Question

The rate of diffusion of a unknown gas and chlorine are in the ratio 6:5.veper density of chlorine is 36.find out the molecular weight of unknown gas?

Answer 1

`50`

Explanation:

From Graham's Law of Diffusion,

We know,

The rate of diffusion of a gas is inversely proportional to the square root of molecular weight of the gas.

So, We get,

`r prop 1/sqrt(M)`

From that, we get,

`r_1/r_2 = sqrt(M_2/M_1)`....................................(i)

Now, We know, `"Molecular Weight" = 2 xx "Vapour Density"`.

So, Average Molecular Weight of Chlorine = `2 xx 36` = `72`

Now, From (i),

`color(white)(xxx)6/5 = sqrt(72/M_"unknown")`

`rArr 36/25 = 72/M_"unknown"` [Squaring both sides]

`rArr 25/36 = M_"unknown"/72`

`rArr M_"unknown" = (25 * cancel(72)^2)/cancel(36)`

`rArr M_"unknown" = 50`

So, The Molecular Weight of the Unknown Gas is `50`.

Hope this helps.