Question

The results given in the below table were obtained during kinetic studies of the following reaction:
$A+2B\to C+D$

Experiment	Initial concentration [A]	Initial concentration [B]	Initial rate of formation of D
1	0.1	0.1	$6\times {10}^{-3}$
2	0.3	0.2	$7\times {10}^{-2}$
3	0.3	0.4	$2.8\times {10}^{-1}$
4	0.4	0.1	$2.4\times {10}^{-2}$

What will be correct rate law expression for the given reaction?

• A. $Rate=k\left[A\right]\left[B\right]$
• B. $Rate=k\left[A\right][B{]}^2$
• C. $Rate=k\left[A{]}^2\right[B{]}^2$
• D. $Rate=k\left[A{]}^2\right[B]$

Answer 1

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

In experiment 2 and 3 (Keeping the concentration of A constant), when the concentration 'B' is doubled, the rate gets quadrapled.
So, by initial rate method,
$\frac{7\times {10}^{-2}}{2.8\times {10}^{-1}}={\left(\frac{0.2}{0.4}\right)}^b$
$\frac{1}{4}={\left(\frac{1}{2}\right)}^b$
Thus, $b=2$
Thus, order w.r.t to B is 2.

In experiment 1 and 4 (Keeping the concentration of B constant), when the concentration quadrapled the rate quadrapled.
So, by initial rate method,
$\frac{6\times {10}^{-3}}{2.4\times {10}^{-2}}={\left(\frac{0.1}{0.4}\right)}^a$
$\frac{1}{4}={\left(\frac{1}{4}\right)}^a$
Thus, $a=1$
Thus, order w.r.t to A is 1.

So, rate law expression is.
$Rate=k\left[A\right][B{]}^2$