Chemistry - Chemical Kinetics Question with Solution | TestHub

Given reaction:

$A+B\to C+D$

Rate law:

$Rate=k[A{]}^{1/2}[B{]}^{1/2}$

Initial:

$[A{]}_0=[B{]}_0=1M$

At time t:

$[A]=0.25M$

Since A and B are consumed in a 1:1 ratio:

$[A]=[B]$

So:

$Rate=k[A{]}^{1/2}[A{]}^{1/2}$

$Rate=k[A]$

Hence, the reaction becomes **first order**.

For first order:

$t=\frac{2.303}{k}\log \frac{[A{]}_0}{[A]}$

Substitute:

$t=\frac{2.303}{2.303\times 10^{-3}}\log \frac{1}{0.25}$

$t=\frac{1}{10^{-3}}\log 4$

$t=1000\times \log 4$

$\log 4=2\log 2=2(0.30)=0.60$

$t=1000\times 0.60$

$t=600sec$