Moles and Molar Mass

When we look at the periodic table each element has two numbers associated with it. The atomic number (the number of protons in the elements) and the atomic mass (the relative weighted average atomic mass). Since the atomic number is a number it has no units. The average atomic mass has units of atomic mass units (u). The average atomic mass is the mass in u's of a single atom of the element. Previously we had defined an atomic mass unit as one twelfth the mass of one atom of the isotope of 12C.

1 amu = 1.66054 x 10-24 grams

So for the element sodium it average atomic mass is 22.99 u. It is possible to calculate the mass of one atom of sodium in grams. We can do this by converting from u's to grams using the conversion factor that relates u's to grams.

So the mass of one atom of sodium is determined by the following conversion;

22.99 u * (1.66057 x 10-24 grams/1 u) = 3.818 x 10-23 grams

This is the mass of one atom of sodium in grams.

What is the mass of 100 atoms of sodium?

100 atoms * (3.818 x 10-23 grams/1 atom) = 3.818 x 10-21 grams

What is the mass of 10,000 atoms of sodium?

10,000 atoms * (3.818 x 10-23 grams/1 atom) = 3.818 x 10-19 grams

What is the mass of 6.022 x 1023 atoms of sodium ?

6.022 x 1023 sodium atoms * (3.818 x 10-23 grams/1 atom) = 22.99 grams

hmmm...now isn't that interesting!

What is the mass of 1 mol of sodium atoms?

The answer to this question is found in the definition of a mol,

a mol 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 6.022 x 1023 units of the substance.

Remember a unit is an atom, a molecule or a formula unit.

So if a mol of sodium atoms is 6.022 x 1023 atoms than the mass of one mol of sodium atoms is,

6.022 x 1023 sodium atoms * (3.818 x 10-23 grams/1 atom) = 22.99 grams

hmmm...now isn't that interesting!

The mass in grams of a mol of an element is equal to the atomic mass. In the case of sodium, its atomic mass is 22.99 u (this is the relative weighted average atomic mass for sodium in atomic mass units). The mass of 1 mol of sodium atoms is the atomic mass expressed in grams, or 22.99 g.

COOL!

Consider the balanced equation

We can balance the equation and we recognize it is an example of a formation reaction. How do we read this equation?

This equation reads 1 atom of magnesium combines with one molecule of chlorine to form one formula unit of the ionic compound magnesium chloride. If we wanted to do this reaction to prepare some magnesium chloride it would be difficult to find a single atom of magnesium and a single molecule of chlorine, even for the most experienced chemist. In the chemistry laboratory we must measure amounts of substances by mass. What is the relationship between the amount of substance and the number of atoms or molecules? How are we able to perform quantitative chemical reactions? There is an answer!

So if I have 1 mol of 12C, how many atoms of 12C do I have? Answer

If I have 1 mol of Mg atoms, how many Mg atoms do I have? Answer

If I have 1 mol of Cl2 molecules, how many molecules of Cl2 do I have? Answer

How many atoms of chlorine do I have in 1 mol of Cl2 molecules? Answer

How many formula units are in 1 mol of MgCl2? Answer

According to our definition of a mol, 1 mol of 12C weighs 12 g. Interestingly the relative atomic mass of 12C is 12.000 u. 12.000 u is the relative atomic mass of one 12C atom. 12.000 g is the mass of 1 mol of 12C atom. And 1 mol of 12C has 6.02 x 1023 12C atoms. The mass of one 12C atom in grams is;

12.000 g / 6.022 x 1023 12C atoms = 1.99 x 10-23 g per atom

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 or formula mass expressed in grams and is called the molar mass of the substance.

How much does 1 mol of Mg atoms weigh? Answer

How much does 1 mol of Cl2 weigh? Answer

How much does 1 mol of MgCl2 weight? Answer

How much does 1 mol of C6Hl2O6 weigh? Answer

A molar mass is the mass in grams of 1 mol of a substance. So for the compounds listed above,

Formula

Molar Mass (g/mol)

Mg

24.305

Cl2

70.9

MgCl2

95.2

C6Hl2O6

180

It is now possible to 'count' atoms, molecules or formula units when weighing chemicals in the laboratory. For the reaction we discussed earlier,



weighing 24.3 grams of magnesium atoms and 71 g of chlorine means we have 6.022 x 1023 atoms of magnesium and 6.022 x 1023 molecules of chlorine. According to the balanced chemical equation magnesium and chlorine combine in equal numbers. The reaction will produce 6.022 x 1023 formula units of MgCl2 which weighs 95.3 g.


So the equation can be read as 1 mol of magnesium reacts with 1 mol of chlorine to produce 1 mol of magnesium chloride.

The relationship between a mol, Avogadro's number and the atomic or formula weight expressed in grams are important unit factors.



A sample problem will demonstrate the use of these unit factor.

Here are few additional calculations.

Calculate how many mol are in 10.0 grams of glucose (C6Hl2O6).

To answer this question we need to convert grams to mol. Since 1 mol of has a mass of 180 g we can set up the conversion as;

How many molecules of glucose are in 10.0 g of C6Hl2O6?

We can now convert from mol of C6Hl2O6 to moelcules using Avogadro's number.

How many oxygen atoms are there in 10.0 grams of C6Hl2O6?

 

 

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;

 

Calculate the number of magnesium atoms in 10.0 g of magnesium.

Answer

 

Here is one of my favorite problems;