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!

Lets return to the periodic table. In the periodic table the mass number for an element is given below the symbol.

The relative weighted average atomic mass for magnesium is 24.3 u. This is obtained by summing the product of the mass of each isotope of the element times the fractional abundance of that isotope. We usually shorten this and say the atomic mass of magnesium is 24.3 u. The atomic mass for chlorine is 35.45 u. The symbol for chlorine is Cl. The formula for elemental chlorine is Cl2. The molecular mass for elemental chlorine, Cl2, is 70.90 u, just two times the atomic mass. We can obtain the mass of a formula unit of MgCl2 by simply summing the atomic masses for each of the atoms in the formula. Therefore the formula mass of MgCl2 is 95.35 u.

But we still have a problem! The balances in the laboratory measure mass in units of grams, not u's. We need a relationship between atomic mass units (u) and grams. That relationship is given to us by the definition of the atomic mass unit. The 'u' is defined as one-twelfth of the mass of the isotope of 12C. The value is 1.66057 x 10-24 grams. Now we have a way to determine the mass of a single atom of an element, a molecule of an element or compound and the mass of a formula unit of an ionic compound.

Let's see how we can use this information to calculate the mass of an atom of magnesium in grams. First we can obtain the atomic mass of a magneium atom. From the periodic table this value is 24.305 u. Now we can use a unit factor to convert from u's to grams.

This is a very small number!

Calculate the mass of a molecule of chlorine in grams; The formula of chlorine is Cl2 so its molecular mass is 2 x 35.453 u which is 70.906 u. Now we can use a unit factor to convert from u's to grams;

Finally, let's go ahead and calculate the mass of a formula unit of magnesium chloride in grams; The formula of magnesium chloride is MgCl2 so its formula mass is 24.305 u + 2 x 35.453 u which is 95.211 u. Now we can use a unit factor to convert from u's to grams;

So let's try one more substance. Calculate the mass, in grams, of a molecule of sucrose, C12H22O11.

First the molecular mass of the compound must be determined;

for C: 12 x 12.0 u = 144 u

for H: 22 x 1.01 u = 22.22 u

for O: 11 x 16.0 u = 176 u

Total = 342 u (molecular mass for one molecule of C12H22O11)

Now convert from units of 'u' to units of grams;

In all of the above examples we have determined the mass of a single atom, molecule or formula unit of a substance. Let's try a different kind of calculation which extends the ideas a little further.

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

In this question we need to determine how many magnesium atoms are contained in the 10.0 gram sample. If we knew the mass of one magnesium atom we could use that information to determine how many magnesium atoms were in 10.0 grams. We do know how much one magnesium atoms weighs, we calculated it above. We know the atomic mass of magnesium is 24.305 u. When we convert that to grams that is the mass of one magnesium atom. We used the conversion that 1 u = 1.66057 x 10-24 grams, as shown below.

So the mass of one magnesium atom is 4.0360 x 10-23 grams. Now we can determine the number of atoms in 10.0 g of magnesium,

As one additional calculation using this same approach let's calculate the number of magnesium atoms in 24.305 g. Since we already know the mass of one magnesium atom we can set this problem up just as we did above.

We see that in 24.305 g of magnesium there are 6.022 x 1023 atoms of magnesium.

Now calculate how many sucrose molecules there are in 10.0 grams of sucrose.

To answer this question we need to know the mass of a single sucrose molecule. We calculated that earlier and it was 5.68 x 10-22 grams. Therefore, the number of molecules of sucrose in 10.0 grams is;

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

We know how many sucrose molecules there are in 10.0 grams and we also know how many oxygen atoms there are in each sucrose molecule. We can answer the question with those two pieces of information;

Now let's consider a similar question asked above, how many molecules of sucrose are there in 342 grams of sucrose?

We solve this question just like the question about the number of molecules in 10.0 grams,

We see that in 342 g of sucrose there are 6.022 x 1023 molecules of sucrose.

Earlier we also determined there are 6.022 x 1023 atoms of magnesium in 24.305 g of magnesium.

Do you notice something interesting?