Question

Reaction $A+B\to C+D$ follows following rate law: rate $=k\left[A{]}^{+\frac{1}{2}}\right[B{]}^{\frac{1}{2}}.$ Starting with initial conc. of $1M$ of $A$ and $B$ each, what is the time taken for concentration of $A$ to become 0.25 M?

(Given : $K=2.303\times {10}^{-3}se{c}^{-1}$)

• A. 300 sec
• B. 600 sec
• C. 900 sec
• D. 1200 sec

Answer 1

The correct option is B 600 sec

Rate$={K\left[A\right]}^{1/2}{\left[B\right]}^{1/2}$

Overall order of reaction is = 1/2+1/2=1

$\therefore$ It is a $1^{st}$ order reaction.

For concentration of $A$ to become $0.5M:-t_{1/2}=\frac{0.693}{K}=\frac{0.693}{2.303\times {10}^{-3}}=300sec.$

It will require $2$ half times for the concentration of $A$ to become $0.25M.$

$\therefore$ Time taken=$2\times t_{1/2}=2\times 300=600sec$