Question

The reaction $2 A+B \longrightarrow C+D$ goes to completion and follows the rate law $-d\{B\} / d t=K[A] 2[B]$, Calculate the values of $(x +y)$ in the following data:

Set	$\left[A_{0}\right] \times 10^{-3} M$	$\left[B_{0}\right] \times 10^{-3} M$	Half life $(\sec)$
1	$300$	$4$	$62.5$
2	$300$	$6$	$x$
3	$5$	$300$	$625$
4	$10$	$300$	$y$

Answer 1

$\frac{-d B}{d t}=K[A]^{2}[B]$
from set $1$ and set $2$ .
$\because\left[A_{0}\right] \gg\left[B_{0}\right]$
$\therefore $ Order will be dependent on $[B]$ only
hence first order reaction
$\therefore $ half life is independent of $[B]$
$\therefore x=62.5\, \sec$
[If rate constant remains same]
from set $3$ and set $4$
$\because\left[B_{0}\right] \gg\left[A_{0}\right]$
$\therefore $ Order will be dependent only on $[A]$
hence second order reaction
$\therefore $ half life is inversely dependent on $\left[A_{0}\right]$.
$\therefore \left(\frac{5}{10}\right)=\left(\frac{y}{625}\right)$
$y=\frac{625}{2}=312.5$
$\therefore x+ y=312.5+62.5$
$\Rightarrow 375$