Question

the ratio of rates of diffusion of a gas and carbon dioxide is 300:200. Find the relative density of the gas


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Answer 1

Given:

Ratio of diffusion of a gas and carbon dioxide is 300:200.

To find:

Relative density of the gas

Concept:

Graham's Law of Diffusion states that the rate of of diffusion of any gas is inversely proportional to the square root of the density of that gas.

Let rate be denoted by r and density be d:

$\boxed{ \sf{r \: \propto \: \dfrac{1}{ \sqrt{d} } }}$

If carbon dioxide is considered to be a reference, the relative density of the gas will be equal to the the density of the gas divided by the density of carbon dioxide.

Calculation:

Let rate of diffusion of gas be r1 and that of carbon dioxide be r2

$\therefore \: \dfrac{r1}{r2} = \dfrac{300}{200}$

$= > \sqrt{ \dfrac{d2}{d1} } = \dfrac{300}{200}$

$= > \sqrt{ \dfrac{d1}{d2} } = \dfrac{200}{300} = \dfrac{2}{3}$

$= > \dfrac{d1}{d2} = {( \dfrac{2}{3}) }^{2}$

$= > \dfrac{d1}{d2} = \dfrac{4}{9}$

$= > rel. \: density = \dfrac{4}{9}$

$= > rel. \: density = 0.44$

So final answer:

Relative density of Gas with respect to Carbon dioxide is 0.44