States of Matter - Result Question 85
####51. The value of $d$ in $cm$ (shown in the figure), as estimated from Graham’s law, is
(a) 8
(b) 12
(c) 16
(d) 20
Match the Columns
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Solution:
- PLAN This problem can be solved by using the concept of Graham’s law of diffusion according to which rate of diffusion of non-reactive gases under similar conditions of temperature and pressure are inversely proportional to square root of their density.
$$ \text { Rate of diffusion } \propto \frac{1}{\sqrt{\text { molar weight of gas }}} $$
Let distance covered by $X$ is $d$, then distance covered by $Y$ is $24-d$.
If $r _X$ and $r _Y$ are the rate of diffusion of gases $X$ and $Y$,
$$ \begin{aligned} \frac{r _X}{r _Y} & =\frac{d}{24-d}=\sqrt{\frac{40}{10}}=2 \ d & =48-2 d \ \Rightarrow \quad 3 d & =48 \Rightarrow \quad d=16 cm \end{aligned} $$
Hence, (c) is the correct choice.
