Why is van der Waals equation used?

Question

Noah Aldrich · Accepted Answer

Well, real gases have intermolecular forces, don't they?

And thus, we use the van der Waals equation of state to account for such forces:

#P = (RT)/(barV - b) - a/(barV^2)#

These forces manifest themselves in:

and these modify the true molar volume, #barV -= V/n#. Upon solving for the cubic equation in terms of the molar volume,

#barul|stackrel(" ")(" "barV^3 - (b + (RT)/P)barV^2 + a/PbarV - (ab)/P = 0" ")|#

For this, we need

Then this can be solved via whatever method you want to solve this cubic. This is gone into more detail here.

Three solutions arise:

To know what you have just gotten, compare with the other #barV# to see if you have found the largest one. If you did not maximize #barV#, try a different guess until you do.

Mateo Aguilar · Answer

undefined The van der Waals equation is used to describe the behavior of real gases more accurately than the ideal gas law, especially at high pressures and low temperatures. It accounts for the volume occupied by gas molecules and the attractive forces between them, which are neglected in the ideal gas law.

Luna Chen · Answer

undefined The van der Waals equation is used to describe the behavior of real gases more accurately than the ideal gas law. It considers two corrections to the ideal gas law: the volume occupied by gas molecules themselves and the attractive forces between gas molecules.

1. Volume Correction: In the ideal gas law, gas molecules are assumed to have zero volume, leading to inaccurate predictions, especially at high pressures and low temperatures. The van der Waals equation incorporates a correction for the volume occupied by gas molecules, which improves the accuracy of predictions.

2. Pressure Correction: The ideal gas law assumes that gas molecules do not interact with each other. In reality, there are attractive forces between gas molecules, particularly at short distances. These intermolecular forces reduce the pressure exerted by the gas on the container walls. The van der Waals equation includes a correction term to account for these attractive forces, making it more suitable for describing real gas behavior.

Overall, the van der Waals equation provides a more accurate description of gas behavior under various conditions, especially at high pressures and low temperatures, where deviations from ideal behavior are significant. Therefore, it is used in situations where the ideal gas law fails to provide accurate predictions.