Q29 / 160 · AP EAMCET 2021 (20 Aug Shift 1) · Chemistry

For zero order reaction, a plot of $t_{1 / 2}$ versus $[A]_{0}$ will be

A
A straight line passing through the origin and slope $= K$
B
A horizontal line (parallel to $x$ - axis)
C
A straight line with slope $- K$
Correct answer
D
A straight line passing through origin and slope $= \frac{1}{2 K}$

Solution

For zero order reaction :-

Rate = $K {[conc .]}^{0}$

$[A]_{0}$ is the initial concentration and $[A]_{t}$ is the concentration after some time.

Over the half life, the concentration also becomes $\frac{[A]_{0}}{2}$ .

So, $K = \frac{[A]_{0} - \frac{[A]_{0}}{2}}{t_{\frac{1}{2}}} = \frac{\frac{[A]_{0}}{2}}{t_{\frac{1}{2}}} So, t_{\frac{1}{2}} = \frac{[A]_{0}}{2 k}$

Graph :-

Hence, the straight line passing through origin and slope $= \frac{1}{2 K}$ .

Hence, the correct answer is option: 'D'.