Real Gas

The air we breathe is mostly made up of a mixture of various gases. Air contains 78% nitrogen, 21% oxygen, and 1% other types of gases such as argon, carbon dioxide, hydrogen, helium, neon, methane, etc.

The gaseous state of matter is easy to remember because gas particles have no fixed shape, no fixed volume, and because of the empty space that exists between them, gases are able to randomly move around the container.

• This article is about real gases.
• First, we will define real gases.
• Then we will jump into the real gas law and the van der Waals equation.
• Lastly, we will apply the real gas formula to solve problems.

Ideal Gases

The Kinetic molecular theory is a theory that makes assumptions about the behavior of gases. Gases that behave in the same way as stated in this theory are called ideal gases.

The main points that the kinetic molecular theory states about the behavior of ideal gases are:

• The particles of gases are in constant, random motion.
• Gas molecules have kinetic energy.
• The collisions between gas molecules are elastic - gases do not lose or transfer energy during collisions.
• The volume of gases is negligible because of the huge amount of empty space between gas particles.
• Gas particles have no attractive or repulsive forces between neighboring molecules.

At high temperature and low pressure, gases tend to behave like ideal gases because high temperature makes intermolecular forces become insignificant. However, no gases behave exactly as you would expect an ideal gas to behave. Ideals gases are hypothetical and are not really part of real life!

Fig. 1: Expected Behavior of an ideal gas - Isadora Santos, StudySmarter Originals.

What is the definition of a real gas?

Under high pressure and low temperature, gases deviate from being considered an ideal gas. Instead, there are called real gases.

The factors that make them real gases instead of ideal gases are:

• Real gases do occupy some volume.
• Real gases have some intermolecular (attractive) forces present.

Examples of ideal gases include noble gases (group 18 of the periodic table), diatomic molecules such as H₂, O_2, Cl_2, and polyatomic molecules like NH₃, CO_2, and water vapor. Really any gases you can think of are real gases, except for the theoretical ideal gases.

Deviation from Ideal Gases

Gases deviate from the behavior of ideal gases when they are at low temperatures and high pressures. At high pressures, the gas particles get closer together. As pressure increases, volume decreases. When gases have low temperatures, their kinetic energy is low since temperature, and kinetic energy is directly proportional to one another. This low temperature makes it great for the attractive forces to be able to interact with the gas molecules because of their slower speed. The low temperature also makes the gas more compressible.

Real Gas Law

Johannes van der Waals, a Dutch physics professor, wanted to adapt the ideal gas law into a law that would be suitable for the behavior of real gases. So, in 1873, van der Waals derived the real gas law from the ideal gas law.

How exactly did Van der Waals do this? First, he looked at the ideal gas equation.

$$$P\cdot V=n\cdot R\cdot T$

Remember that:

• Pressure (P) is in Pascal (Pa)
• Volume (V) is in Liters
• n is the number of moles of gas
• R is the universal gas constant
• Temperature (T) is the Kelvin

Since gases do have volume, he made adjustments to correct the volume. He saw that the real volume of gases increased with the increase of the number of moles of gas present. Van der Waals proposed that suggested that the correct volume should be the volume of gas minus the number of moles (n) of gas multiplied by a constant b. So, the formula for the correct volume:

$$=V-nb$$

He also corrected pressure to account for the attractive forces, which are stronger at low pressure and higher density. Van der Waals added a new constant a for this. The greater the constant a, the greater the intermolecular forces holding the gas molecules together. The corrected pressure formula was equal to

$$P+\frac{an^{2}}{V^{2}}$$

Van der Walls then needed to modify the equation to account for the finite volume of the gas particles and the presence of intermolecular forces. So he came up with a formula for calculating real gas, which he called the van der Waals equation for real gases.

$$[P+a(\frac{n}{V})^{2}]\cdot [V-bn]=n\cdot R\cdot T$$

The values for Van de Waals constants a and b depend on the type of gas we are dealing with:

Calculations Involving Van der Waals Equation

Know that we know a formula for real gases (non-ideal gases), we can use it to solve problems that you might encounter during your exam.

Van der waals equation:

$$[P+a(\frac{n}{V})^{2}]\cdot [V-bn]=n\cdot R\cdot T$$

What if the question asks you to compare the pressure of gases behaving as an ideal and a real gas? In this case, we would need to find the answer for the gas using both the ideal gas equation and the Van der Waals equation. A general rule for comparing the pressure and volume of gases behavior ideally or non-ideally is:

• The pressure of a real gas (P_real) < Pressure of an ideal gas (P_ideal).
• The volume of a real gas (V_real) > Volume of an ideal gas (V_ideal).

_References:

_{Moore, J. T., & Langley, R. (2021). AP Chemistry. McGraw-Hill.}

_{Zumdahl, S. S., Zumdahl, S. A., & DeCoste, D. J. (2016). Chemistry. Cengage Learning}