## 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 1023 atoms. Here's another way: there are 6.022 x 1023 atoms of carbon in 12 grams of carbon-12.

Let's say that real clearly: one mole of ANYTHING contains 6.022 x 1023 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."

Avogadro's Number has been very carefully measured in a number of ways over many decades. 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.

Here it is again: one mole of ANY specified entity contains 6.022 x 1023 of that entity. For example:

• One mole of donuts contains 6.022 x 1023 donuts
• One mole of H2O contains 6.022 x 1023 molecules
• One mole of nails contains 6.022 x 1023 nails
• One mole of Fe contains 6.022 x 1023 atoms
• One mole of dogs contains 6.022 x 1023 dogs
• One mole of electrons contains 6.022 x 1023 electrons
• One mole of ChemTeam members contains 6.022 x 1023 poor, suffering (I mean happy, joyful) high school students

Get the idea?

6.022 x 1023 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. (Someday, the ChemTeam hopes to tell the story for the WWW.)

Avogadro's Number has a unit associated with it. It is mol¯1, as in 6.022 x 1023 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.

Consequently, units names in the numerator are not used and a one is used instead.

Getting back to Avogadro's Number role in chemistry; please note that counting atoms or molecules is very difficult 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 because it is used all the time.

• A molar mass is the weight in grams of one mole.
• One mole contains 6.022 x 1023 entities.

Therefore, a molar mass is the mass in grams of 6.022 x 1023 entities.

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

The molar mass of a substance is the molecular weight in grams.

All you need to do is calculate the molecular weight and stick the unit "g/mol" after the number and that is the molar mass for the substance in question.

Calculate the molar mass of Al(NO3)3

(1 x 26.98) + (3 x 14.007) + (9 x 16.00) = 213.00 g/mol

213.00 grams is the mass of one mole of aluminum nitrate.

213.00 grams of aluminum nitrate contains 6.022 x 1023 entities of Al(NO3)3

The World-Wide Web contains molecular weight calculators, both ones that are on-line and programs you can download. Here are several on-line molecular weight calculators:

A scientific calculator with molecular weight calculator built-in
A no-frills calculator.
Set up as a periodic table
Set up as a list of elements in alphabetical order
Return to Mole Table of Contents

### Practice Problems

For the ChemTeam's class: calculate the mass of one mole for five (picked at random) of these substances. Show the calculation set-up for at least three of the five.

```1. AlCl3 	14. Ba(SCN)2	27. LiH		40. Ba(BrO3)2	53. AlBr3	66. HCl
2. TeF4		15. K2S		28. CO		41. Hg2Cl2	54. P2O5		67. K2SO4
3. PbS 		16. NH4Cl	29. SnI4		42. Cr2(SO3)3	55. NH4NO3	68. NaCl
4. Cu2O		17. KH2PO4	30. KOH		43. Al(MnO4)3	56. Ba(OH)2	69. LiI
5. AgI 		18. C2H5NBr	31. K2O		44. CoSO4	57. PbSO4	70. Hg2O
6. N2O		19. Ba(ClO3)2	32. H2SO4	45. Ca(NO3)3	58. Ba3(PO4)2	71. HF
7. MoCl5 	20. Fe(OH)3	33. Hg3N2	46. NaH2PO4	59. NaC2H3O2	72. FeCl3
8. Hg2Br2 	21. (NH4)2S	34. SiF4		47. (NH4)3PO4	60. Ba(OH)2	73. NaHSO4
9. Ta2O5		22. CoCl2	35. NH4OH	48. KAl(SO4)2	61. NaHCO3	74. Ag2O
10. HgF2		23. KMnO4	36. N2O5		49. Hg2SO4	62. Al(OH)3	75. Pb(ClO2)2
11. KCl		24. CaSO4	37. SnCrO4	50. Al2(SO4)3	63. NH4MnO4	76. CoF3
12. KF		25. H2CO3	38. Al2O3	51. FePO4	64. Fe2O3 	77. Al(C2H3O2)3
13. ZnO		26. CO2		39. CuCO3	52. Ca(C2H3O2)2	65. CaCO3	78. Na2Al2(SO4)4

79. (HOOCCH2)2NCH2CH2N(CH2COOH)2
80. (NH4)2CH(CH2)5COOH
```
Answers