### The Mole & Molar Mass

The mole is the standard method in chemistry for communicating how much of a substance is present.

Here is how the International Union of Pure and Applied Chemistry (IUPAC) defines "mole:"

The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

This is the fundamental definition of what one mole is. One mole contains as many entities as there are in 12 grams of carbon-12 (or 0.012 kilogram).

In one mole, there are 6.022 x 10^{23} atoms. Here's another way: there are 6.022 x 10^{23} atoms of carbon in 12 grams of carbon-12.

I want to say this real clearly: one mole of ANYTHING contains 6.022 x 10^{23} entities.

The word "entities" is simply a generic word. For example, if we were discussing atoms, then we would use "atoms" and if molecules were the subject of discussion, the word entities would be replaced in actual use by "molecules."

6.022 x 10^{23} is so important in chemistry that it has a name. It is called Avogadro's Number and has the symbol N. It is so named in honor of Amedeo Avogadro, an Italian chemist, who, in 1811, made a critical contribution (recognized only in 1860 after his death) which helped greatly with the measurement of atomic weights. The term Avogadro's Number was first used about 1906 and has been very carefully measured in a number of ways in the decades since. It actually has a few more digits than the 6.022 part, but 6.022 is enough for now.

Here it is again:

one mole of ANY specified entity contains 6.022 x 10^{23}of that entity.

For example:

- One mole of donuts contains 6.022 x 10
^{23}donuts - One mole of H
_{2}O contains 6.022 x 10^{23}molecules - One mole of nails contains 6.022 x 10
^{23}nails - One mole of Fe contains 6.022 x 10
^{23}atoms - One mole of cats contains 6.022 x 10
^{23}cats - One mole of electrons contains 6.022 x 10
^{23}electrons - One mole of high school students contains 6.022 x 10
^{23}poor, suffering (I mean happy, joyful) high school students

Hopefully, you're getting the idea.

By the way, the symbol for mole is "mol." Why does a four-letter word have a three-letter symbol? That's really the wrong question. Here's why.

Avogadro's Number has a unit associated with it. It is mol¯^{1}, as in 6.022 x 10^{23} mol¯^{1}. The superscripted minus one means the unit mol is in the denominator. There is an understood numerator of one, as in 1/mol.

Why is there no unit in the numerator? There could be, but it would vary based on the entity involved. If we were discussing an element, we might write atoms/mol. If we were discussing a compound, we would say "molecules per mol." What is in the numerator depends on what "entity" (atom, molecule, ion, electron, etc.) is being used in the problem.

What happens often is that unit names are not used in the numerator and a one is used instead.

Getting back to Avogadro's Number role in chemistry; please note that counting atoms or molecules is essentially impossible since they are so small. However, we can "count" atoms or molecules by weighing large amounts of them on a balance.

When we weigh one mole of a substance on a balance, this is called a "molar mass" and has the units g/mol (grams per mole). This idea is very critical in chemistry because it is used all the time.

- A molar mass is the weight in grams of one mole.
- One mole contains 6.022 x 10
^{23}entities.

Therefore, a molar mass is the mass in grams of 6.022 x 10^{23} entities.

OK. How does one calculate a molar mass? Get ready, because you should already know how to calculate a molar mass.

The molar mass of a substance is the molecular weight, but it is expressed in grams, not in amu.

All you need to do is calculate the molecular weight and stick the unit "g/mol" (grams per mole) after the number (instead of amu) and that is the molar mass for the substance in question.

**Example #1:** Calculate the molar mass of Al(NO_{3})_{3}

(1 x 26.98) + (3 x 14.007) + (9 x 16.00) = 213.00 g/mol213.00 grams is the mass of one mole of aluminum nitrate.

213.00 grams of aluminum nitrate contains 6.022 x 10

^{23}entities of Al(NO_{3})_{3}

**Example #2:** Calculate the molar mass of Ba(SCN)_{2}.

barium ---> 137.33 x 1 = 137.33

sulfur ---> 32.065 x 2 = 64.130

carbon ---> 12.011 x 2 = 24.022

nitrogen ---> 14.007 x 2 = 28.014Add 'em up ---> 137.33 + 64.130 + 24.022 + 28.014 = 253.50 g/mol

**Example #3:** Calculate the molar mass of CO

This one should be pretty easy.12.011 + 15.9994 = 28.010 g/mol

**Example #4:** Calculate the molar mass of N_{2}.

14.007 x 2 = 28.014 g/molOne mole of nitrogen gas contains 6.022 x 10

^{23}molecules of N_{2}. In this case, the entity is a molecule.

**Example #5:** Calculate the molar mass of Ar.

39.948 x 1 = 39.948 g/molThere are Avogadro Number of argon atoms in one mole of Ar. In this case, the entity is an atom.

## Calculate some molar masses

**Example #6:** Calculate the molar mass of HCl.

Aha! A simple one.1.008 + 35.453 = 36.461 g/mol

Please be aware that different sources will give slightly different answers. It all depends on how much rounding off was done for the atomic weights that are used.

**Example #7:** Calculate the molar mass of CaSO_{4} **⋅** ^{1}⁄_{2}H_{2}O

The dot does not mean multiply!What we will do is figure of the CaSO

_{4}and the H_{2}O separately, the then divide the H_{2}O value by two. Then, we'll add.CaSO

_{4}---> 136.139 g/mol (I used a molar mass calculator.

H_{2}O ---> 18.015 g/mol (Water is the first example in the video.)136.139 + (18.015 / 2) = 145.146 g/mol

By the way, it appears that this one (with a fractional coefficient must be done manually.

**Example #8:** (HOOCCH_{2})_{2}NCH_{2}CH_{2}N(CH_{2}COOH)_{2}

In the video, I give the address of a molar mass calculator. Go to it and calculate the molar mass of the given compound.Be aware that your teacher might teach simple formulas, then ask you a more complex one on the test.

**Example #9:** Ca(C_{2}H_{3}O_{2})_{2}

calcium ---> 40.078 x 1 = 40.078

carbon ---> 12.011 x 4 = 48.044

hydrogen ---> 1.008 x 6 = 6.048

oxygen ---> 15.999 x 4 = 63.996sum ---> 158.166 g/mol

An assignment for you: do a search, locate a molar mass calculator you like and do Ca(C

_{2}H_{3}O_{2})_{2}.I was intrigued by this one. Its title is "Molecular weight and molar mass for chemistry problems." There's a bit of explanation about molecular weights and molar masses as well.

**Example #10:** Calculate the molar mass of nitrogen.

I'm going to do this by entering the word nitrogen into Google.Look to the right-hand column and look for "Atomic mass." Next to it will be the value of 14.0067 u. Be careful because that is the weight of ONE atom of nitrogen, whereas nitrogen (as in nitrogen gas) is composed of TWO atoms of nitrogen bonded together.

In other words, be careful around the diatomic elements. You may have to use the context to determine if N or N

_{2}is intended.In this example, the context is the term 'molar mass.' Moe likely than not, the answer using N

_{2}is the correct one.

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