## Graham’s Law of Diffusion

Graham’s law of diffusion states that the rate of diffusion of a gas at a given temperature is inversely proportional to the square root of its molecular mass, m.

I.e. R α 1/√m

Also, vapour density (ρ) = molar mass (g)/molar volume (v)

Molar mass = vapor density (ρ) x molar volume (v)

Therefore, R α 1/√ρv

For two gases with molecular masses m1 and m2 ; and rates of diffusion R1 and R2:

R1/R2 = √m2/√m1 – (1)

R1/R2 = √ρ2v2 /√ρ1v1 – (2)

Also, rate of diffusion = volume/time I.e. the greater the rate, the shorter the time.

Comparing the rates of diffusion of equal volumes of two gases in times t1 and t2, we have R1 = V/t1 and R2 = V/t2

Note:

- The lighter or less dense a gas is, the greater is its rate of diffusion.

- If the gases are at the same temperature and pressure, they must have the same molar volumes. Therefore,

R1/R2 = √ρ2 /√ρ1 – (3)

R1/R2 = t2/t1 – (4)

Therefore, R1/R2 = t2/t1 = √m2 /√m1 = (5)

By the above last equation, equation (5), you could determine the value of any of the parameters by establishing an equation with those whose values are given.

Note:

- The vapour density (v.d.) of a gas is equal to half its relative molecular mass(r.m.m.).

I.e. r.m.m. = 2 x v. d.

### Calculation Based on Graham's Law of Diffusion

30 cm3 of a gas, the empirical formula of which was CH3, diffuses through a porous partition in 45.2 s. 30 cm3 of hydrogen diffused in 11.7 s under the same conditions. Calculate (i) the vapour density of the gas (ii) the molecular formula of the gas?

Solution:

(i). The two gases are of equal volumes,

tx/tH = √mx /√mH

45.2/11.7 = √(mx/2)

2(45.2/11.7)2 = mx

mx = 2 x 14.92 = 29.84 (g)

r.m.m. = 2 x v.d.

v.d. = r.m.m./2

v.d. = 29.84/2 = 14.92

(ii). xCH3 = 30

15x = 30

x = 2

Therefore, molecular formula = C2H6