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?

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Answer 1 · 2018-05-14T09:52:20

$9$ units.

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.