Q. For a first order reaction, the initial concentration of a reactant is 0.05 M. After 45 min it is decreased by 0.015 M. calculation half reaction time $\left( t_{1/2} \right)$

A) 87.42 min
B) 25.90 min
C) 78.72 min
D) 77.20 min
Explanation

(a)
For first order reaction
$k = \frac{2.303}{t}\log\frac{\lbrack A_{0}\rbrack}{\lbrack A\rbrack}$
$k = \frac{2.303}{45}\log\frac{0.05}{0.035}$
$k = \frac{2.303}{45}\log{1.42}$
$k = \frac{2.303 \times 0.1523}{45} = 0.0078$
$t_{1/2} = \frac{0.693}{0.0078} = 88\ min$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.