Question

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

• A. 2ln 2 M
• B. 2 M
• C. In 2 M
• D. In 4 M

Answer 1

The correct option is A 2ln 2 M

For zero order reaction,

$A\stackrel{R}{\to }{P}_1$

$t_{1/2}=\frac{{\left[A\right]}_0}{2k}$ -------- [equation 1]

For first order reaction,

$B\stackrel{R}{\to }{P}_2$

$t_{1/2}=\frac{ln2}{k}$ ------- [equation 2]

On equating equation 1 and equation 2, we get -

$\frac{ln2}{k}=\frac{{\left[A\right]}_0}{2k}$

$\Rightarrow {\left[A\right]}_0=2ln2M$

Hence, option $\left(A\right)$ is correct.