Avogadro’s Hypothesis

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 1023 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 CO2 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 CO2 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:

292

 

65.5 L of CO2 gas at STP contain 2.92 moles.

Sample Problem

How many liters are occupied by 3.44 moles of CH4 gas at STP?

Wanted: ? liters

Given: 3.44 moles of CH4 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:

771

3.44 moles of CH4 gas at STP occupy 77.1 L.