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)
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Solution:
(i) For the same amount of gas being effused
$\dfrac{r _1}{r _2} =\dfrac{t _2}{t _1}=\dfrac{p _1}{p _2} \sqrt{\dfrac{M _2}{M _1}} $
$\Rightarrow \quad \dfrac{57}{38} =\dfrac{0.8}{1.6} \sqrt{\dfrac{M _2}{28}} $
$\Rightarrow \quad M _2 =252 \hspace {1mm} g \hspace {1mm} mol^{-1}$
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, $p \propto T$
$ \Rightarrow \dfrac{1}{1.1} =\dfrac{T}{T+10} \quad \text { where, } T=\text { Kelvin temperature }$
$\Rightarrow T =100 K=t+273 $
$\Rightarrow t =-173^{\circ} C $
$ \text { Volume } =\dfrac{n R T}{p}=\left(\dfrac{12}{120}\right) \times \dfrac{0.082 \times 100}{1}=0.82 L$
BETA
