Stoichiometry Note #2: Converting Moles to Molecules

Previous: The Mole and the Avogadro Constant                                   Next Molar Mass

The above formula is the formula for converting the number of moles into the number of molecules.

Variables:

• N: Number of molecules
• n: Number of moles
• N_A :The Avogadro constant 

Explanation: 

This should be quite straight-forward. We know that the Avogadro constant is  6.22×10²³, meaning that there are 6.22×10²³ molecules for every mole present, and therefore we multiply the Avogadro constant by the number of mols to obtain the number of molecules. This is the same as dozens. If one dozen equals to twelve, then three dozens equal to 3*12, which is 36. 

You can also use this equation to convert the number of molecules to the number of moles. You just change the equation a bit:

 

Other Important Information
One thing that you need to keep in mind is that the variable n is the number of molecules, which is different from the number of atoms. For example, say you have 10 molecules of H₂O, you will actually have 20 atoms of hydrogen because for every molecule of H₂O, you'll have two hydrogen atoms (look at the subscript!)

Examples:
A) How many atoms of magnesium are in 0.76 mol of a magnesium sample?
B) If there are  3.11×10²⁴ molecules of gold in a sample of a metal, how many mols of gold are present in the sample?

C) How many atoms of potassium are in 0.880 mol of  K₂O?
.
.
.
Answers:

A) Substitute n=0.76 and N_A  =6.22×10²³  into the formula N= n × N_A, and solve for N. You should get  N= 4.73×10²³
   

B) Substitute N_A  =6.22×10²³ and N  =3.11×10²⁴  into the formula n= N ÷ N_A, and solve for n. You should get n=5 

C) To find the number of molecules of  K₂O, substitute n=0.880 and N_A  =6.22×10²³  into the formula N= n × N_A, and solve for N. You should get N=5.4736×10²⁴. Then, since there are two potassium atoms for each molecule of K₂O, multiply N by 2, and you should get 10.9 as you answer.

Previous Note: The Mole and the Avogadro Constant
Next Note:  Molar Mass