To solve the problem of finding the ratio of the molecular weight of two gases X and Y, given that gas X diffuses 10 times faster than gas Y.
The rate of diffusion of a gas is inversely proportional to the square root of its density.
This relationship can be expressed mathematically as:
Therefore, we can write:
Rate of X / Rate of Y = √DY/√DX
Rate of diffusion of gas Y be RY and the rate of diffusion of gas X be RX.
According to the problem, gas X diffuses 10 times faster than gas Y:
RX = 10 RY
Substituting
10RY / RY = √DY / √DX
10 = √DY / √DX
To eliminate the square root, we square both sides of the equation:
102 = (√DY / √DX)2
100 = DY/DX
(D = M/V where, D is density, M is mass, V is volume)
So,
DY/DX = 100
DX/DY = 1/100
MX/MY = 1/100
