Question

In a certain gaseous reaction between $A$ and $B , A +3 B \rightarrow AB _3$. The initial rates are reported as follows:

[A]	[B]	Rate
$0.1\,M$	$0.1\,M$	$0.002\,Ms^{-1}$
$0.2\,M$	$0.1\,M$	$0.002\,Ms^{-1}$
$0.3\,M$	$0.2\,M$	$0.008\,Ms^{-1}$
$0.4\,M$	$0.3\,M$	$0.018\,Ms^{-1}$

The rate law is

• A. $r=k[ A ][ B ]^3$
• B. $r=k[ A ]^0[ B ]^2$
• C. $r=k[ A ][ B ]$
• D. $r=k[ A ]^0[ B ]^3$

Answer 1

Answer: (B)

In experiment I and II, $[ B ]$ is constant and $[ A ]$ is doubled. The rate does not change. So order w.r.t $[ A ]=$ zero
Let rate $=k[ A ]^0[ B ]^x$
$r_2=0.002 \,M s ^{-1}=k[0.1]^x$
$r_3=0.008 \,M s ^{-1}=k[0.2]^x$
$\frac{r_3}{r_2}=4=(2)^x $
$\therefore(2)^2=(2)^x$
$x=2$
So order w.r.t. $[ B ]=2$
Rate $=k[ A ]^0[ B ]^2$