States of Matter - Result Question 72
####72. (i) One mole of nitrogen gas at $0.8 atm$ takes $38 s$ to diffuse through a pin-hole, whereas one mole of an unknown compound of xenon with fluorine at $1.6 atm$ takes $57 s$ to diffuse through the same hole. Calculate the molecular formula of the compound.
(ii) The pressure exerted by $12 g$ of an ideal gas at temperature $t^{\circ} C$ in a vessel of volume $V$ litre is one atm. When the temperature is increased by $10^{\circ} C$ at the same volume, the pressure increases by $10 %$. Calculate the temperature $t$ and volume $V$.
$($ Molecular weight of the gas $=120)$
(1999, 5M)
Show Answer
Answer:
Correct Answer: 72. $\left(123 g mol^{-1}\right)$
Solution:
- (i) For the same amount of gas being effused
$$ \begin{array}{rlrl} & & \frac{r _1}{r _2} & =\frac{t _2}{t _1}=\frac{p _1}{p _2} \sqrt{\frac{M _2}{M _1}} \ \Rightarrow \quad & \frac{57}{38} & =\frac{0.8}{1.6} \sqrt{\frac{M _2}{28}} \ \Rightarrow \quad & M _2 & =252 g mol^{-1} \end{array} $$
Also, one molecule of unknown xenon-fluoride contain only one $Xe$ atom $[M(Xe)=131]$, formula of the unknown gas can be considered to be $XeF _n$.
$\Rightarrow 131+19 n=252 ; n=6.3$, hence the unknown gas is $XeF _6$.
(ii) For a fixed amount and volume, $p \propto T$
$$ \begin{array}{rlrl} \Rightarrow & \frac{1}{1.1} & =\frac{T}{T+10} \quad \text { where, } T=\text { Kelvin temperature } \ \Rightarrow & T & =100 K=t+273 \ \Rightarrow & t & =-173^{\circ} C \ & & \text { Volume } & =\frac{n R T}{p}=\left(\frac{12}{120}\right) \times \frac{0.082 \times 100}{1}=0.82 L \end{array} $$
