# Avogadro’s Hypothesis

Avogadro’s Hypothesis says that equal volumes of gases at the same temperature and pressure contain the same number of moles.

In other words, a mole of oxygen molecules with a molar mass 32.00 g/mol and a mole of radon atoms with a molar mass of 222 g/mol occupy the same volume at equal temperature and pressure. But if the particles are larger, we would anticipate that 1 mole would take up a greater amount of space. Common sense would tell us that the bigger the molecule, the more space a mole of it would take up. This is true for solids and liquids; but not for gases.

You see, a gas is very different from a solid or a liquid. The molecules in a solid or liquid are very close together. I cannot put my hand through a piece of wood, but I can easily do so through air. This is because air is made up of mostly empty space, about 99.9% empty. On a molecular level, there’s a tremendous distance between the molecules compared to their size. If a gas is about 99.9% empty space, then the size of a molecule has really no effect on the volume of the gas.

There’s a certain number of particles that is very important in chemistry. That number is the mole. Which is approximately 6.02 x 10^{23} particles.

The volume that one mole of gaseous molecules occupies depends on:

**Temperature and Pressure**

**Temperature.** The higher the temperature, the greater the volume gas particles occupy. We know this from Charles’s Law.

**Pressure.** The higher the pressure, the smaller the volume gas particles occupy. We know this from Gay-Lussac’s Law.

So chemists established a standard temperature and pressure when they compare gases. They set standard temperature and pressure as 0 ºC and 1 atm, respectively.

### The volume that 1 mole of any gaseous substance occupies at standard temperature and pressure, known as the molar volume, is 22.414 L.

Molar volume is a conversion factor we can use to solve stoichiometry problems involving gases at standard temperature and pressure (STP).

Warning: This conversion factor 22.414 L = 1 mol applies ONLY to gases, and ONLY at STP.

**Sample Problem**

How many moles are contained in 65.5 liters of CO_{2} gas at STP?

Since 1 mol of a gas at STP occupies 22.414 L, we would expect 65.5 L to occupy more than 1 mole.

Wanted: ? Moles

Given: 65.5 L of CO_{2} gas at STP

We want to go from 65.5 L of a gas at STP to moles. Our conversion factor is that, for any gas at STP, 1 mole = 22.414 L.

Conversion Factor: 1 mole of a gas at STP = 22.414 L

Setting up our problem:

*65.5 L of CO _{2} gas at STP contain 2.92 moles.*

**Sample Problem**

How many liters are occupied by 3.44 moles of CH_{4} gas at STP?

Wanted: ? liters

Given: 3.44 moles of CH_{4} gas at STP

Since we want to go from our given, 3.44 moles of a gas at STP, to liters, our conversion factor is that 1 mole of any gas at STP occupies a volume of 22.414 L.

Conversion Factor: 1 mole of a gas at STP = 22.414 L

Setting up our problem:

*3.44 moles of CH _{4} gas at STP occupy 77.1 L.*