# Question #d628f

Nov 3, 2017

$P + \left(\frac{{n}^{2} a}{V} ^ 2\right) \left(V - n b\right) = n R T$

#### Explanation:

The Van der Waal equation is simply a modification of the ideal gas law to make it a bit more "realistic". It takes into account to two major approximations that the ideal gas law makes:

• All collisions between particles are elastic , meaning that energy is conserved (i.e. no intermolecular forces).
• The particles of gas themselves have negligible volume .

This is a part of what is known as the Kinetic-Molecular Theory of gases.

Both of the above are estimations that are not necessarily true, as has been shown experimentally. The Van der Waal equation corrects for this using the factors $a$ and $b$:

• $a$ takes into account the fact that gas particles attract/repel one another through intermolecular forces.
• $b$ takes into account that the particles of gas occupy a finite volume.

Both of the above are constants specific to individual gases, and would be something that you'd look up on a table.

Another useful piece of information to know is that the you will have the most significant deviations from the predictions of the ideal gas law at high pressure and low temperature.

Why? Well, think about it logically: if a bunch of gas molecules are at low temperature, it means that they are moving relatively slowly. This means that the effects of any IMFs become much more apparent. If they are at high pressure, it means that they are all compressed into a small area. This makes the volumes occupied by the individual particles of gas much more appreciable.

Hope that helps :)