Tuesday, 29 November 2016


Volume and Pressure Correction By Van der Waals's Equation

     Van der Waals pointed out that both volume and pressure factors in ideal gas equation needed correction to make it applicable to the real gases.
Volume Correction
(i) Compression of a Gas: When a gas is compressed, the molecules are pushed so close together that the repulsive forces operate between them. When pressure is increased further, it is opposed by the molecules themselves. Actually, the molecules have definite volume, no doubt, very small as compared to the vessel, but it is not negligible.
(ii) Van der Waals' Postulate: Van der Waals postulated that the actual volume of molecules can no longer be neglected in a highly compressed gas. If the effective volume of the molecules per mole of a gas is represented by b, then the volume available to gas molecules is the volume of the vessel minus the volume of gas molecules.
Vfree = Vvessel - b (where Vfree is the volume available to gas molecules)
(iii) Excluded Volume "b": The volume of a gas which is occupied by 1 mole of gas molecules in highly compressed state, but not in the liquid state, is called excluded volume or effective volume or incompressible  volume (b). It is a constant and characteristic of a gas. It value depends upon the size of the molecules. It is also a Van der Waals constant. It is not equal to the actual volume of gas molecules. In fact, it is four times the actual volume of molecules.
b = 4Vm (where Vm is actual volume of one mole of gas molecules. 
Pressure Correction
(i) Attraction Between Molecules: A molecule in the interior of a gas is attracted by other molecules on all sides, so these attractive forces are cancelled out. However, when a molecule strikes the wall of a container, it experiences a force of attraction towards the other molecules in the gas. The decreases the force of its impact on the wall.
(ii) Pressure on the Wall of Container: Consider a molecule "A" which is unable to create pressure on the wall due to the pressure of attractive forces due to "B" type molecule. Let the observed pressure on the wall of the container is "P". The pressure is less than the actual pressure Pi by an amount P'. So,
P = Pi - P'
Where Pi is the true kinetic pressure, if the forces of attraction would have been absent. P' is the amount of pressure lessened due to attractive forces. Ideal pressure Pi is;
Pi = P + P'     ..... (i)
It is suggested that a part of the pressure "P" for one mole of a gas used up against inter-molecular attractions should decrease as volume increases.  
(iii) Value of P': The value of P' in terms of a constant "a" which accounts for the attractive forces and the volume V of vessel can be written as:
P' = a/V² ..... (ii) 
Greater the attractive forces among the gas molecules, smaller the volume of vessel, greater the value of lessened pressure P'. "a" is a coefficient of attraction or attraction per unit volume. It has a constant value for a particular real gas. 
(iv) Value of Pi: Putting the value of P' from equation (ii) into (i)
Pi = P + a/V²
(v) For One Mole of a Gas:
(vi) For "n" Moles of a Gas
     This is called van der Waals's equation. "a" and "b" are called van der Waals's constants. 
(vii) Common and SI Units of "a" and "b"

No comments:

Post a Comment