Question

The reaction $2A+B⟶C+D$ goes to completion and follows the rate law $-d\{B\}/dt=K[A]2[B]$, 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

Answer: 375

$\frac{-dB}{dt}=K[A{]}^2[B]$
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 $\left[A_0\right]$.
$\therefore \left(\frac{5}{10}\right)=\left(\frac{y}{625}\right)$
$y=\frac{625}{2}=312.5$
$\therefore x+y=312.5+62.5$
$\Rightarrow 375$