GRAHAM’S LAW OF DIFFUSION/EFFUSION
The ability of a gas to spread and occupy the whole available volume irrespective of other gases present in the container is called diffusion.
Effusion is the process by which a gas escapes from one chamber of a vessel through a small opening or an orifice. r = volume diffused / time taken = V / T
Thomas Graham in 1831 proposed the law of gaseous diffusion. The law states under similar conditions of temperature and pressure, the rates of diffusion of gases are inversely proportional to the square roots of their densities.
r ∝ 1 / √d where is the rate of diffusion and d is the density of the gas.
Now, if there are two gases A and B having r1 and r2 as their rates of diffusion and d1 and d2 their densities respectively. Then
r1 ∝ 1 / √d1 and r2 ∝ 1 / √d2 or, √d2/d1 (at same T and P)
r1/r2 = √M2 / 2 M1 / 2 = √M2 / M1 = V1 / V2 T1 / T2
Here M1 and M2 are the molecular masses of the gases having densities d1 and d2 respectively.
Graham’s law of diffusion also holds good for effusion.
Effect of pressure on state of diffusion
The rate of diffusion (r) of a gas at constant temperature is directly preoperational to its pressure
r ∝ P at constatnt temperature
r ∝ 1 / √d at constant temperature
r1 / r2 = P1 / P2 × √M2 / M1
Illustration 9. Which of the two gases ammonia and hydrogen chloride will diffuse faster and by what factor?
Solution: rNH3 / rHCl = (MHCl / MNH3)1/2
= (36.5 / 17)1/2 = 1.46 or rNH3 = 1.46 rHCl
Thus ammonia will diffuse 1.46 times faster than hydrogen chloride gas
Illustration 10. A certain gas diffuses from two different vessels A and B. The vessel A has a circular orifice while vessel B has a square orifice of length equal to the radius of the orifice of vessel A. The ratio of the rates of diffusion of the gas from vessel A to vessel B, assuming same temperature and pressure is;
(A) π (B) 1/π
(C) 1:1 (D) 2:1
Solution: The rate of diffusion is directly proportional to the area of orifice.
∴ dA α πr2
dB α r2
∴ dA / dB = π
Hence, (A) is correct.
A gaseous mixture of O2 and X containing 20% of X diffused through a small hole in 134 secs while pure O2 takes 124 secs to diffuse through the same hole. Find molecular weight of X?
A straight glass tube of 200 cm length has two inlets X and Y at the two ends. HCl gas through inlet X and NH3 gas through inlet Y are allowed to enter in the tube at the same time and same pressure. White fumes first appear at a point P inside the tube. Calculate the distance of P from X.
Exercise 8. For 10 minute each, at from two identical holes nitrogen and an unknown gas are leaked into a common vessel of 3 L capacity. The resulting pressure is 4.18 bar and the mixture contains 0.4 mole of nitrogen. What is the molar mass of unknown gas?