Woman blowing up a balloon (Deagreez, iStockphoto)

# Avogadro and the Ideal Gas Law

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Learn about the theory of Avogadro’s Law and the Ideal Gas Law and explore examples in everyday life.

There are four laws, known as Gas Laws, which describe how gases behave. The four laws are Boyle’s Law, Charles’s Law, Gay-Lussac’s Law and Avogadro’s Law.

Amadeo Avogadro was an Italian physicist who stated, in 1811, that the volume of any gas is proportional to the number of molecules of gas (measured in Moles – symbol mol). In other words if the amount of gas increases, then so does its volume.

One important lesson we learn from this law is that if samples of any gas are compared that have the same volume, temperature and pressure, then they will all have the same number of molecules in them. You can see this on the following chart:

Here are three different gases all occupying the same volume (22.4 L), at the same pressure (1 atm) and the same temperature (273 K or 0 °C). Even though their masses are all different, the amounts of each gas are the same (1 mol). One mole (SI unit for the amount of a substance) of a gas (or any substance for that matter), contains the same number of molecules. So we can say that these three gases all contain the same number of molecules. The number of molecules in 1 mole is known as Avogadro’s Number, and is huge (6.02x1023)! Note, we are not restricted to these conditions. For example, we could change the volume for these gases to be higher or lower and change the pressure and temperature to be equally higher or lower as well. As long as all three conditions are the same for all gases, we can then say that they all have the same number of molecules! The number may not be Avogadro’s number any more, but the number of molecules can still be calculated.

### Avogadro’s Law in Everyday Life

You have probably experienced this example of Avogadro’s Law yourself. When you blow up a balloon, you are adding molecules of gas into it. The result is that the volume of the balloon increases – and in order to do this, you decrease the number of molecules in your lungs (which decreases their volume)! A bicycle pump does the same thing to a bicycle tire.

## Ideal Gas Law

The volume, pressure, temperature, and quantity (amount) of gas all can affect one another. Since different gases act similarly, it is possible to write a single equation relating all of these properties. The Ideal Gas Law combines several laws, including Boyle's LawCharles’ Law, Gay-Lussac’s Law and Avogadro’s Law, into one neat and tidy formula! This law is commonly used to calculate how the volume of a gas will change if temperature, pressure or amount of gas is changed.

In the Ideal Gas Law, the behaviour of a gas can be summarized using the following equation:

## PV = nRT

Where:

• P is pressure
• V is volume
• n is the number of gas molecules in moles
• R is a number known as the ideal gas constant (The value for R is often, but not always, 8.314 J/mol ˖ K)
• T is temperature (which has to be in Kelvin)

The chart below shows how all the above gas laws are present in this ideal gas law.

 Law Variables Symbols in Formula Boyle pressure & volume P, V Charles volume & temperature V, T Gay-Lussac pressure & temperature P, T Avogadro volume & amount V, n

Although in reality no gas is an ‘ideal gas’, some do come very close. Therefore, the Ideal Gas Law allows us to roughly predict the behaviour of a gas.

This formula is often used when you want to determine the amount of gas that is present in a container. For example, you could find the mass of gas in a container by weighing the gas in the container, pumping out the gas and then reweighing the container. However, since gases have such low weight, the difference would be so small it would be hard to measure. Instead, all you need to know is the pressure - which can be obtained from a pressure gauge - the volume of the container, and the temperature of the gas. Then put these values into the formula and solve for n, from which the mass can be obtained.

### Spotlight on Innovation

ZooShare Biogas Cooperative

A unique arrangement is underway between the animals at the Toronto Zoo, a major Canadian grocery store and non-profit renewable energy co-operative called ZooShare. ZooShare is in the process of developing North America's first zoo biogas plant at the Toronto Zoo using biomass – essentially poop – from the zoo animals along with food waste from local grocery stores. On the zoo property, ZooShare is going to build a bioreactor, which is a large enclosed tank where the zoo and food waste will be broken down by microorganisms. The microorganisms will be breaking down the materials in the absence of oxygen. This type of digestion is called anaerobic digestion. The products of anaerobic digestion are biogas (made up mainly of methane and carbon dioxide) and digestate (the leftover solid material which can be used for fertilizer).

Methane can be combusted (burned in the presence of oxygen) to release energy. The ZooShare facility will convert the heat energy from burning the methane into mechanical energy which can operate an electrical generator. Running at nameplate capacity (full capacity), the ZooShare electrical generator is anticipated to generate 500 kW (kilowatts) of electricity.

You could say the ZooShare project is a win-win-win. The zoo has a way to dispose of the poop generated by the animals (so that the poop does not have to go to a landfill site), the grocery stores have a place for their food waste (so that it also does not go to landfill sites), and Ontario has a source of electricity generation which does not come from the burning of fossil fuels.