Question

A constant temperature and volume $X$ decomposes as,
$2X\left(g\right)⟶3Y\left(g\right)+2Z\left(g\right)$
$P_X$ is the partial pressure of $X$.

Observation No.	Time $\left(min\right)$	$P_X\left(inmmHg\right)$
$1$	$0$	$800$
$2$	$100$	$400$
$3$	$200$	$200$

$\left(i\right)$ What is the order of the reaction with respect to $X$?
$\left(ii\right)$ Find the rate constant.
$\left(iii\right)$ Find the time for $75$% completion of the reaction.
$\left(iv\right)$ Find the total pressure when pressure of $X$ is $700$ $mm$ $Hg$.

Answer 1

$\left(i\right)$ Data shows that half life of the reaction is constant, i.e., $100$ $min$; hence, it is a first order reaction.
$\left(ii\right)$ $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{100}=6.93\times {10}^{-3}{min}^{-1}$
$\left(iii\right)$ $t_{75},$ i.e., $t_{3/4}=2\times t_{1/2}=2\times 100=200$ $min$
$\left(iv\right)$ $2X\left(g\right)⟶3Y\left(g\right)+2Z\left(g\right)$
$\begin{array}{cccc}t=0& 800& 0& 0\\ dt& 800-2X& 3X& 2X\end{array}$
Total pressure $=800-2X+3X+2X=800+3X$ ...(i)
$800-2X=700$
$X=50$
$\therefore$ Total pressure $=800+3\times 50=950$ $mm$ $Hg$