Question

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

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

• A. $r=k\left[A\right][B{]}^3$
• B. $r=k\left[A{]}^0\right[B{]}^2$
• C. $r=k\left[A\right]\left[B\right]$
• D. $R=k\left[A{]}^0\right[B{]}^3$

Answer 1

The correct option is B $r=k\left[A{]}^0\right[B{]}^2$

In experiments I and II, [B] is constant and [A] is doubled. The rate does not change. So order w.r.t. [A] $=$ Zero.

Let rate $=k\left[A{]}^0\right[B{]}^x$

$r_2=0.002M{s}^{-1}=k[0.1{]}^x$

$r_2=0.008M{s}^{-1}=k[0.2{]}^x$

$\frac{r_3}{r_2}=4=(2{)}^x$

$\therefore (2{)}^2=(2{)}^x$

$x=2$

So order w.r.t. $\left[B\right]=2$

Rate $=k\left[A{]}^0\right[B{]}^2$