The coefficient of compression or compressibility or elasticity of gases and the effect of temperature and pressure on it.
Gas Behavior and Deviation from Ideal State
Definition: The ratio of the product of pressure and volume of a gas to the product of its temperature and the molar gas constant is defined as the Compressibility Factor (Z) of that gas. It is universally denoted by Z.
For n moles of an ideal gas, the equation of state is given by: PVi = nRT
Since real gases do not obey the ideal gas equation under ordinary conditions, for real gases: PV ≠ nRT
Let us consider the equation for real gases as: PV = ZnRT
Here, Z represents the compressibility factor for the real gas.
If 1 mole of gas is considered (n = 1), then: Z = PV / RT
Alternatively, if Vi is the molar volume of an ideal gas, then: Z = V / Vi (Actual Volume / Ideal Volume)
Gas Behavior Based on the Value of Z:
At extremely low pressures and high temperatures, real gases behave ideally. For real gases, this unique condition perfectly occurs at the Boyle Temperature.
At identical temperature and pressure, the real gas is less compressible than an ideal gas, showing deviation from ideal behavior. This phenomenon is termed as positive deviation.
At identical temperature and pressure, the real gas is more compressible than an ideal gas, showing deviation from ideal behavior. This phenomenon is termed as negative deviation.
For real gases, the magnitude of the compressibility factor (Z) fundamentally depends on two key parameters: i) Pressure (P) and ii) Temperature (T).
i) Effect of Pressure
At extremely low pressures, real gases exhibit ideal behavior (Z ≈ 1). This happens because the intermolecular distances between gas particles are remarkably large, rendering mutual intermolecular attractive forces completely negligible.
In the case of H2 and He: Due to their extremely low molecular mass, attractive forces are virtually absent between their molecules. Consequently, with an increase in pressure, the value of Z increases beyond 1 right from the beginning. Their plots do not display any concave dip or downward curve.
In the case of O2, N2, and CO2: At moderate pressures, intermolecular forces of attraction become effectively operational. Therefore, as pressure increases, the value of Z initially drops below 1 (Negative Deviation). After reaching a characteristic minimum point, any further increase in pressure causes the value of Z to steadily rise above 1 (Positive Deviation).
ii) Effect of Temperature
Varying the temperature dramatically alters the deviation and compressibility characteristics of real gases. As clearly demonstrated in Figure 2:
- At Low Temperatures (e.g., 200K): The kinetic energy of the molecules is low, allowing intermolecular forces of attraction to be highly effective. Consequently, the value of Z drops steeply at first, creating a deep concave dip.
- At High Temperatures (e.g., 1000K): The intense kinetic energy of the molecules completely overpowers intermolecular attractions. As a result, the value of Z remains greater than 1 from the very outset.
- Boyle Temperature (Tb): The specific temperature at which a real gas strictly obeys Boyle’s law and behaves ideally over an extended range of pressure is defined as the Boyle Temperature (represented by the 500K curve in the graph).
