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# Ideal Gas Law

The Ideal Gas Law combines the ideal gas equation with the kinetic gas theory to explain how an ideal gas behaves. It also shows us the relationship between pressure, volume, and temperature in a gas.

• In this article we will discuss the relationship between the properties of a gas.
• You will learn about the ideal gas law and how to use the ideal gas equation.
• We will look at the assumptions of The Kinetic Theory of Gases and learn about the difference between real gases and ideal gases.
• Finally you will learn about the limitations of the ideal gas law.

## Gases

Gases have three natural properties: volume, pressure, and temperature. Scientists have known for a long time that there is a relationship between these three properties. Gas particles constantly move in one direction until they bump into something. When you put gas in a container- for example, a spray can- the particles move around inside, colliding with the sides of the spray can. When the particles of a gas bounce off the inside of a container, it creates pressure. Pressure depends on the frequency and speed of particles bouncing off the sides of a container.

Raising the temperature of the gas increases the pressure. The hotter the molecules of gas, the faster they move and the more often they collide with the sides of a container. That's why aerosol cans blow up when you heat them!

You can increase the pressure by making the container smaller. The gas molecules don't have as much space to travel, so they collide with the walls more often.

You can also increase the pressure in a container of gas by adding more gas. More gas means more particles to bounce off the wall of the container, raising the pressure.

### Factors that affect the volume of a gas

When we talk about the volume that a gas occupies, we must consider a few things: the temperature, the pressure and the amount of gas.

• Gas particles with a higher temperature move faster and occupy more space.

• Gases under high pressure become compressed and occupy less space.

• The more particles (or moles) present in a gas, the more volume it occupies.

We can sum this up by saying:

• Temperature and volume have a proportional relationship (as one increases,so does the other).

• The number of moles and volume have a proportional relationship.

• Pressure and volume have an inverse relationship (as one increases the otherdecreases).

1 mole of any gas has the same volume as 1 mole of another gas at the same temperature and pressure. This is also known as Avogadro’s Law.

## What is the ideal gas law?

The Ideal Gas Law combines the ideal gas equation with the kinetic gas theory to explain how an ideal gas behaves. It also shows us the relationship between pressure, volume and temperature in a gas.

### What is the ideal gas law equation?

The ideal gas equation explains the relationship between pressure, volume and temperature in a gas. You write the equation like this:

PV = nRT

• P= pressure

• V= volume

• n = number of moles

• R = the gas constant

• T = temperature

#### Pressure

When using this equation, you must use standard international (S.I.) units. We measure pressure in pascals (Pa, sometimes written as ). Remember to convert to pascals if a question gives you the pressure in a different unit.

• 1 kPa = 1000 Pa

• 1 atm = 1001325 Pa

• 1 bar = 100,000 Pa

#### Volume

In the international standard, we measure volume in cubic meters- m3.

• 1 = 100 = 1,000,000

#### Number of moles

You can find the number of moles (n) by using the equation .

m equals the mass of the substance in grams and, M is the mass of 1 mole of it in grams.

#### The gas constant

The gas constant has a value of 8.31441 in the international standard. You won't need to remember the gas constant because it will be in your exam questions!

#### Temperature

You must use the kelvin (K) as the unit for temperature in the ideal gas equation. You add 273 to convert degree Celsius to kelvin.

### Using the ideal gas equation

We can use the ideal gas equation to calculate the molar volume of a gas. That means the volume of 1 mole of an ideal gas at 0°C and 1 atmosphere pressure (standard temperature and pressure).

0°C is 237 K

T = 237 K

1 atm is 101325 pa

P = 101325 pa

We would like to figure out the volume of 1 mole

n = 1

R = 8.31441 J

PV = nRT

V = 0.0224 m3

So at standard temperature and pressure (STP) 1 mole of any gas occupies a volume of 22.4 litres!

We can also get the relative formula mass by using the ideal gas equation. Watch out, this one’s a little tricky!

The density of ethane is 1.264 at 20°C and 1 atmosphere. Calculate the relative formula mass of ethane.

1.264 means that 1 of ethane weighs 1.264 grams

1 atm is 101325 pa

P = 101325 pa

1 = 0.001

R = 8.31441

20°C = 293 K

PV =nRT

101325 x 0.001 = n x 8.31441 x 293

101325 x 0.001 = mass (g)mass of 1 mole (g) x 8.31441 x 293

101325 x 0.001 = 1.264 (g)mass of 1 mole (g) x 8.31441 x 293

Mass of 1 mole = 1.26 x 8.31441 x 293101325 x 0.001

Mass of 1 mole = 30.4 g

** the mass of 1 mole of a substance equals it’s relative formula mass

Mr = 30.4

## What is the kinetic theory of gases?

The kinetic theory of gases helps us understand how ideal gases behave. We have discussed that gases contain tiny particles that move around quickly and constantly.

In the Kinetic Theory, gas particles move about randomly because they regularly collide with each other.

They move so fast we can't predict where they will go next!

### Kinetic theory assumptions

The kinetic theory assumes the behaviour of gases that meet a defined checklist at standard temperature and pressure. These assumptions are:

1. Gases consist of tiny particles that move about constantly.

2. Gas particles regularly collide with each other and the walls of a container.Their collisions are elastic- they don't lose energy when they crash.

3. There is plenty of space between each particle. The particles are like tiny dots compared to the space between them.

4. Gas particles don't have interactive forces (attraction or repulsion) between them.

5. The speed of a gas particle depends on the temperature of the gas.

### What is an ideal gas?

An ideal gas is an imaginary or theoretical gas. We call a gas ideal when it meets the following criteria:

The molecules of an ideal gas act like point particles that bounce off each other in perfectly elastic collisions.

We count their intermolecular forces as negligible because they are relatively far apart from each other.

At standard temperature and pressure, most real gases behave in an ideal way.

### What is a real gas?

You have learned that most gases obey the assumptions of the kinetic theory of gases and satisfy the ideal gas equation at standard temperature and pressure. However, this is not true for all gases.

Real gases do not obey the Ideal Gas Law.

They prefer to do their own thing!

## Limitations of the ideal gas equation

What happens when a gas does not behave ideally? Ideal gases exist under the assumptions of the kinetic theory of gases. Under certain conditions, they stop being ideal.

• For one thing, the Kinetic Theory assumes that the volume an ideal gas takes up is negligible. But in reality, gas molecules do take up space! You notice this more when you compress a gas at high pressures. Imagine squashing together the particles of gas so much they have nowhere to move.

Let's say the volume of the container of gas is 500cm3 but the particles only occupy 20cm3 of it. The V in the ideal gas equation expresses the amount of free space a gas moves about in. In this case, V would equal 460cm3, not 500cm3. If you keep decreasing the volume and increasing the pressure, the size of the molecules will begin to matter.

Fig. 1 - Kinetic theory

Kinetic theory also assumes that the molecules of an ideal gas have no intermolecular forces between them. That cannot be true for any gas! How would we be able to condense a gas to a liquid otherwise? If the temperature is low enough, all gases turn to liquid. That is because molecules move slower at lower temperatures. Slow enough for them to form interactive forces with each other.

## Ideal Gas Law - Key takeaways

• Temperature and volume have a proportional relationship. As one increases, so does the other.
• The number of moles and volume have a proportional relationship
• Pressure and volume have an inverse relationship. As one increases the other decreases.
• 1 mole of any gas has the same volume as 1 mole of another gas at the same temperature and pressure.
• The ideal gas equation is expressed PV = nRT where P is pressure, V is volume, n is number of moles, R is the gas constant and T is temperature. You must use standard international units when using the ideal gas equation.
• The Kinetic Theory of Gases assumes that gases consist of tiny particles that move about constantly. Gas particles regularly have elastic collisions with each other and the walls of a container. There is plenty of space between each particle. The particles are like tiny dots compared to the space between them. Gas particles don't have interactive forces (attraction or repulsion) between them. The speed of a gas particle depends on the temperature of the gas.
• The molecules of an ideal gas act like point particles that bounce off each other in perfectly elastic collisions. We count their intermolecular forces as negligible because they are relatively far apart from each other.
• Real gases do not behave according to the kinetic theory of gases.
• At high pressures and low temperatures, ideal gases stop behaving ideally.

We write the ideal gas equation as PV = nRT.

We use standard international units when using the ideal gas equation.

• We measure pressure in pascals.

• We measure volume in cubic
meters (m^3).

• We calculate the number of moles
with the formula n = m/M.

• The ideal gas constant has a value
of  8.31441 JK^-1mol^-1 in the
international standard.

• We measure temperature in Kelvin.

The Ideal Gas Law explains how an ideal gas behaves and shows us the relationship between pressure, volume, and temperature in an ideal gas. The ideal gas law combines the ideal gas equation with the kinetic theory of gases.

1. Gases consist of tiny particles

2. Gas particles regularly collide
with each other and the walls
of a container. Their collisions
are elastic - they don't lose
energy when they crash.

3. There is plenty of space
between each particle.
The particles are like tiny dots
compared to the space
between them.

4. Gas particles don't have
interactive forces (attraction or
repulsion) between them.

5. The speed of a gas particle
depends on the temperature of
the gas.

The molecules of an ideal gas act like point particles or tiny dots that bounce off each other in perfectly elastic collisions. That means the molecules don’t lose energy when they collide. We count their intermolecular forces as negligible because the particles  are relatively far apart from each other.

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