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gas A having molecular weight 4 diffuses thrice as fast as the gas B at a given T. The molecular weight of gas B is?

gas A having molecular weight 4 diffuses thrice as fast as the gas B at a given T. The molecular weight of gas B is?
 

Grade:11

2 Answers

Ashwani Dubey
17 Points
5 years ago
Solution:- (C) 36
The rate of diffusion (r) is inversely proportional to the molecular weight (M).
$$r \propto \cfrac{1}{\sqrt{M}}$$
$$\therefore \; \cfrac{{r}_{A}}{{r}_{B}} = \sqrt{\cfrac{{M}_{B}}{{M}_{A}}}$$
Here, $${r}_{A}$$ and $${r}_{B}$$ are the rates of diffusion of the gas A and the gas B and $${M}_{A}$$ and $${M}_{B}$$ are the molecular weight of gas A and gas B respectively.
Let the rate of diffusion of the gas B be r, i.e., $${r}_{B} = r$$.
As the gas A diffuses thrice as fast as the gas B.
$$\therefore$$ rate of diffusion of the gas A $$\left( {r}_{A} \right)= 3r$$
Given that molecular weight of A $$\left( {M}_{A} \right) = 4$$
$$\therefore \; \cfrac{3r}{r} = \sqrt{\cfrac{{M}_{B}}{4}}$$
$$\Rightarrow \; {M}_{B} = 36$$
Hence, the molecular weight of B is 36.
Ashish
13 Points
5 years ago
Use graham law of diffusion i.e. rate is inversely proportional to square root of Density but as D =MP÷RT but at this condition P,R,T is constant so D is directly proportional to M. So this law can be used as r is Inversely proportional to square root of Molecular weight

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