Ideal Behaviour

An ideal gas is a fossil gas composed of many random particles that are not subject to particle interaction. An ideal gas concept is useful because it complies with proper gas law, a simplified calculation of state, and is allowed to be analysed under mechanics.

Under varying degrees of temperature and pressure, many real gases behave like ideal gases when gas molecules play the role of proper particles. Many gases such as nitrogen, oxygen, hydrogen, other heavy gases such as carbon dioxide and compounds such as air can be treated as suitable gases between reasonable tolerances over a range of parameters around normal temperatures and pressures. In general, gas behaves as an ideal gas at high temperatures and low pressures, as potential forces due to intermolecular forces become very small compared to the kinetic energy of the particles, and the molecular mass is large compared to the empty space between them.

Ideal gas behaviour derivation:

Gas is the basic element of matter. A gas is a group of molecules with a considerable distance between their molecules. Because of this distance, colour gases are invisible to the human eye and are analysed using four measurable parameters: pressure (P), volume (V), number of moles (n), and temperature (T). Ideal gas law is a mathematical calculation related to all these parameters. It is a combination of several laws that describe the behaviour of gases.

Boyle’s law:

In 1662, Robert Boyle confirmed the earlier discovery related to the pressure of gas in its volume. Boyle’s law states that gas pressure is inversely proportional to its volume if the temperature and number of gas moles are maintained.

P α 1/V

Therefore, it gives P1V1 = P2V2 for calculating the new pressure or volume.

Charle’s and Gay – Lussac law:

In the 1780s, the unprinted work of French scientist Jacques Charles was lauded by French scientist Joseph Louis Gay-Lussac for describing the direct relationship between volume and gas temperature.

Given as V α T

Hence it can be written as V1 / T1 = V2 / T2

Gussac’s law extended the law proposed by Charles and related the pressure and temperature. As per Gussac’s law, pressure is directly proportional to temperature. It is given as

P α T

For calculating the new pressure and temperature, it is given as

P1 / T1 = P2 / T2

Avogadro law:

At last, Avogadro proposed a law that states that volume is directly proportional to the number of moles of gas. This is given by

V α n

And for calculating the new volume and moles, it is given by

V1 / n1 = V2 / n2

Ideal gas law:

In 1834, Emil Clapeyron combined all these gas laws and proposed an ideal gas law. Ideal gas law causes pressure (P), volume (V), gas moles (n), and temperature (T), with a constant rigid equilibrium, positive rigid gas (R). The universal gas constant, R, is equivalent to 8.314 J · K-1 mol-1.

It is given as

PV = nRT

The universal gas constant R is a number that satisfies the pressure-volume-temperature-equity ratio. R has different values and units depending on user pressure, volume, moles, and temperature specifications. Various R values are not an online site, or the user can use size analysis to change the rental units of pressure, volume, moles, and temperature to match the known R value. As long as the units agree, either method is acceptable. The temperature in Ideal Gas Law should be in whole units (Rankine [degrees R] or Kelvin [K]) to prevent the right side from becoming zero, which violates the pressure-volume-temperature relationships. Conversion to full temperature units is a simple addition to Fahrenheit (F) or Celsius (C) temperature: 

Degrees R = F + 459.67 and K = C + 273.15.

Assumptions of a gas to be ideal:

1. The particles of gas should have negligible volume.

2. There should be equally sized particles, and there should not be any intermolecular forces between the molecules.

3. The gas particles follow Newton’s laws of motion and move randomly.

4. Perfect elastic collisions are observed in gas particles with no energy loss.

Ideal gas behaviour:

There are no ideal gases. Any gas particles have a volume within the system, violating initial assumptions. Additionally, gas particles can have different sizes; for example, hydrogen gas is much smaller than xenon gas. The gases in the system are powerful intermolecular and adjoining gas particles, especially at low temperatures where the particles do not move rapidly and communicate with each other. Even if the gas particles can move randomly, they do not have complete expandable friction due to energy and pressure conservation within the system.

When systems are not under low pressure or high temperature, gas particles can interact; this communication severely restricts the accuracy of the Ideal Gas Law. There are, however, other models, such as the Van der Waals Equation of State, accounting for the volume of gas particles and intermolecular interactions.

Ideal gas types:

There are three different types of ideal gases. These are:

1. Classical or Maxwell – Boltzmann ideal gas

2. Ideal quantum Bose gas

3. Ideal quantum Fermi gas

The classical ideal gas can be divided into classical thermodynamic gas and Boltzmann’s quantum gas. Both are the same, except that the classical thermodynamic gas is derived from classical mechanics, and specific thermodynamic parameters such as entropy are specified only within the fixed constant. Boltzmann’s qualified quantum gas overcomes this limit by taking the quantum limit of Bose gas and quantum Fermi gas at the maximum temperature limit to specify these additional components.

Conclusion:

There is no real gas indicating ideal gas behaviour, although many real gases estimate it over various conditions. Deviations in ideal gas behaviour can be observed in PV / nRT compared to P at a given temperature; for optimal gas, PV / nRT compared to P = 1 under all conditions. 

At high pressures, more real gases show higher PV / nRT values than predicted by the proper gas law, while at lower pressures, more real gases show higher PV / nRT values close to those predicted for the proper gas law. Gases are closely related to ideal gas behaviour at high temperatures and low pressures. The van der Waals equation can explain deviations from the proper behaviour of gas law, which includes empirical constants to adjust the actual volume of gas molecules and measure pressure reduction due to the gravitational force between the molecules.