- 1). Learn, first, the equation for the ideal gas law. It is,
PV = nRT,
where P is the pressure of the system, V is its volume, n is the number of moles of gas, R is the ideal gas constant in relevant units, and T is the temperature of the system. - 2). Recognize the limited application of the ideal gas law. It is best applied to helium gas. An evaluation of helium gas and what changes when a more complicated gas is used will lead to improvements of the ideal gas law equation.
- 3). Consider, first. There is need for a volume correction. Atoms have a definite size and volume of their own. To be completely accurate in calculations, the size of the atoms (or molecules) needs to be taken into account and subtracted from the total, resulting in the total available volume. Thus,
P(V-nb) = nRT,
where b is the actual volume of a mole of molecules. Since the volume of the gas molecules depends upon the number of moles of gas, the subtractive term becomes --nb. - 4). Now reflect on why the ideal gas law works best at low pressures and/or higher temperatures. It is because of attractive forces between neighboring molecules. When they are drawn closer together, the system loses pressure. An added term is necessary to quantitatively explain the lowered pressure. Van der Waals chose +an²/V².
(P+an²/V²)(V-nb) = nRT
The above equation is Van der Waals modification of the ideal gas law. As might be expected, a liquid with a high boiling point has a large value for "a." - 5). Make the adjustments. The volume of the atoms or molecules can be approximated by assuming they are spherical. Base the calculation on the atomic radius or radii in the case of molecules. Unfortunately, the value of "a" must be determined experimentally. Some values for Van der Waal's constants have already been evaluated, and are available to use, such as the ones on the websites referred to in the references, below.
next post