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Diffusion of Gases

It is a matter of common observation that the gases intermix freely without the help of any external agency. For example, if a cylinder containing hydrogen gas is inverted over another cylinder containing reddish brown nitrogen dioxide gas and the lid separating the two cylinders is removed then both the cylinders gradually become reddish brown. This indicates the intermixing of hydrogen and nitrogen dioxide forming a uniform mixture.

This property of intermixing of gases is referred to as diffusion. Diffusion may, thus, be defined as the process of intermixing of two or more gases irrespective of density relationship and without the help of external agency.

The diffusion in gases is attributed to rapid movement of gas molecules and existence of large empty space between the molecules. When the two gases are brought in contact with each other, the molecules of one gas move into the empty spaces of other gas gradually and this ultimately leads to the formation of homogeneous mixture.



Effusion is a process by which a gas under pressure escapes from the vessel through a small opening or an orifice. Escaping of air through the punctured type, or football bladder, escaping of perfume molecules through the atomizer are common examples of effusion. The process of effusion is always followed by diffusion.



Thomas Graham put forwarded a generalisation after studying rates of diffusion of different gases, which is known after his name as Graham s law of 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.

where r is the rate of diffusion and dis the density of the gas.

Now, if there are two gases A and B having r 1 and r2 as their rates of diffusion and d 1 and d2 their densities respectively. Then

We know that molecular mass is twice the vapour density. Therefore, the abo\e expression may be written as

where M 1 and M2 are the molecular masses of the gases having densities d1 and d2 respectively. Thus, Graham’s law may also be stated as:


Under similar conditions of temperature and pressure the rates of diffusion of gases are inversely proportional to the square root of their molecular masses.


Again, rate of diffusion of the gas is equal to the volume of the gas which diffuses per unit time, i.e.,

Rate of diffusion = volume of the diffused / timed taken for diffusion

or                                   r = V / t


H V 1 and V 2 are the volumes of the gases diffusing in the time t 1 and t2 respectively under similar conditions, then

r1 = V1 / t1  and  r2 = V2/ t2

 Thus, putting the values of r 1 and r2 we arrive at the following formula:

Now , if                       V1 = V2 = V, we get

This implies that time taken for the diffusion of equal volumes of the two gases under similar conditions of temperature and pressure is directly proportional to the square root of their densities or molecular masses.

Similarly, if t1 = t2 = t, then

It means that volumes of the two gases which diffuse in the same time under similar conditions are inversely proportional to the square roots of their densities or molecular masses.



We have studied in the previous unit that process of diffusion also occurs in liquids but the rate of diffusion in liquids is very slow. The slow rate of diffusion in liquid can be observed by the following simple experiment:

1. Take water in a long, clean transparent glass jar.

2. With the help of long pipette put 4-5 drops of concentrated blue coloured solution of copper (II) tetraoxo-sulphate (VI) at the bottom of the jar. Keep it undisturbed and observe the change.

3. You will notice slow intermixing of liquids and it will take quite long time for the blue colour to become uniform throughout the jar.


Why Diffusion in Liquids is Slow?

The molecular motion in gases is very rapid and intermolecular voids are large. On the other hand, molecular motion in liquids is much slower and restricted. This makes the intermixing of liquids very slow.