States of Matter - Result Question 64
64. A closed vessel with rigid walls contains 1 mole of ${ }{92}^{238} \mathrm{U}$ and 1 mole of air at 298 K . Considering complete decay of ${ }{92}^{238} \mathrm{U}$ to ${ }_{82}^{206} \mathrm{~Pb}$, the ratio of the final pressure to the initial pressure of the system at 298 K is
(2015 Adv.)
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Answer:
Correct Answer: 64. (9)
Solution:
$$ \begin{aligned} & { }{92} \mathrm{U}^{238} \longrightarrow{ }{82} \mathrm{~Pb}^{206}+8{ }2 \mathrm{He}^4(\mathrm{~g})+6{ }{-1} \beta^0 \\ & n \text { (gas) [Initial] }]=1 \text { (air) } \\ & n(\text { gas) [Final] }]=8(\mathrm{He})+1 \text { (air) }=9 \end{aligned} $$ $\Rightarrow$ At constant temperature and volume;
So, $$ \begin{aligned} p & \propto n . \\ \frac{p_f}{p_i} & =\frac{n_f}{n_i}=\frac{9}{1}=9 \end{aligned} $$
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