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Atoms and Molecules




Bonds and Octet Rules
Chemical Equations
The Mole




Functional Groups
Periodic Table


Practice Quiz I
Practice Quiz II
Practice Quiz III

The Mole

Chemical equations are the written representation of reactions that occur in the world and in the chemistry laboratory. Most chemical reactions involve atoms and molecules, which are too small to be measured in the laboratory. As a result, chemists have created a special mathematical quantity called the mole to make it possible to work with chemical reactions on a larger scale.

The mole is not a random number, but was specifically calculated based on the carbon-12 atom. Because of the way it was calculated, the mole allows scientists to calculate the number of atoms or molecules present in a sample of matter based entirely on the matter's mass.

A mole is an amount of a substance that contains the same number of units as there are atoms in exactly 12 grams of carbon-12. That number is 6.02 x 1023. Thus,12 grams of carbon-12 contain 6.02 x 1023 atoms of carbon. The mole is analogous to the dozen. Just as a dozen books, a dozen people, and a dozen buildings, for example, are characterized by 12 units in each case, a mole of any element contains 6.02 x 1023 atoms and a mole of any molecular substance, such as water or alcohol (ethanol), contains 6.02 x 1023 molecules.

12 books = 1 dozen books


6.02 x 1023 atoms of aluminum = 1 mole of aluminum.
6.02 x 1023 molecules of water = 1 mole of water.
Images are not drawn to the scale

 A mole of any substance is equal to its molar mass, which is its formula mass expressed in grams. The molar mass is expressed in the unit “grams per mole,” which is abbreviated “g/mol". In order to find the formula mass of a substance, add all the atomic masses of the atoms that comprise that substance. Thus, for a monoatomic element the formula mass is its atomic mass. For example, the formula mass of carbon-12 is 12 amu and its molar mass is 12 g/mol. For an ionic compound, such as sodium chloride (NaCl), the molar mass is the sum of the atomic masses of the sodium and chlorine atoms comprising the formula. The following table summarizes this information within the context of specific examples, including NaCl.

Substance Formula Mass Mass of One Mole (Molar Mass)
Copper (Cu) atom 63.5 amu 63.5 g/mol
Table salt (NaCl) ionic compound 58.5 amu (Na = 23.0 amu; Cl = 35.5 amu) 58.5 g/mol
Water (H2O) molecule 18.0 amu (2H = 2.0 amu; O = 16.0 amu) 18.0 g/mol
Carbon dioxide (CO2) molecule 44.0 amu (C = 12.0 amu; 2O = 32.0 amu) 44.0 g/mol

Using copper (Cu) as an example, we can show how the concept of the mole allows chemists to move from the scale of atoms to the more tangible scale of grams. Let us calculate the mass of copper in a penny, assuming a penny contains 9 x 1021 copper atoms. Keep in mind that Avogadro's number, 6.02 x 1023 , can also be written as 602 x 1021, which reflects the same power of 10, namely 1021 , as is associated with the assumed number of copper atoms in a penny.

Mole Math

Note that, because of the way the equation above has been set up, the mole units “cancel” each other out, so that you obtain the desired units, grams.

Moles in Chemical Equations

The concept of the mole is important because reactions work entirely on numbers. A reaction only happens because the right atoms in the right amount are all present under the right conditions. If only 1 hydrogen atom and 1 oxygen atom are present, no water will form; there must be 2 hydrogen atoms and 1 oxygen atom for 1 water molecule to form. This 2:1 ratio between hydrogen and oxygen is the “recipe” of the reaction, and is the information the scientist needs in order to do the reaction properly in his laboratory. This “recipe” can be found in the balanced chemical equation. If we look at the balanced equation depicting the reaction of hydrogen (H2) with oxygen (O2) to produce water, shown below, we see that the large numbers to the left of each participant in the equation—which are called coefficients—show us that 2 molecules of hydrogen and 1 molecule of oxygen are needed to produce 2 molecules of water.

Depiction of balanced water equation

The coefficients establish a proportion in the reaction between hydrogen, oxygen, and water, a constant ratio of 2:1:2. Since the ratio is constant, the reaction could also be expressed as 2 dozen molecules of hydrogen and 1 dozen molecules of oxygen producing 2 dozen molecules of water. We can go an extra step and express the ratio in terms of moles: 2 moles of hydrogen molecules and 1 mole of oxygen molecules will produce 2 moles of water molecules.

With the equation expressed in terms of moles, a scientist can know the exact quantity of each ingredient needed to make the reaction work, because he/she can use the concept of the mole to determine the masses of each reactant in terms of grams.