2.7: The Mole and Mole-Mass Conversions

Learning Objectives

• To define the mole unit.
• To convert quantities between mass units and mole units.

The Mole

We need 2 hydrogen atoms and 1 oxygen atom to make 1 water molecule. If we want to make 2 water molecules, we will need 4 hydrogen atoms and 2 oxygen atoms. If we want to make 5 molecules of water, we need 10 hydrogen atoms and 5 oxygen atoms. The ratio of atoms we will need to make any number of water molecules is the same: 2 hydrogen atoms to 1 oxygen atom as shown in figure 2.7.1.

Figure 2.7.1: The ratio of hydrogen atoms to oxygen atoms used to make water molecules is always 2:1, no matter how many water molecules are being made.

Chemists use the term mole to represent a large number of atoms or molecules. Just as a dozen implies 12 things, a mole (abbreviated as mol) represents 6.022 × 10²³ things. The number 6.022 × 10²³, called Avogadro’s number after the 19th-century chemist Amedeo Avogadro, is the number we use in chemistry to represent macroscopic amounts of atoms and molecules. Thus, if we have 6.022 × 10²³ Na atoms, we say we have 1 mol of Na atoms. If we have 2 mol of Na atoms, we have 2 × (6.022 × 10²³) Na atoms, or 1.2044 × 10²⁴ Na atoms. Similarly, if we have 0.5 mol of benzene (C₆H₆) molecules, we have 0.5 × (6.022 × 10²³) C₆H₆ molecules, or 3.011 × 10²³ C₆H₆ molecules.

A mole represents a very large number! If 1 mol of quarters were stacked in a column, it could stretch back and forth between Earth and the sun 6.8 billion times.

Mole to Mass Conversions

With such a large # it is extremely difficult, if not impossible, to organize atoms one at a time. We deal with billions of atoms at a time. How can we keep track of so many atoms (and molecules) at a time? We do it by using mass rather than by counting individual atoms. We use atomic weight in grams (molar mass) as a conversion factor in a mole-mass conversion (or its reverse, a mass-mole conversion).

1 mol of Al has a mass of 26.98 g (Example \(\PageIndex{1}\)). Stated mathematically,

1 mol Al = 26.98 g Al

We can divide both sides of this expression by either side to get one of two possible conversion factors:

\[\mathrm{\dfrac{1\: mol\: Al}{26.98\: g\: Al}\quad and \quad \dfrac{26.98\: g\: Al}{1\: mol\: Al}} \nonumber \]

The first conversion factor can be used to convert from mass to moles, and the second converts from moles to mass.

Example \(\PageIndex{1}\)

What is the mass of 3.987 mol of Al?

Solution

The first step in a conversion problem is to decide what conversion factor to use. Because we are starting with mole units, we want a conversion factor that will cancel the mole unit and introduce the unit for mass in the numerator. Therefore, we should use the \(\mathrm{\dfrac{26.98\: g\: Al}{1\: mol\: Al}}\) conversion factor. We start with the given quantity and multiply by the conversion factor:

\(\mathrm{3.987\: mol\: Al\times\dfrac{26.98\: g\: Al}{1\: mol\: Al}}\)

Note that the mol units cancel algebraically. (The quantity 3.987 mol is understood to be in the numerator of a fraction that has 1 in the unwritten denominator.) Canceling and solving gives

\(\mathrm{3.987\: mol\: Al\times \dfrac{26.98\: g\: Al}{1\: mol\: Al}=107.6\: g\: Al}\)

Our final answer is expressed to four significant figures.

Exercise \(\PageIndex{1}\)

How many moles are present in 100.0 g of Al? (Hint: you will have to use the other conversion factor we obtained for aluminum.)

Answer

\(\mathrm{100.0\: g\: Al\times \dfrac{1\: mol\: Al}{26.98\: g\: Al}=3.706\: mol\: Al}\)

To Your Health: Minerals

For our bodies to function properly, we need to ingest certain substances from our diets. Among our dietary needs are minerals, the noncarbon elements our body uses for a variety of functions, such developing bone or ensuring proper nerve transmission. The US Department of Agriculture has established some recommendations for the RDIs of various minerals. The accompanying table lists the RDIs for minerals, both in mass and moles, assuming a 2,000-calorie daily diet.

Table \(\PageIndex{1}\): Essential Minerals and their Composition in Humans

Mineral	Male (age 19–30 y)		Female (age 19–30 y)
Ca	1,000 mg	0.025 mol	1,000 mg	0.025 mol
Cr	35 µg	6.7 × 10^−7 mol	25 µg	4.8 × 10^−7 mol
Cu	900 µg	1.4 × 10^−5 mol	900 µg	1.4 × 10^−5 mol
F	4 mg	2.1 × 10^−4 mol	3 mg	1.5 × 10^−4 mol
I	150 µg	1.2 × 10^−6 m ol	150 µg	1.2 × 10^−6 mol
Fe	8 mg	1.4 × 10^−4 mol	18 mg	3.2 × 10^−4 mol
K	3,500 mg	9.0 × 10^−2 mol	3,500 mg	9.0 × 10^−2 mol
Mg	400 mg	1.6 × 10^−2 mol	310 mg	1.3 × 10^−2 mol
Mn	2.3 mg	4.2 × 10^−5 mol	1.8 mg	3.3 × 10^−5 mol
Mo	45 mg	4.7 × 10^−7 mol	45 mg	4.7 × 10^−7 mol
Na	2,400 mg	1.0 × 10^−1 mol	2,400 mg	1.0 × 10^−1 mol
P	700 mg	2.3 × 10^−2 mol	700 mg	2.3 × 10^−2 mol
Se	55 µg	7.0 × 10^−7 mol	55 µg	7.0 × 10^−7 mol
Zn	11 mg	1.7 × 10^−4 mol	8 mg	1.2 × 10^−4 mol

Table \(\PageIndex{1}\) illustrates several things. First, the needs of men and women for some minerals are different. The extreme case is for iron; women need over twice as much as men do. In all other cases where there is a different RDI, men need more than women.

Second, the amounts of the various minerals needed on a daily basis vary widely—both on a mass scale and a molar scale. The average person needs 0.1 mol of Na a day, which is about 2.5 g. On the other hand, a person needs only about 25–35 µg of Cr per day, which is under one millionth of a mole. As small as this amount is, a deficiency of chromium in the diet can lead to diabetes-like symptoms or neurological problems, especially in the extremities (hands and feet). For some minerals, the body does not require much to keep itself operating properly.

Although a properly balanced diet will provide all the necessary minerals, some people take dietary supplements. However, too much of a good thing, even minerals, is not good. Exposure to too much chromium, for example, causes a skin irritation, and certain forms of chromium are known to cause cancer (as presented in the movie Erin Brockovich).

Key Takeaway

• A mole is 6.022 × 10²³ things.
• It is possible to convert between moles of material and mass of material.