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States of Matter
   Introduction to States of Matter by S.S. Education
   The Gaseous State S.S. Education
   Gas Laws - Boyle's Law by S.S. Education
   Charle's Law by S.S. Education
   Avogadro's Law by S.S. Education
   Dalton's Law of Partial Pressures by S.S. Education
   Graham's Law of Diffusion by S.S. Education
   Ideal Gas Equation by S.S. Education
   Ideal and Real Gases by S.S. Education
   Kinetic Molecular Theory of Gases by S.S. Education
   Liquefaction of Gases by S.S. Education
   Relationship between Critical Constant and Van der Waal's Constants by S.S. Education
   Maxwell's Distribution of Molecular Speeds by S.S. Education
   The Liquid State by S.S. Education
   Properties of Liquids - I by S.S. Education
   Properties of Liquids - II by S.S. Education
   The Solid State by S.S. Education
   Classification of Solids by S.S. Education
   Crystalline Solids by S.S. Education
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   Differential Equation Tutorials
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Graham's Law of Diffusion

Gases have the tendency to spontaneously intermix and form a homogenous mixture without the help of external agency. This is due to the presence of large amount of empty space between the gas molecules that makes their movement rapid into each other. The gases move from a region of higher concentration to a region of lower concentration until the mixture attains uniform concentration.
Graham studied the rate of diffusion of various gases and gave this law. It states that under similar conditions of temperature and pressure, the rates of diffusion of gases are inversely proportional to the square roots of their densities.
Rate of diffusion a
If r1 and r2 are the rates of diffusion of two gases 'A' and 'B' and r1 and r2 are their densities, then
r1 a and r2 a
(same T and P)
Molecular mass is twice the vapour density, substituting this in the above equation, we have

where M1 and M2 are the molecular masses of the two gases. Thus, the rate of diffusion of gases are inversely proportional to the square root of their molecular masses.
Rate of diffusion is also equal to the volume of the gas, which diffused per unit time,

r = V/t
If V1 and V2 are the volumes of the gases diffusing in time t1 and t2 respectively, then r1 = (V1 / t1) and r2 = (V2 / t2)
Therefore,

If the volume diffused is the same, (V1 = V2)
Then,

Graham's law is useful in:
Separation of gases having different densities by diffusion.
Determining the densities and molecular masses of unknown gases by comparing their rates of diffusion with known gases.
Separating the isotopes of some of the elements.
Effusion
When the gases contained in a vessel are allowed to escape through a small aperature, it is effusion.

Fig: - Process of diffusion and effusion
Problem
4. An unknown gas diffuses four times as quickly as oxygen. Calculate the molecular mass of the gas.
Solution
Let the rate of diffusion of oxygen be r(O2) = r1
The rate of diffusion of the unknown gas r (x) = 4r
Molecular mass of O, M(O) = 32
Molecular mass of unknown gas M (x) = M
From Graham's Law of diffusion,

or

Squaring on both sides,
(1/16) = (M(x) / 32)
M(x) = (32/16) = 2


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