The interesting observation is that both 24.305 grams of magnesium and 342 grams of sucrose have the same number of particles. The number of magnesium atoms in 24.305 grams of magnesium is the same as the number of sucrose molecules in 342 grams of sucrose. That number is 6.022 x 10²³.

This number is special, it is called Avogadro's number and it is a fundamental unit in the SI system. Specifically this number is called a mol and is defined as the number of ¹²C atoms in 12 g of ¹²C. This number has been experimentally determined as 6.022 x 10²³ atoms. A mol of any substance is defined as the amount of the substance which contains the same number of units as are in 12 g of ¹²C or 6.023 x 10²³ units of the substance.

So a mol is several things; it is an amount of substance which contains the same number of atoms, molecules or formula units as 12 grams of ¹²C. We saw earlier than 24.305 grams of magnesium and 342 grams of sucrose contain the same number particles. In the case of magnesium it is atoms, in the case of sucrose it is molecules. But whichever...atoms or molecules...the number is the same. Therefore we refer to 24.305 grams of magnesium as one mol of magnesium. Similarly 342 grams of sucrose is one mol.

How many grams of chlorine, Cl₂, are in one mol?

This can be determined by finding the molecular mass of Cl₂.

2 x 35.453 u = 70.906 u

The molecular mass of Cl₂ is 70.906 u. When this mass is expressed in units of grams, 70.906 grams, that mass of chlorine contains 6.022 x 10²³ molecules of Cl₂ and is also a mol. So there are 70.9 grams in one mol of Cl₂.

A mol of ¹²C atoms contains 6.023 x 10²³ atoms of ¹²C.

A mol of Cl₂ molecules contains 6.023 x 10²³ molecules of Cl₂.

A mol of MgCl₂ contains 6.023 x 10²³ formula units of MgCl₂.

A mol of ¹²C atoms weighs the same in grams as the atomic mass of ¹²C, 12 g. The weight of any substance which contains 6.023 x 10²³ units is given by its atomic, molecular or formula mass expressed in grams and is called the molar mass of the substance.

A mol of ¹²C atoms has a mass 12 g: the molar mass of ¹²C is 12 g.

A mol of Cl₂ molecules has a mass 70.90 g: the molar mass of Cl₂ is 70.90 g.

A mol of MgCl₂ has a mass 58.5 g: the molar mass of MgCl₂ is 95.2 g.

Sample Problem:

Determine the number of moles of N₂O₅ in 45.6 g of N₂O₅ gas and the number of nitrogen atoms.

Solution:

The molar mass of N₂O₅ is 108 g­mol^-1. The sample is 45.6 g so we know there is less than a mol since a mol of N₂O₅ weighs 108 g. To calculate the number of moles we setup the problem in the following way;

To determine the number of nitrogen atoms in the sample we must first determine how many N₂O₅ molecules.

Now we can determine the number of nitrogen atoms;

Here is one of my favorite problems;