**Stoichiometry: Chemical Formulas and Equations**

The Mole

The Mole

Even tiny samples of chemicals contain huge numbers of atoms, ions or molecules. For convenience sake, some kind of reference for a collection of a large number of these objects would be very useful (e.g. a "dozen" is a reference to a collection of 12 objects). In chemistry we use a unit called a ** mole **(abbreviated

A mole is defined as the amount of matter that contains as many objects as the number of atoms in exactly 12 grams of ^{12}C.

Various experiments have determined that this number is...

6.0221367 x 10^{23 }

This is usually abbreviated to simply 6.02 x 10^{23}, and is known as ** Avogadro's number**.

One mole of atoms, volkswagens, people, etc. contains 6.02 x 10^{23} of these objects. Just how big is this number? One mole of marbles spread over the earth would result in a layer *three miles* thick.

Molar Mass

A single ^{12}C atom has a mass of 12 *amu*. A single ^{24}Mg atom has a mass of 24 *amu*, or twice the mass of a ^{12}C atom. Thus, one mole of ^{24}Mg atoms should have twice the mass as one mole of ^{12}C atoms. Since one mole of ^{12}C atoms weighs 12 grams (by definition), one mole of ^{24}Mg atoms must weigh 24 grams.

Note that the mass of one atom in atomic mass units (amu) is numerically equal to the mass of one mole of the same atoms in grams (g).

The mass in grams of 1 mole (mol) of a substance is called its *molar mass**.*

The molar mass (in grams) of any substance is always numerically equal to its formula weight (in amu).

One H_{2}O molecule weighs 18.0 amu; 1 mol of H_{2}O weighs 18.0 grams

One NaCl ion pair weighs 58.5 amu; 1 mol of NaCl weighs 58.5 grams

Interconverting masses, moles, and numbers of particles

Keeping track of units in calculations is necessary when interconverting masses and moles. This is formally known as **dimensional analysis**.

"Igor! bring me 1.5 moles of calcium chloride"

Chemical formula of calcium chloride = CaCl_{2 }

Molecular mass of Ca = 40.078 amu

Molecular mass of Cl = 35.453 amu

Therefore, the ** formula weight** of CaCl

Therefore, one mole of CaCl_{2} would have a mass of 110.984 grams.

so, 1.5 moles of CaCl2 would be:

(1.5 ~~mole~~)(110.984 grams/~~mole~~) = 166.476 grams

"Igor! I have 2.8 grams of gold, how many atoms do I have?"

Molecular formula of gold is: Au

Molecular weight of Au = 196.9665 *amu *

Therefore, 1 mole of gold weighs 196.9665 grams. So, in 2.8 grams of gold we would have:

(2.8 ~~gram~~)(1 mole/196.9665 ~~gram~~) = 0.0142 mole

From Avogadro's number, we know that there are approximately 6.02 x 10^{23} atoms/mole. Therefore, in 0.0142 moles we would have:

(0.0142 ~~mole~~)(6.02 x 10^{23} atoms/~~mole~~) = 8.56 x 10^{21} atoms

1996 Michael Blaber