Question

The decomposition of ${NH}_3$ gas on a heated tungsten surface gave the following results:

Initial pressure (mm of $Hg$)	$65$	$105$	$y$	$185$
Half-life (sec)	$290$	$x$	$670$	$820$

Calculate approximately the values of $x$ and $y$

Answer 1

Half life is given as:-

$t_{1/2}=\frac{2^{n-1}-1}{K[A_o{]}^{n-1}}$

Thus, $t_{1/2}\propto \frac{1}{[A_o{]}^{n-1}}⟶\left(1\right)$

$\Rightarrow \left[\frac{65}{185}\right]={\left[\frac{820}{290}\right]}^{n-1}={\left[\frac{290}{820}\right]}^{1-n}$

$\Rightarrow 0.35=[0.35{]}^{1-n}$

$1-n=1$ $n=0$

Thus, the reaction is zero order.

$t_{1/2}\propto [A_o{]}^1$

So, by using equation 1

$\Rightarrow \frac{65}{105}=\left[\frac{290}{x}\right]\Rightarrow x=468.5$

$\Rightarrow \frac{65}{y}=\frac{290}{670}\Rightarrow y=150$