# Real Gas

Did you know that the air we breathe is mostly made up of a mixture of different gases? Yup, it's true! Nitrogen makes up 78% of the air, while oxygen makes up 21%. The remaining 1% is a mix of other gases like argon, carbon dioxide, hydrogen, helium, neon, and methane.

Now, let's talk about real gases. Real gases are different from ideal gases because they don't follow all the gas laws perfectly. That's where the real gas law and the van der Waals equation come in handy. These equations help us understand how real gases behave in different conditions.

So, how do we use these equations to solve problems? We start by applying the real gas formula. This helps us figure out things like pressure, volume, and temperature of a real gas in a container. Overall, understanding real gases is important because it helps us better understand the air we breathe and how different gases behave in different conditions. Plus, it's just pretty interesting stuff!

## Ideal Gases

The Kinetic Molecular Theory is a theory that helps us understand how gases behave. When gases behave exactly as this theory describes, they are called ideal gases.

According to this theory, gas particles are always moving around randomly and quickly. They have energy, which we call kinetic energy. When gas particles collide with each other, they don't lose or gain energy. This is because the collisions are elastic.

Gas particles are also so small and far apart from each other that their volume is negligible. Plus, there are no attractive or repulsive forces between gas particles.

At high temperature and low pressure, gases tend to behave more like ideal gases. However, no gas behaves exactly like an ideal gas because they are hypothetical and not part of real life.

Understanding the Kinetic Molecular Theory is important because it can help us predict the behavior of gases in different conditions. It's pretty cool to think about how tiny gas particles are always moving around and colliding with each other!

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? Answer: 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 ideal behavior when they are at low temperatures and high pressures. This is because at high pressures, gas particles are closer together, and as pressure increases, volume decreases. At low temperatures, the kinetic energy of gas particles is low, making it easier for attractive forces to interact with gas molecules. This low temperature also makes the gas more compressible.

Real gases have two properties that cause deviation from ideal behavior: finite volume and intermolecular forces of attraction between gas molecules. In contrast, ideal gases have no volume and no attractive or repulsive forces between neighboring molecules.

To measure how much a gas deviates from the ideal gas law, two properties are used: fugacity and compressibility factor. Fugacity is similar to activity for gases but is harder to find values for. Compressibility factor (Z) is often used in industrial applications, and values can be easily measured.

The compressibility factor equation helps determine how close a gas is to being ideal. If Z = 1, the gas is ideal, and the larger the deviation, the less ideal the gas is. Most common gases are actually pretty close to ideal gases at room temperature. For example, the compressibility factor of hydrogen at standard temperature and pressure is around Z = 1.0006, which means there is only a 0.06% difference between ideal and real hydrogen at this temperature and pressure.

**Real Gas Law**

Van der Waals derived the real gas law from the ideal gas law in 1873. He made adjustments to the ideal gas equation to account for the fact that gases do have volume and attractive intermolecular forces. He proposed a new constant, b, to correct volume, and a new constant, a, to adjust pressure to account for attractive forces.

The resulting equation is known as the van der Waals equation for real gases. This equation relates pressure, volume, temperature, and the amount of gas in real gases, accounting for finite volume and the presence of intermolecular forces.

The values for Van der Waals constants a and b depend on the type of gas being measured. The lower the value of constant a, the weaker the intermolecular forces interacting with the surrounding gas molecules. Therefore, the gas with the strongest intermolecular force will have the highest value for constant a.

Based on this, the gas with the strongest intermolecular forces present among the given options is Cl2, as it has the highest value for constant a. So the correct answer choice is E.

**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:

You have 0.750 moles of O2 in 2.000 L at 25.0 °C. Using the Van der Waals formula, calculate the pressure for O2. a = 1.36 atm·L2/mol2b = 0.0318 atom/molR = 0.0821 atm/mol·K1. convert 25 °C into Kelvin by using the formula: °K = °C + 2732. Plug in all of the values into the equation to solve for pressure (P).

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 (Preal) < Pressure of an ideal gas (Pideal)The volume of a real gas (Vreal) > Volume of an ideal gas (Videal)

Using the same question above, find the pressure of O2 , assuming that it is behaving as an ideal gas. We can use the Ideal gas law formula = to find the pressure of O2.

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

References:

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

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

## Real Gas

**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) = nRTWhere: 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.