## About Graham’s law of diffusion

In 1833, Graham established a relation ship between the rate of diffusion of gases and their densities which is terms as Graham’s law of diffusion.

### Statement

The rates of diffusion of gases are inversely proportional to the square root of their densities under same condition of temperature and pressure

#### Mathematic Expression:

Mathematically it may be written as

r ∞ 1 / vd

OR

r = K / vd

#### Explanation:

Graham also studied the comparative rates of diffusion of two gases. On this basis the law os defined as The comparative rates of diffusion of two gases under same condition of temperature and pressure are inversely proportional to the square root of their densities.

If the rate of diffusion of gas A is r1 and its density is d1 then according to Graham’s law

r1 ∞ 1 / vd1

OR

r1 = K / vd1

Similarly the rate of diffusion of gas B is r2 and its density is d2 then

r2 ∞ 1 / vd2

OR

r2 = K / vd2

Comparing the two rates

r1 / r2 = (K / vd1) / (K / vd2)

r1 / r2 = vd2 / d1 ………………. (A)

But density d = mass / volume

Therefore,

For d1 we may write as

d1 = m1 / v1

And for d2

d2 = m2 / v2

Substituting these values of d1 & d2 in equation (A)

r1 / r2 = v(m2 / v2) / (m1 / v1)

But v1 = v2 because both gases are diffusing in the same volume.

Therefore,

r1 / r2 = vm2 / m1

Hence Graham’s law can also be stated as,

The comparative rates of diffusion of two gases are inversely proportional to the square root of their masses under the same condition of temperature and pressure.

It means that a lighter gas will diffuse faster than the heavier gas. For example compare the rate of diffusion of hydrogen and oxygen.

Rate of diffusion of H2 / Rate of diffusion of O2 = vMass of O2 / Mass of H2 = v32/ 2 = v16 = 4

It shows that H2 gas which is lighter gas than O2 will diffuse four times faster than O2

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