Question

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

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

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 $=k[A{]}^0[B{]}^x$
$r_2=0.002M{s}^{-1}=k[0.1{]}^x$
$r_3=0.008M{s}^{-1}=k[0.2{]}^x$
$\frac{r_3}{r_2}=4=(2{)}^x$
$\therefore (2{)}^2=(2{)}^x$
$x=2$
So order w.r.t. $[B]=2$
Rate $=k[A{]}^0[B{]}^2$