Question

At 100 the gas reaction $A⟶2B+C$ was observed to be of first order. On starting with pure $A$ it is found that at the end of 10 minutes the total pressure of system us 176 mm. $Hg$ and after a long time 270 mm $Hg$. From these data find (a) initial pressure of $A$ (b) the pressure of $A$ at the end of 10 minutes (c) the specific rate of reaction and (d) the half life period of the reaction?

Answer 1

$A\left(g\right)⟶2B\left(g\right)+C\left(g\right)$

$t=0$ $P_i$ - -

$t=10min$ $Pi-P$ $2P$ $P$

at $t=\infty$ - $2Pi$ $Pi$

$P_T,$ Total pressure at $t=10=Pi+2P=176mm$ of $Hg$

$P_{\infty },$ Total pressure at $t=\infty \Rightarrow 3Pi=270mm$ of $Hg$

$Pi=\frac{270}{3}=90mm$ of $Hg$

$P=\frac{176-Pi}{2}=43mm$ of $Hg$

Thus,

(a) Initial pressure of $A=Pi=90mm$ of $Hg$

(b) The pressure of $A$ at the end of $10$ minute

$\Rightarrow Pi-P=90-43=47mm$ of $Hg$

(c) The specific rate of reaction

Rate= $K\left[P_A\right]$

$\Rightarrow K=\frac{2.303}{10}\log \frac{Pi}{Pi-P}$

$\Rightarrow K=\frac{2.303}{10min}\log \frac{90}{47}=0.0649mi{n}^{-1}$

Rate= $0.0649\left[47\right]$

Rate= $3.05mm$ of $Hg$ $mi{n}^{-1}$

(d) Half life

$t_{1/2}=\frac{0.693}{K}$ for first order

$\Rightarrow t_{1/2}=\frac{0.693}{0.0649}mi{n}^{-1}$

$\Rightarrow t_{1/2}=10.66$ minute

Thus half life of the reaction is $10.66$ minutes.