Question

Rate of a reaction; $A+B\to$ Products; is given below as a function of different initial concentrations of A and B.

[A] mol $litr{e}^{-1}$	[B] mol $litr{e}^{-1}$	Initial rate mol $litr{e}^{-1}tim{e}^{-1}$
0.01	0.01	0.005
0.02	0.01	0.010
0.01	0.02	0.005

The half life of A in the reaction is :

• A. 1.667 min
• B. 1.386 min
• C. 0.01 min
• D. 0.05 min

Answer 1

The correct option is B 1.386 min

$rate=k\left[A{]}^m\right[B{]}^n$
$0.005=k\left[0.01{]}^m\right[0.01{]}^n$
$0.010=k\left[0.02{]}^m\right[0.01{]}^n$
$0.005=k\left[0.01{]}^m\right[0.02{]}^n$
on solving
$m=1;n=0$
$k=\frac{0.005}{0.01}$
$t_{\frac{1}{2}}=0.693/k=1.386$.