Question

The reaction $A\stackrel{K}{\to }Product$, is a zero order while the reaction $B\stackrel{K}{\to }Product$, is a first order reaction. For what initial concentration of 'A' are the half lives of the two reactions equal? (Rate constant values are the same for both the reactions)

• A. $\left({\text{log}}_{e}4\right)M$
• B. $2M$
• C. $\text{log}2M$
• D. $ln2M$

Answer 1

The correct option is A $\left({\text{log}}_{e}4\right)M$

For a zero order reaction,
$a=kt$
$\therefore \frac{a}{2}=k\times t_{\left(\frac{1}{2}\right)}$,
From the second reaction, which has an order of 1,
$t_{\left(\frac{1}{2}\right)}=\frac{{\text{log}}_{e}2}{\text{k}}$
$\Rightarrow a=2ln2={\text{log}}_{e}4\text{M}$