States of Matter 1 Question 64
64. A closed vessel with rigid walls contains 1 mole of ${ }{92}^{238} \mathrm{U}$ and 1 mole of air at $298 \mathrm{~K}$. 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 $298 \mathrm{~K}$ is
(2015 Adv.)
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Answer:
Correct Answer: 64. (9)
Solution:
- ${ }{92} \mathrm{U}^{238} \longrightarrow{ }{82} \mathrm{~Pb}^{206}+8{ }{2} \mathrm{He}^{4}(g)+6{ }{-1} \beta^{0}$
$n$ (gas) [Initial] $=1$ (air)
$n$ (gas) $[$ Final $]=8(\mathrm{He})+1$ (air) $=9$
$\Rightarrow$ At constant temperature and volume;
$$ \begin{aligned} p & \propto n . \ \text { So, } \quad \frac{p_{f}}{p_{i}} & =\frac{n_{f}}{n_{i}}=\frac{9}{1}=9 \end{aligned} $$
