 # What does Van der Waals' equation mean? The Van der Waals equation of state for gases is very similar to the ideal gas law shown above.  In fact, in this form it can be seen that his equation is merely the ideal gas law, modified by two factors, a and b a and b are different for every compound as they describe the interactions between the molecules of the compound.  a describes the Van der Waals forces at work, while b is related to the size of the molecules.  To understand this equation molar volume, Vm must be understood.  As Van der Waals' equation applies only as an equation of state for gases the molar volume is a measure of the volume taken up by one mole of a gas, generally under non-standard conditions.

#### Molar volume and a

a is simply a number derived from consideration of all the intermolecular attractions between molecules of a gas.  These will always include London force and may also include Keesom force, hydrogen bonding and others.  As can be seen in the last part of the equation, a is divided by Vm implying that as the volume increases and the molecules become more spread out the effect of these forces on neighbouring molecules decreases, and so the behaviour of the gas becomes more ideal.  So, if a = 0, then the Van der Waals equation becomes the ideal gas equation modified only by b.  The negative sign is significant in that a high value of a would lead to a recorded pressure lower than the true pressure.  To correct for this, the a term adds to the pressure: #### Molar volume and b

b is related to the volume of the gas molecules themselves.  It is in fact the effective molar volume of the gas, with units of m3 mol-1.  If the molecules are small, b is insignificant.  If however the molecules are large enough, or their container is small enough, the volume of the molecules is significant with respect to the volume of the container.  In this case:

The actual volume of the container = measured volume - ( number of moles x effective molar volume)

Vactual = V - nb