# Converting Between Mass & Amount

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

In this lesson, we will learn how to convert the mass of atoms or molecules to the number of atoms or molecules and then go in reverse. We will learn about moles and Avogadro's number.

If you were told to go buy a dozen eggs, you would automatically know that meant 12 eggs. A dozen is another way to say 12. When talking about mass and amount in chemistry we also have a word to refer to a particular number of atoms. This is a mole. A mole refers to a specific number of atoms or molecules. The atomic mass of each element as listed on the periodic table is the mass of one mole of that element.

So how many atoms or molecules are in a mole? There are 602 sextillion (that is 602 with 21 zeroes after it.) This is typically written using scientific notation as 6.02 x10^23. This number is called Avogadro's number. This number is much bigger than a dozen which makes sense since atoms are very tiny. You would need a lot of atoms in order to have enough to measure them with typical laboratory equipment.

If you look at the periodic table you can see the atomic mass of each element. This number is different for each element. So, if we know that mass of oxygen is 8 g/mole and 1 mole has 6.02 x 10^23 atoms in it, then we know that 1 gram of oxygen has 7.5 x 10^22 atoms in it.

Why is this important? It is important to know the number of moles of an element or compound in a reaction so that we can compare reactants and products to determine information such as the limiting reactant or how much product will be produced. We cannot compare mass of one compound to mass of another compound. We can, however, compare moles of an element or compound to moles of another element or compound. So, we will practice converting between mass and amount so that you can apply this information later.

## Example Using Eggs

To start let's make sure we understand what a mole is by comparing it to eggs. Let's say you have been given a box with a bunch of eggs in it, but you can't see inside the box. You want to know how many eggs are in the box. You know that the mass of an egg is 65 g. This means that the mass of 1 dozen of eggs is 780 g. You determine that the mass of the contents of the box (minus the weight of the box) is 2730 g. How many dozen eggs are in the box?

So the 'g of eggs' cancel each other out and we have 3.5 dozen eggs, which we know is equal to 42 eggs (3.5 times 12). You see how we can go from the mass of eggs to the number of eggs. We can do this same thing with atoms and molecules.

## Mass to Number of Atoms

Let's start with a simple example. From the example with eggs we knew the total mass of the eggs, the mass of 1 egg, and how many eggs are in a dozen, but we didn't know how many eggs were in the box. Now let's compare this to chemistry. We know from the periodic table that the atomic mass of carbon is 12 g/mole. Let's say we have 50 g of carbon. How many moles of carbon do we have? How many carbon atoms are there? Remember there are 6.02 x 10^23 atoms of carbon in a mole of carbon.

So now let's determine how many atoms there are in 50 g of carbon:

There are 2.5 x 10^24 atoms of carbon in 50 g of carbon.

## Sugar Digestion Example

When you eat something with sugar in it, your body breaks that sugar down into simpler compounds. This is the basic reaction:

Let's start with 105 g of sugar. How many molecules of sugar are in this reaction? First, we need to determine the mass of sugar in a mole. If you look at the periodic table you will see that there are several numbers in each block. The smaller, whole number is the atomic number. The larger number, that may be a decimal, is the atomic mass of the element. This is the number we are looking for.

In one molecule of sugar, we see that there are 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen. From the periodic table we see that the atomic mass of carbon is 12 g/mole, the atomic mass of hydrogen is 1 g/mole, and the atomic mass of oxygen is 16 g/mole.

One molecule of sugar has a mass of about 180 g/mole.

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