Avogadro's Number

6.0220×1023 of anything equals Avogadro's number of those items, particles, or substances. However, Avogadro's number is far too large to be useful for counting everyday items. The number of people alive on the planet, or the number of humans that have ever lived, is not close to Avogadro's number. The same is true for the number of pennies, paperclips, or apples. Consider the following chart:
Number of people on the planet (approx. 2014)   7 000 000 000
Carlos Slim's net worth (dollars): 69 000 000 000
Number of cells (approx.) in an adult human: 100 000 000 000 000
Avogadro's number (rounded): 602 200 000 000 000 000 000 000

The Mole

1 mole = 6.0220×1023 particles = Avogadro's Number

Avogadro's number is so large it is only effective for counting the number of atoms, molecules, or ions in a substance. If a glass of water contained 6.0220×1023 molecules of water, you could say the glass contained Avogadro's number of water molecules. It is also acceptable, because of the relationship above, to say the glass contains 1 mole of water molecules. Referring to numbers of particles in terms of moles is commonplace. This is easier than saying "Avogadro's number" or writing out the exact number (since it will be very long). It is also more convenient to speak in terms of moles since it is highly unlikely a substance will contain Avogadro's number of particles or an exact multiple of that number. This is comparable to speaking of eggs or doughnuts in terms of the dozen. Rather than a chef saying he used 42 eggs this morning, he may say that he used 3.5 dozen eggs. Both of those numbers (42 and 3.5) are small enough for the brain to put into context easily, so there is no significant difference as to which one is used. However, it would be markedly different for the human brain to hear that a glass contains 1.204×1024 molecules of water rather than 2 moles of water. When a chemical reaction takes place, the reactants combine in very specific ratios that are determined when a reaction equation is balanced. It would be wasteful to mix random amounts of reactants with each when attempting to create a desired product. It is important to determine how many particles of each reactant should be used before the reaction is started. This quickly introduces the problem of how to count the number of particles needed for each reactant. Counting particles directly is impossible for two reasons. First, molecules and atoms are not tangible objects and are too small to be seen with a microscope anyway. Secondly, the number of particles needed to accumulate any amount that could be massed would be such a large number no human could possibly count a fraction of that number in a lifetime. Fortunately, the periodic table allows us to accurately determine the number of particles in a substance by taking its mass.

Mole Calculations

The mass of each element on the periodic table is often referred to as the molar mass of that element. For example, carbon's molar mass is 12.01 grams. This means that 1 mole of carbon atoms has a mass of 12.01 g. Lead has a molar mass of 207.2 grams, so 1 mole of lead atoms has a mass of 207.2 grams. The number of atoms in 1 mole of an element is always the same, but the mass of those atoms varies from element to element. This is similar to saying that the number of items in 1 dozen of something (e.g. apples, bowling balls) will always be the same, but the mass of those items will always be different. It is easy to imagine that 1 dozen apples and 1 dozen bowling balls will have very different masses, yet each grouping has 12 members in it. Often, it is necessary to find the number of particles in a mass that is not equal to the molar mass. Consider the following problem:
Find the number of atoms in 100.0 grams of sulfur:

Empirical Formula vs. Molecular Formula

Sometimes an unknown compound can be analyzed and its percent composition by mass can be determined. This is extremely useful information since it can b used to determine the formula of the compound. However, care must be taken to differentiate between the empirical and molecular formula. People are most familiar with the molecular formula, as it gives the exact number of atoms of each element per molecule. Molecular formulas are what are used to write reaction equations that you see on every page on this site. The empirical formula is different. It is the smallest whole number ratio of elements in a formula. For many compounds the empirical and molecular formula are the same, as is the case for water - H2O. The ratio of two hydrogens to one oxygen is not only the smallest whole number ratio of elements in the compound but it is actually the number of atoms of each element per molecule. For many organic compounds, there is a difference. Benzene, with its molecular formula C6H6, has an empirical formula of CH.

Determination of a Formula

There are generally three steps to finding the formula of a compound:
1. Use the percentages given to find the mass of each element (if no molar mass is given, assume 100 g)
2. Convert the mass of each element to moles
3. Divide each molar quantity by the smallest quantity of moles present. Hopefully, this will give an integer ratio of elements to one another.

Consider the following problem:
A compound containing only nitrogen and oxygen is found to contain 25.9% nitrogen by mass. Find the empirical formula of the compound.

First, realize that since 25.9% is nitrogen the balance (74.1%) must be oxygen. The percentages must always add to 100%. Second, since no molar mass was given, assume that 100 g of the compound is present. It truly doesn't matter what the mass is since percentages are constant for a compound. However, assuming 100 g makes for easy math as 25.9% nitrogen immediately equates to 25.9 g of nitrogen. The full calculation is shown below: