Question

The reaction $A\stackrel{k}{⟶}$ products, is of a zero order while the reaction $B\stackrel{k}{⟶}$ products, 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 reactions)

• A. $\left(\ln 4\right)$ M
• B. 2 M
• C. $\left(\log 2\right)$ M
• D. $\left(ln2\right)$ M

Answer 1

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

For a zero order reaction, concentration at any time
$x=kt\therefore \frac{a}{2}=k\times t_{1/2},t_{1/2}=\frac{a}{2k}⟶\left(i\right)$
For a first order Reaction, $t_{1/2}=\frac{{\log }_{e}2}{k}⟶\left(ii\right)$
From (i) and (ii),
$\frac{a}{2k}=\frac{{\log }_{e}2}{k}$ $\Rightarrow a=\left({\log }_{e}4\right)$ M