If gas $A$ diffuses 9 times faster than $B$ , then the ratio of the densities of $A$ and $B$ is ...........

9 : 1

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1 : 9

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81 : 1

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1 : 81

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Solution

The correct option is D 1 : 81
According to Graham's law of diffusion; $\frac{r_{1}}{r_{2}} α \sqrt{\frac{d_{2}}{d_{1}}}$
Given that $r_{1}$ = 9 $r_{2}$
Therefore $\frac{9 r_{2}}{r_{2}} α \sqrt{\frac{d_{2}}{d_{1}}}$
$\frac{d_{2}}{d_{1}} = \frac{81}{1}$
Therefore $d_{1}$ : $d_{2}$ = 1 : 81

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