Question

The reaction, $A\stackrel{k}{\to }$ Product, is zero order while the reaction, $B\stackrel{k}{\to }$ Product, is first order reaction. For what initial concentration of $A$ are the half lives of the two reactions equal?

• A. $\left(\ln 4\right)M$
• B. $2M$
• C. $\left(2\log 2\right)M$
• D. $\left(\ln 2\right)M$

Answer 1

The correct option is A $\left(\ln 4\right)M$

For zero order reaction,
$x=kt$
$\therefore \frac{a}{2}=k\times t_{1/2}$, i.e., $t_{1/2}=\frac{a}{2k}$ ....(i)
For first order reaction,
$t_{1/2}=\frac{{\log }_{e}2}{k}$ ....(ii)
From equations (i) and (ii), $\frac{a}{2k}=\frac{{\log }_{e}2}{k}$
$a={\log }_{e}4M$