Question

For a zero order reaction which of the following relation is correct, where $t_{1/2}anda$ are half-life and initial concentration respectively.

• A. $t_{1/2}\propto a$
• B. $t_{1/2}\propto \frac{1}{a}$
• C. $t_{1/2}\propto a^2$
• D. $t_{1/2}\propto \frac{1}{a^2}$

Answer 1

The correct option is A $t_{1/2}\propto a$

When zero order kinetic rate law is followed, let $\left[A\right]$ is the current concentration, $[A{]}_0$­ is the initial concentration, and $k$ is the reaction constant and $t$ is time
Then relation is given by $\left[A\right]=[A{]}_0­-k$

In order to find the half life we need to isolate t on its own, and divide it by 2. We would end up with a formula as such depict how long it takes for the initial concentration to dwindle by half given by -:
$⟹t_{1/2}=\frac{[A{]}_0­}{2k}$