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Ideal and Real Gases

Gas is a weird state of matter - gases take the shape of the container they're in and don't have a fixed volume. All gases behave differently and unpredictably. There is no single equation which can describe the behaviour of all gases under all conditions of pressure and temperature. To make things easier, a reference gas is needed which will…

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# Ideal and Real Gases

Ideal and Real Gases
• Chemical Analysis • Chemical Reactions • Chemistry Branches • Inorganic Chemistry • Ionic and Molecular Compounds • Kinetics • Making Measurements • Nuclear Chemistry • Organic Chemistry • Physical Chemistry • The Earths Atmosphere Save the explanation now and read when you’ve got time to spare. Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Nie wieder prokastinieren mit unseren Lernerinnerungen. Gas is a weird state of matter - gases take the shape of the container they're in and don't have a fixed volume. All gases behave differently and unpredictably. There is no single equation which can describe the behaviour of all gases under all conditions of pressure and temperature. To make things easier, a reference gas is needed which will behave exactly as predicted, under all conditions. Thus a theoretical gas called an ideal gas is assumed.

• You will learn what Ideal and Real gases are.
• The Ideal Gas Law.
• The differences and similarities between ideal gases and real gases.
• The conditions at which real gases behave like an ideal gas, and the conditions at which they deviate from ideal gas behaviour.

Ideal gas is a hypothetical gas which follows the Ideal Gas Law at all conditions of temperature and pressure.

All gases which exist in the environment are Real Gases. Real gases follow Ideal Gas Law only under conditions of high temperature and low pressure.

So, ideal gas is not a real gas! (pun intended).

Ideal Gas Law explains the behaviour of ideal gases. It is also called the General Gas Equation. It says that for an ideal gas, $PV=nRT$ is always true, where -

• P: pressure.
• V: Volume.
• n: amount of gas (number of moles).
• R: Gas Constant = 8.314 J⋅K−1⋅mol−1.
• T: Temperature.

The equation given by the Ideal Gas Law:

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

It is also called the equation of state, as it describes behaviour of gas using state variables such as Temperature, Pressure, and Volume.

Different state-of-matter-equations are used to describe all types of matter - gases, liquids, solids, and even plasma! Plasma is the fourth state of matter which is made up of charged particles such as ions and electrons. Did you know that stars are made up of plasma? In this article, we will only discuss about gases.

Calculate the volume of 1 mole of an ideal gas at 0°C and 1 atmosphere pressure.

Given:

T = 0°C = 237 K

P = 1 atm = 101325 pa

n = 1

We know that:

R = 8.31441 JK-1·mol-1

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

$$V=\frac{n\cdot R\cdot T}{P}$$

$$V=\frac{1\cdot 8.31441JK^{-1}\cdot mol^{-1}\cdot 237k}{101325Pa}$$

$$V = 0.0224 m^{3}$$

$$V = 22.4 L$$

Therefore, at 0°C and 1 atmosphere pressure, an ideal gas occupies 22.4 Litres.

## Properties of Ideal and Real Gases

### Ideal Gas and Real Gas: How Are They Different?

Ideal gas is a theoretical gas that behaves in a very ideal manner. No gas which exists in the environment acts perfectly as an ideal gas, though some do come really close to it under certain conditions of temperature and pressure. Since ideal gas is a theoretical gas, there are some assumptions that are made for its behaviour, which can be considered as properties of ideal gas

• Ideal gas follows the gas laws at all temperatures and pressures.

• The gas molecules are solid, spherical particles, which do attract or repel each other.

• The motion of these molecules is completely random.

• The particles travel in a straight line until they hit another particle or the wall of the container.

• Collision of these particles with each other or the wall of the container is completely elastic. I.e. no energy is lost in the collision and therefore the kinetic energy of the gas remains constant.

• The average distance between the particles is much larger than the size of the molecules.

• Kinetic energy of each particle can vary but the average kinetic energy of all particles remains constant.

Any gas that exists in reality is a real gas. Some gases come close to ideal gas behaviour under some conditions, but can never be perfectly ideal. This is because:

• Gases are made up of matter - atoms and molecules - which will always have some forces of attraction or repulsion between them.
• Atoms and molecules can never be point-sized as they will always occupy some volume.
• Under some conditions of high pressure or low temperature, the size of atoms/molecules can no longer be considered negligible as compared to distance between the particles.

Generally, the behaviour of gases tends towards ideal gas behaviour at high temperatures and low pressures. Gases generally deviate from ideal gas behaviour at low temperatures or high pressures.

At standard temperature and pressure pure gases of diatomic molecules such as Hydrogen, Oxygen, Nitrogen and noble gases like Helium and Neon show behaviour close to that of ideal gases. These gases come close to the ideal behaviour because the molecules are light and small. Also, the average distance between the molecules is much larger than their size. Therefore there is minimal interaction between the molecules.

Standard temperature and pressure (STP) is defined as temperature of 273.25K (0oC), and absolute pressure of 105 Pa (1 bar). This is defined by IUPAC (International Union for Pure and Applied Chemistry),

Since there is no intermolecular forces of attraction between particles of an ideal gas, it can never be liquified. Conversely, real gases can be liquified - as under certain conditions, the intermolecular forces of attraction will overcome the kinetic energy of the particles, and coalesce to form liquid.

## Ideal Gas vs Real Gas: Similarities, Differences, and Examples

Although ideal gas and real gas seem to be completely different, let's not forget, they're both gases and have some similarities:

Similarities: Ideal and Real Gas
Ideal Gas
Particles of ideal gas have kinetic energy.Particles of real gas also have kinetic energy.
Particles exhibit random motion.Particles of real gas also exhibit random motion.

Distance between the particles is much larger than their size.

Distance between the particles is much larger than their size at most temperatures and pressures.

Particle collision is perfectly elastic i.e. particle momentum and kinetic energy is conserved.

Particle collision is perfectly elastic i.e. particle momentum and kinetic energy is conserved.

We can tabulate all the differences between ideal and real gases like so:

Differences: Ideal and Real Gases
Ideal Gas
Follow ideal gas law at all temperatures and pressures.Follow ideal gas law at only high temperatures and low pressures.
Particles are point-sized and do not occupy any space.Particles have volume and occupy space.
No intermolecular interaction at any condition of temperature and pressure.Intermolecular forces are present. Negligible at high temperature and low pressure, but not negligible at low temperature and pressure.
Can't be liquified.Can be liquified.
Size of particles is negligible compared to distance between them.Size of particles can't be neglected at conditions of low temperatures and high pressures.

The random motion of particles in a gas as a result of collisions with surrounding particles is called Brownian Motion.

Examples of Ideal gases are - Hydrogen, Oxygen, Nitrogen and noble gases like Helium and Neon. These gases show behaviour that is very close to that of ideal gases at conditions of standard temperature and pressure (STP).

All gases found in the environment are examples of real gases. Even Hydrogen, Oxygen, and Nitrogen behave like real gases at conditions of low temperatures and high pressures - That is why it is possible to liquify them.

It's important to remember that ideal gas is a theoretical gas and does not exist!

The following points will help you understand the ideal behaviour of the real gases around you right now.

• Most real gases behave like ideal gases under conditions of high temperature and low pressure.
• Any pressure including atmospheric pressure is considered low pressure. Pressure is considered to be high only when it is forcing the particles to be in close proximity. Examples of high pressured gases are-

1. CNG gas cylinders in cars.

2. oxygen cylinders for scuba diving.

• The kinetic energy of gas particles is directly proportional to temperature. Higher the temperature, higher the kinetic energy of the gas particles. When the particles have high kinetic energy, the intermolecular forces have minimal effect in the movement of the particles.
• Room temperature is a high enough temperature for gas particles to have enough kinetic energy to overcome intermolecular forces and behave like ideal gases.

## Deviation of Gases from Ideal Gas Behaviour

### Conditions of Ideal Gas Behaviour

Imagine there is a container of large volume containing a real gas in it. The temperature inside the container is high. Fig. 1: Large Container with Real Gas at High Temperature | Kanishk Singh Vaia Originals

By “large volume", we mean that the size of the particle, and the average distance between particles is negligible compared to the size of the container. And by “high temperature”, we mean that the kinetic energy of the particles is high enough so that intermolecular attraction/repulsion is negligible (the long red arrows are indicators of high kinetic energy of particles). The gas inside the container has the right conditions for it to behave like an ideal gas.

Therefore, the pressure of this gas can be determined by the ideal gas equation -

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

Rearranging:

$$P=\frac{n\cdot R\cdot T}{V}$$

Have you ever wondered what causes gas to exert pressure on the container it is in? The particles of the gas are always colliding with the walls of the container and bouncing back off it. Thus, each particle is exerting a force on the container. You might remember that pressure is force per unit area. The pressure of the gas is the net force that is being exerted (by the gas) on the container per unit area of the container.

Amongst the real gases, Helium behaves the most like an ideal gas. This is due to Helium existing as a monatomic gas, which means it exists as a single atom and not a molecule. Furthermore, the helium atom is very small and has a completely filled outermost electron shell, which minimizes the intermolecular interactions.

### Deviation from Ideal Gas Behaviour due to Low Temperature

Now, let’s cool down the same container to a very low temperature. Volume of the container is the same. Fig. 2: Large Container with Real Gas at Low Temperature | Kanishk Singh Vaia Originals

Looking at the equation for pressure from ideal gas equation:

$$P=\frac{n\cdot R\cdot T}{V}$$

Temperature is in the numerator. Therefore, if we reduce the temperature, pressure should reduce. Let’s compare this with what is happening inside the container.

As the temperature of the gas is reduced, gas particles now have very low kinetic energy (the small blue arrows are indicators of the low kinetic energy possessed by the particles). This will reduce the speed at which these particles hit the wall of the container, reducing the pressure. But, reducing the temperature had another effect - Since the particles don’t have much kinetic energy, the intermolecular forces of attraction or repulsion between the particles are not negligible anymore. This further reduces the speed at which the particles collide with the container. Due to this, the pressure drops more than what is predicted by the ideal gas equation. The behaviour of the gas can no longer be accurately predicted by the ideal gas equation, and therefore, the gas is said to be deviated from ideal gas behaviour.

### Deviation from Ideal Gas Behaviour due to High Pressure

Now, let's take another container with the same amount of the same gas. Temperature is set to high, same as before. But this time, the volume of the container is small, and by "small" we mean that the size of the molecules are not negligible compared to the size of the container. Fig. 3: Small Container with Real Gas at High Temperature Kanishk Singh Vaia Originals

Looking at the equation of P from the ideal gas equation:

$$P=\frac{n\cdot R\cdot T}{V}$$

We can see that volume is in the denominator. So when we decreased the volume, the value of the overall expression increased, and therefore pressure increased.

Since the amount of gas is the same as before and volume is smaller, the molecules are more densely packed. Therefore, the size and the average distance between the molecules is not negligible compared to the size of the container. This means that the space to move around for the particles is even lesser and the number of molecular collisions is higher. Due to this, the particles collide with the walls of the container with more vigour. This results in pressure increasing more than what was predicted by the ideal gas equation. The behaviour of the gas can no longer be predicted accurately by the ideal gas law, and the gas is said to be deviated from ideal gas behaviour.

Therefore, you learnt that under conditions of low temperature or high pressure, the behaviour of real gases tends to deviate from ideal gas behaviour.

## Ideal and Real Gases - Key takeaways

• Ideal gas is a hypothetical gas, and does not exist in the environment.
• Ideal gas follows the Ideal Gas Law - $PV=nRT$ at all values of temperature and pressure.
• Real gases are real, as the name suggests, and exist in the environment.
• Real gases behave like ideal gases under conditions of high temperature and low pressure.
• Diatomic gases (Hydrogen, Oxygen, Nitrogen,) and noble gases (Helium, Neon) behave like ideal gases at Standard Temperature and Pressure (0oC, 1bar).
• Behaviour of real gases starts deviating away from ideal gas behaviour with decrease of temperature, or increase of pressure.

Ideal gas is a hypothetical gas  which follows Ideal Gas Law at all conditions of temperature and pressure.

Real gases are those which exist in the environment. They follow Ideal Gas Law only under conditions of high temperature and low pressure.

Gases like Hydrogen, Oxygen, Nitrogen, Helium Neon behave like ideal gas under conditions of Standard Temperature and Pressure (0oC, 1bar).

A real gas behaves like an ideal gas under conditions of high temperature and low pressure.

Volume of ideal gas at certain temperature and pressure will be determined by the formula

V = nRT/P

Volume of a real gas will be more than that predicted by this formula because unlike ideal gas particles, real gas atoms/molecules have volume and occupy  space.

Particles of a gas are always in random motion. They are continuously colliding with other particles and with the walls of the container. When particles collide with the container, they exert force on it. Pressure of a gas is the net force of all particles on the container walls, per unit area of the walls.

## Ideal and Real Gases Quiz - Teste dein Wissen

Question

What Law explains the behaviour of Ideal Gas?

Ideal Gas Law

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Question

Where can you find Ideal Gas in the environment?

Nowhere. Ideal gas is a hypothetical gas. It does not exist in the environment.

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Question

Which real gas behaves the most like an ideal gas?

Helium.

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Question

What is Standard Temperature and Pressure (STP) defined as and who defines it?

STP is defined as T = 273.15K (0oC) and P = 105 Pa (1bar).

It is defined by the IUPAC (International Union of Pure and Applied Chemistry)

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Question

What kind of collision do molecules/atoms of a real gas have?

Elastic

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Question

Under what conditions do real gases deviate from ideal gas behaviour?

High pressure and low temperature.

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Question

Can ideal gas be liquified?

No

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Question

Why can't you liquify an Ideal Gas?

Because there are no intermolecular forces of attraction between particles of an ideal gas.

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Question

Name 4 real gases which act as ideal gases under standard conditions of temperature and pressure.

Oxygen. Hydrogen. Helium, Neon, Nitrogen

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Question

Can air be considered as an ideal gas?

Yes. Air is a mixture of mostly Nitrogen and Oxygen, with small percentage of Carbon Dioxide, Argon and other gases. Most of these gases act as ideal gases under atmospheric conditions.

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Question

Consider 2 real gases A and B. Particles of A have greater intermolecular forces of attraction than B. Which gas will deviate from ideal gas behaviour more easily?

Gas A.

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Question

What is the name of the random motion that gas particles exhibit?

Brownian motion

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Question

What is 0oC in Kelvin?

273.15K

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Question

What is 1bar in Pascals?

105 Pa or 100kPa

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