States of Matter - Result Question 64
####64. A closed vessel with rigid walls contains 1 mole of ${ } _{92}^{238} U$ and 1 mole of air at $298 K$. Considering complete decay of ${ } _{92}^{238} U$ to ${ } _{82}^{206} Pb$, 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:
- ${ } _{92} U^{238} \longrightarrow{ } _{82} Pb^{206}+8{ } _2 He^{4}(g)+6{ } _{-1} \beta^{0}$
$n$ (gas) [Initial] $=1$ (air)
$n$ (gas) $[$ Final $]=8(He)+1$ (air) $=9$
$\Rightarrow$ At constant temperature and volume;
$$ \begin{aligned} p & \propto n . \ \text { So, } \quad \frac{p _f}{p _i} & =\frac{n _f}{n _i}=\frac{9}{1}=9 \end{aligned} $$
