Question

Which of the following relation is correct for zero order reaction?

• A. $t_{1/2}\propto [R{]}_0$
• B. $t_{1/2}\propto \frac{1}{[R{]}_0^2}$
• C. $t_{1/2}\propto \frac{1}{[R{]}_0}$
• D. $t_{1/2}$ is independent of $[R{]}_0$

Answer 1

The correct option is A $t_{1/2}\propto [R{]}_0$

Zero order reaction means

$rate=\frac{-d\left[R\right]}{dt}=k[R{]}^0=k$

integrated rate equation is thus:

$\left[R\right]=[R{]}_0-kt$

half-life for zero order reaction:at $t=t_{1/2},\left[R\right]=\frac{[R{]}_0}{2}$

$\frac{[R{]}_0}{2}=[R{]}_0-k{t}_{1/2}$

$t_{1/2}=\frac{[R{]}_0}{2k}$

$t_{1/2}\propto [R{]}_0$

option A is correct