this mechanism?

What is the order of reaction for $A + B \to C$?

$Observation$ $[A] \ (mol \ L^{-1})$ $[B] \ (mol \ L^{-1})$ $Rate \ (mol \ L^{-1} \ sec^{-1})$

$1$ $0.1$ $0.1$ $2 \times 10^{-3}$

$2$ $0.2$ $0.1$ $4 \times 10^{-3}$

$3$ $0.1$ $0.2$ $8 \times 10^{-3}$

For the reaction $aA \to xP$,the rate is $2.4 \ mMs^{-1}$ when $[A] = 2.2 \ M$. When the concentration of $A$ is halved,the rate becomes $0.6 \ mMs^{-1}$. Determine the order of the reaction with respect to $A$.

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