Q. If “a” and “$t_{1/2}$” are initial concentration of reactant and half-life of a zero order reaction respectively, which of the following is correct ?
A) $t_{1/2} \propto \frac{1}{a}$
B) $t_{1/2} \propto a$
C) $t_{1/2} \propto \frac{1}{a^{2}}$
D) $t_{1/2} \propto a^{2}$
Explanation
(b)
For zero order reaction integrated rate equation is
$kt = \lbrack A\rbrack_{0} - \lbrack A\rbrack$
If ${\lbrack A\rbrack}_{0} = a,\lbrack A\rbrack = \frac{a}{2},t = t_{1/2}$
$kt_{1/2} = a - \frac{a}{2}$
$kt_{1/2} = \frac{a}{2}$
$t_{1/2} = \frac{a}{2k}$
$\therefore\ t_{1/2} \propto a$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.