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.

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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.

• 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.

Before you jump into the interesting world of real gases, you want to have a good grasp of the "Ideal Gas Law", if you are ready we can move on, otherwise read up on that first!

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.

Real gases (also known as non-ideal gases) are gases that do not follow the Kinetic molecular theory, so they deviate from being an ideal gas.

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, O2, Cl2, and polyatomic molecules like NH3, CO2, and water vapor. Really any gases you can think of are real gases, except for the theoretical ideal gases.

Under which conditions would a real gas closely behave according to the kinetic molecular theory of gases?

A real gas closely would behave as an ideal gas when pressure is low and temperature is high.

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.

What are the two properties that cause the deviation of real gases from behaving ideally?

Ideal gases do not occupy volume and have no attractive/repulsive forces between neighboring molecules. Real gases have a finite volume and intermolecular forces of attraction between gas molecules.

There are two properties used to measure how much a gas deviates from the ideal gas law. One being fugacity and the other compressibility factor. Fugacity works like the activity for gases and is hard to find values for it. However, the compressibility factor (Z) is often used in industrial applications and you can easily get measured values for it. Here is an equation for this:

$$Z=\frac{R\cdot T}{p\cdot V}$$

Now if you think about this Z is suspiciously like n for ideal gases, right? Well, this is the idea here, if Z = 1, it is an ideal gas, and the bigger the deviation the less ideal the gas is. You can check that around room temperature most common gases are actually pretty close to ideal gases.

For example, the compressibility factor of hydrogen at standard temperature and pressure is around Z = 1.0006 or in percentage, there is a 0.06% difference between ideal and real hydrogen at this temp and pressure.

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.

Real Gases - Key takeaways

• An ideal gas is a gas that has no molecular volume and no interaction between molecules.
• Real gases deviate from behaving ideally at low temperature and high pressure.
• Real gases have a definite volume and the presence of intermolecular interactions between neighboring gas molecules, whilst ideal gases do not have these.
• The equation for real gases is called the Van der Waals equation.
• The Van der Waals formula is $\left[\mathrm{P}+\mathit{}a{\mathit{\left(}\frac{n}{V}\mathit{\right)}}^{\mathit{2}}\mathit{\right]}\mathit{}\mathit{\left(}V\mathit{-}bn\mathit{\right)}\mathit{}\mathit{=}\mathit{}nRT$

References:

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

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

Flashcards in Real Gas 18

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What is real gas?

A real gas is a gas that does not behave ideally.

What is an example of real gas?

An example of real gas would be the group 18 gases (noble gases), and also gas molecules such as H2, O2, and CO2. All gases that actually exist are real gases.

What is the real gas equation?

Real gases do not have a governing equation like ideal gases do. There are multiple equations which you can choose from depending on how precesize you need to be.

The most commonly used real gas equation is also called the Van der Waals equation. The formula for the real gas equation is: [P + a (n /V) 2 ] (V - bn) = nRT

Where: P,V,n,R,T are the standard components of the ideal gas law.  a is a constant describing the intermolecular forces between gas atoms and b is a constant accounting for the size of the gas molecules. These constants differ for every gas.

What is real gas law?

The real gas law is the law describing the behavior of gases that deviate from the ideal gas law.

How are real gases different from ideal gases?

Real gases differ from ideal gases by having finite volume and intermolecular (attractive) forces, while ideal gases occupy no volume and have no attractive or repulsive forces between molecules.

Test your knowledge with multiple choice flashcards

The ________ describes the ideal behavior of gases.

True or false: Collisions between gas particles are elastic

True or false: Ideal gases have a definite volume.

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