Question

$nA\to B$ is a $1^{st}$ order reaction, whose concentration versus time curve is given below

If the half - life for the reaction is 24 minutes, then the value of n is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

$nA\to B$
half life for $1^{st}$ order
$t_{\frac{1}{2}}=\frac{0.693}{n\times k}$
$n\times k=\frac{0.693}{24}\left(i\right)$
At $t=48min$ $\left[A\right]=\left[B\right]$
$nA⟶B$
$t=0A_{0}0$
$t=48A_0-nxx$
$A_0-nx=x\Rightarrow A_0=nx+x$
$[A{]}_{t=48}=x$
On applying integrated rate equation for $t=48$
$-\frac{1}{n}\frac{d\left[A\right]}{dt}=k\left[A\right]$
$-\frac{1}{n}ln\frac{\left[A\right]}{\left[A_0\right]}=k\times t$
$-\frac{1}{n}ln\frac{\left[x\right]}{[nx+x]}=k\times t$
$-ln\frac{1}{[n+1]}=k\times t\times n$
substitute value of $n\times k$ from $\left(i\right)$
$-ln\frac{1}{[n+1]}=48\times \frac{0.693}{24}$
$n=3$