What is the Compressibility Factor of An Ideal Gas?

Before we proceed with all the complex terminology related to an ideal gas, let’s discuss the simple and basic terms related to it. What is an ideal gas? Any gas that obeys the Ideal Gas Law falls under the category of the ideal gas. Now, you may wonder what is the ideal gas law? An ideal gas is defined as a gas with a negligible volume of the molecules as well as the intermolecular forces of attraction. The values are so small that it does not affect the gas. Such gas is termed an ideal gas. An ideal gas depends on temperature, pressure, and volume.

The Ideal Gas Law states that any gas that is analysed under three conditions including pressure, temperature, and volume exhibits certain characteristics where it has no effect on it whatsoever and is termed as the ideal gas. Any gas that fails to meet these criteria does not fall under the ideal gas category. The whole system of the Ideal Gas Law depends on pressure, volume, and temperature. 

Here’s a deeper insight into what is an ideal gas – 

The Ideal Gas Law is an important concept of Physics. It is because the composition or the characteristics of an ideal gas is defined by this alone. The ideal gas does not have any intermolecular forces of attraction between them. This ensures that the particles of gas can move freely across without any boundaries. The volume of molecules present in the gas is also negligible. This adheres to the Ideal Gas Law and makes any gas an ideal one. In simple words, it means that the spheres are present in the same container where they collide with each other but never make any contact with each other. They are present in unison but have no contact as such. 

The Ideal Gas Law also states any change in the overall temperature of the gas. It also causes a significant change in the kinetic energy of the gas. However, the change in kinetic energy is always followed by the change in the temperature of the gas. 

Ideal gas depends solely on three main factors. They are: 

• P: Absolutely Pressure 
• T: Absolute Temperature
• V: Volume 

The deduction of a relationship between them looks like: 

Ideal Gas Law: PV = nRT = NkT 

Herein, R = Universal Gas Constant = 8.3145 J/mol K

• n = number of moles
• k = Boltzmann Constant 1.38066 x 10^-23 J/K = 8.617385 x 10^-5 eV/K
• k = R/NA
• NA = Avagadro’s Number = 6.0221 x 10²³ /mol
•  N = number of molecules

Types of Ideal Gas 

There are three types of ideal gases. They are: 

• The classical ideal gas or the Maxwell-Boltzmann ideal gas 
• The ideal quantum gas or the Bose gas
• The ideal quantum Fermi gas

The classical ideal gas: The classical ideal gas has to adhere to certain rules and norms that make it depend on the entropy of the gas. It is not followed by the ideal quantum Boltzmann gas.

The ideal quantum gas: It is also known as the Bose gas. It contains a high amount of Bosons.

The ideal quantum Fermi gas: This ideal quantum gas consists of Fermions. That is why it is called Fermi gas. 

Critical Compressibility Factor of An Ideal Gas (Z) 

The Critical Compressibility Factor of an Ideal Gas is defined as the deviation of the properties of real gas from that of an ideal gas. It is a ratio that measures the properties of real gas and an ideal gas. It gives us information on how real gases differ from an ideal gas even when they are given the same temperature and pressure conditions. 

The Critical Compressibility Factor of an Ideal Gas (Z) is always 1. However, deviations can be observed in this depending upon the effect that the intermolecular forces have on it. It is a proven fact that the compressibility factor of different gases is different at different temperatures. 

The Ideal  Law is: 

PVm = RT 

The law when stated for non-ideality is: 

PVm = ZRT

Herein, 

• P = Pressure 
• Z= Compressibility Factor 
• R = Universal Gas Constant 
• Vm= Molar Volume of Gas 
• T = Temperature 

Henceforth, 

Z = PVm/RT 

The main drawback of the Critical Compressibility Factor of an Ideal Gas (Z) is that: it does not remain constant and keeps on varying from one gas to another depending upon the conditions. Hence, it should always be derived experimentally. 

Conclusion

In this article, we walked you through the definition of what is an ideal gas? An ideal gas has negligible forces of intermolecular attraction. Further, the volume is negligible as well. When these conditions are obeyed, it is an ideal gas. It should obey the Ideal Gas Law. It states that: The Ideal Gas Law also states any change in the overall temperature of the gas. It also causes a significant change in the kinetic energy of the gas. However, the change in kinetic energy is always followed by the change in the temperature of the gas. The properties of the ideal gas are also dependent on the absolute temperature, pressure, and volume. Due to this, the relationship between the two and the deduction of the equation also involve them. Next, we talked about the compressibility factor of an ideal gas (Z). It is the ratio or deviation of the real gas from the ideal gas.