Question

The relative the rate of diffusion of two gases A and B are found to be 0.3 and 0.2 respectively.if the density of A is 4 then find out the density of B?

Answer 1

`9` units.

Explanation:

From Graham's Law of Diffusion, We get,

`r_A/r_B = sqrt(M_B/M_A)`.............(i)

But, In the Same Conditions of Temperature and Pressure, Molar Mass is directly proportional to Molar Density.

I.e. `M prop D`

So, `M_A/M_B = D_A/D_B`..........................(ii)

From (i) and (ii),

We get,

`r_A/r_B = sqrt(D_B/D_A)`....................................(iii).

Now just plug in the values in equation (iii) to get the answer.

So,

`color(white)(xxx)0.3/0.2 = sqrt(D_B/4)`

`rArr 3/2 = sqrt(D_B/4)`

`rArr 9/4 = D_B/4` [Squaring both sides]

`rArr D_B = 9` [Multiplying both sides by `4`]

So, The Density of B is `9` units.

Hope this helps.