SOLIDS: The mole and Avogadro’s Number

Imagine a world where dollars can be seen with the naked eye, but pennies, nickels, dimes, and quarters are invisible. In this world, you are assigned the task of giving a presentation where, somehow or another, dollars replace pennies as the smallest unit of currency. The relationships between the aforementioned currencies will take on the following form:

1 dollar is used to represent 1 penny

1 nickel = 5 pennies

1 nickel is represented with 5 dollars

1 dime = 10 pennies

1 dime is represented with 10 dollars

1 quarter = 25 pennies

1 quarter is represented with 25 dollars

An interesting trend emerges in such a circumstance. Every invisible unit of of currency can be multiplied by the number 100 to be the equivalent of its dollar representation:

1 penny x 100 = 1 dollar

1 nickel = 5 pennies

1 nickel x 100 = 5 dollars

1 dime = 10 pennies

1 dime x 100 = 10 dollars

1 quarter = 25 pennies

1 quarter x 100 = 25 dollars

In the scenario above, the penny, nickel, dime, and quarter can be compared with atoms or molecules that contain different numbers of atomic mass units ( amu ) in their nucleus. Using this analogy, the penny is the equivalent of an atom that contains 1-amu ( hydrogen ). In the circumstance above, 24 pennies would be represented with 24 dollars in the presentation. Magnesium is made of approximately 24 amu, so what macroscopic mass unit can be used to represent it in a such a manner that the macroscopic and microscopic world converge upon one another??? ).

Within a laboratory setting, it is convenient to allow 1 g to represent 1 amu, because grams can be used with convenience in a laboratory setting: atomic mass units cannot. Having now established such a premise, how much larger is 1 g compared to 1 amu??? Is there some common multiple that can be used to convert any atom or molecule into a proportional quantity of substance to be used in the laboratory??? Here is where the concept of a mole comes into play.

A single amu has an approximate mass of 1.66 x 10^-24 g. By dividing this value into 1 g, we obtain the following value:

( 1 g / 1.66 x 10^-24 g ) = 6.02 x 10²³ atoms

This number is called Avogadro’s number, and its usage is akin to that of the number 100 in the fictitious world previously described. 1 mol of any atom or molecule contains 6.02 x 10²³ parts. In order to determine how many grams of a substance are needed to form a mole, all that is needed is the atomic mass number ( not to be confused with the atomic number!!! ) of the atom or molecule in question. For example, a carbon atom has approximately 12 amu in its nucleus; therefore, a mole of carbon has a mass of 12 grams, and 12 grams of carbon contain 6.02 x 10²³ atoms. A mole of hydrogen has a mass of 1 gram, and a mole of oxygen contians 16 grams, while a mole of an O₂ molecule contains 32 grams, etc., etc., etc.