Some of the most important Physics Topics include energy, motion, and force.
Which Equation is Known as Van der Waals Equation?
If a gas obeys Boyle’s law and Charles’ law accurately, then it is called an ideal gas. But in practice, real gases do not obey these ideal gas conditions in all circumstances. Usual, a real gas behaves as an ideal gas at high temperatures and low pressures. But at low temperatures and high pressures, the behaviour deviates from that of an ideal gas.
The equation of state for 1 mol of an ideal gas is pV = RT. A real gas deviates from this equation chiefly due to the following two reasons:
i) The Kinetic theory assumes that gas molecules are point masses and the volume of the molecules is negligible compared to the total volume of the gas. But every molecule, however small, has a finite volume. So their total volume is not always negligible. In particular, at low temperatures and high pressures, the volume of a gas is comparatively small. In this case, the volume of the gas molecules becomes an important factor. The effective volume for the motion of the molecules inside the gas container of volume V is reduced by an amount b (say). Then the equation of state for 1 mol of the gas becomes p(V – b) = RT.
ii) The kinetic theory further assumes that the molecules do not attract one another. But in particular, at low temperatures and high pressures, the molecules come closer to one another. As a result, the attractive forces are no longer negligible. Now consider a molecule near the wall of the container. It experiences a resultant force towards the interior due to attractions by the other molecules. So it collides with the wall at a comparatively less velocity: As a result, the pressure on the wall becomes less.
Let p’ be the reduction of the pressure on the wall due to all these molecules. van der Waals established that p’ = \(\frac{a}{V^2}\), where a is a constant for a particular gas. Now, if p is the effective pressure on the wall, then the pressure would be p + p’ or p + \(\frac{a}{V^2}\) considering that the gas was ideal. So the equation of state for 1 mol of a real gas becomes
(p + \(\frac{a}{V^2}\)) (V – b) = RT ……. (1)
Equation (1) is called van der Waals equation for a real gas. The constants a and b are known as van der Waals constants; their values depend on the nature of the gas. For n mol of a real gas, let V be its volume. Then molar volume = \(\frac{V}{n}\). Then, we get
This is the form of van der Waals equation for n mol of a real gas.
It is to be noted that the van der Waals equation is only one of several equations of state of real gases, proposed by different scientists.