Ideal Gas - Assumptions

The ideal gas laws resulted in the following ideal gas equation:

PV = nRT

The basis of the equation is on the following three points. For the same number of moles of gas particles:

1. The pressure of the gas is directly proportional to temperature, provided volume of gas is constant.
2. The volume of the gas is directly proportional to the temperature, provided temperature of the gas is constant.
3. The pressure of the gas is inversely proportional to volume of the gas, provided temperature of the gas remains constant. This makes sense as when I increase pressure, the volume of space that the gas particles can move around in becomes smaller.

These three laws result in the two assumption of ideal gases:

1. The intermolecular forces of the gas is insignificant.
2. The size of the gas particles is negligible (or the volume of the gas molecule is negligible)

However, real gas deviates from these assumption because they have intermolecular forces, either Van der Waals' interactions or Hydrogen-bonding. In addition, the size of the gas particles is not negligible - the gas molecule has a volume and it is not a point particle. Therefore, when ideal gas is subjected to increasing pressure, the PV term remain constant. However, when real gas is subjected to increasing pressure, we first observe a dip and then subsequently the PV value soars.

(1) The dip in PV value for real gas.

This can be reasoned. When the pressure starts to increase and it is not sufficiently high, the gas would come close together. This provides the opportunity for the individual gas particles to interact with each other as they are able to cause their intermolecular forces to act upon each other. Once the intermolecular forces act that serves as an additional pull that brings the gas particles closer together and hence the volume of the gas is smaller than predicted hence the PV term is smaller, thus resulting in the dip.

The sheer fact that real gases have intermolecular forces, this is the reason why gases can be condensed to liquid state. The absence of intermolecular force will mean that it is impossible for gases to liquidfy.

(2) The PV value soars.

At a given high pressure imposed on an ideal gas, the PV term remains the same as when the gas experiences a lower pressure. As gases can be compressed, the volume of the gas (which can be seen as the volume of the space the gas particle is traveling in) cannot be directly obtained. It is actually approximated from the volume of the container that contains the gas. Although, the volume of the container consists of the volume of the space the gas can move in and the volume of the molecules, this "guess" is perfectly fine for ideal gas as the particles are point particles (hence the particles have no volume). Thus, the volume of the container is a good approximate to the volume of space that gas particles can travel in.

However, for real gases when it is subjected to high pressure (and if it still remains as a gas), the size of the particles become significant as compared to volume of the space the particles move in. Hence, for a fixed container, the significant size of the particles reduces the volume of the space that the particles can travel in and hence the volume of the gas is actually smaller than the actual volume of the container. Since the volume of the container is used in the calculation, this results in the PV to be larger than expected.

The molecular interpretation of this increase can be seen when we have the gas particles so close together that their respective electron cloud comes into contact with each other.  This results in a repulsion and "pushes" the particles away from each other, increasing their volume.

As we deal with the environment which makes up of a mixture of different gases, it useful to remind ourselves the purpose of Dalton's Law of partial pressure. The law states that when we have a mixture of gases which do not interact chemically with each other, the total pressure of the gas mixture is the sum of the individual partial pressure of the different gases that make up the mixture.

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^{Article written by Kwok YL 2011.}

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