GRAHAM’S LAW OF DIFFUSION/EFFUSION

States of matter of Class 9

GRAHAM’S LAW OF DIFFUSION/EFFUSION

Thomas Graham (1831) studied the rates of diffusion of different gases and observed that lighter gases diffuse at faster rates than the heavier gases. He came out with a generalization called Graham’s law of diffusion/effusion. According to this law.

“Under identical conditions of temperature and pressure, the rate of diffusion/effusion of a gas is inversely proportional to the square of its density (or molecular mass)”.

Mathematically,

GRAHAM’S LAW OF DIFFUSION/EFFUSIONor  GRAHAM’S LAW OF DIFFUSION/EFFUSION.

where, r is rate of diffusion/effusion of gas, d is density of gas and M is molecular mass of gas.

GRAHAM’S LAW OF DIFFUSION/EFFUSIONor  GRAHAM’S LAW OF DIFFUSION/EFFUSION.

If r1, d1, M1 and r2, d2, M2 are rates of diffusion/effusion, densities and molecular masses of gas 1 and 2 respectively then, we have,

GRAHAM’S LAW OF DIFFUSION/EFFUSIONorGRAHAM’S LAW OF DIFFUSION/EFFUSION ..... (i)

andGRAHAM’S LAW OF DIFFUSION/EFFUSION or GRAHAM’S LAW OF DIFFUSION/EFFUSION ..... (ii)

Dividing (i) by (ii), we get,

GRAHAM’S LAW OF DIFFUSION/EFFUSION

Example 7 720dm3 of SO2 diffuse through a porous partition in 60s. What volume of O2 will diffuse under similar conditions in 30s?

Solution: GRAHAM’S LAW OF DIFFUSION/EFFUSION

GRAHAM’S LAW OF DIFFUSION/EFFUSION

GRAHAM’S LAW OF DIFFUSION/EFFUSION.

Example 8 Through the two ends of a glass tube of length 200cm HCl(g) and NH3(g) are allowed to enter. At what distance NH4Cl will first appear?

Solution: NH4Cl will appear first at a distance where HCl(g) and NH3(g) will meet. Let after time ‘t’ they meet at a distance of ‘a’ cm from HCl end as shown below,

GRAHAM’S LAW OF DIFFUSION/EFFUSION

We know, GRAHAM’S LAW OF DIFFUSION/EFFUSION

Here, GRAHAM’S LAW OF DIFFUSION/EFFUSION, GRAHAM’S LAW OF DIFFUSION/EFFUSION, GRAHAM’S LAW OF DIFFUSION/EFFUSION, GRAHAM’S LAW OF DIFFUSION/EFFUSION

GRAHAM’S LAW OF DIFFUSION/EFFUSION.

GRAHAM’S LAW OF DIFFUSION/EFFUSION

Solving for ‘a’ we get, GRAHAM’S LAW OF DIFFUSION/EFFUSION.

It means NH4Cl will first appear at a distance of 81.12 cm from HCl end.

Example9 Which of the two gases ammonia and hydrogen chloride will diffuse faster and by what factor?

Solution: GRAHAM’S LAW OF DIFFUSION/EFFUSION

= GRAHAM’S LAW OF DIFFUSION/EFFUSION = 1.46 or GRAHAM’S LAW OF DIFFUSION/EFFUSION = 1.46 rHCl

Thus ammonia will diffuse 1.46 times faster than hydrogen chloride gas

GRAHAM’S LAW OF DIFFUSION/EFFUSION

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