Question

For the reaction; $A\to B$, the rate expression is $-\frac{d\left[A\right]}{dt}=k[A{]}^{1/2}$. If initial concentration of $A$ is 0, then:

• A. the half life period $t_{1/2}$ = $\frac{0.693}{k}$
• B. the integrated rate expression is $k=\frac{2}{t}\left(\right(A_0^{1/2})-A^{1/2})$
• C. the half life period $t_{1/2}$ = ${\frac{k}{2\left[A\right]}}_0^{1/2}$
• D. the time taken for 75% completion of reaction $t_{3/4}$ = $\frac{\sqrt{[A{]}_0}}{k}$

Answer 1

The correct option is B the integrated rate expression is $k=\frac{2}{t}\left(\right(A_0^{1/2})-A^{1/2})$

Given rate expression : $-\frac{d\left[A\right]}{dt}=k[A{]}^{1/2}$
$⟹k=-\frac{d\left[A\right]}{[A{]}^{1/2}}dt$

Integrating both sides we get :
$⟹k=\frac{2}{t}\left(\right(A_0^{1/2})-A^{1/2})$