# Molar Mass

• ### Introduction

The molar mass of a chemical is how many grams of the chemical are in one mole of atoms/molecules. A mole is merely a measurement of a quantity of something, i.e. $$6.02 \times 10^{23}$$.

The molar masses on a periodic table are always in the units of grams per mole.

Example 1: One mole of carbon dioxide molecules will have $$6.02 \times 10^{23}$$ carbon dioxide molecules.

The molar mass of any chemical can be computed with a periodic table, so whenever you need to compute molar masses, pull out a periodic table and a calculator.

### Rounding Digits

Before jumping into any examples, let us clear one misconception. Periodic tables will almost always contain a molar mass for each element, but the number of digits after the decimal point that are included vary from table to table. As a rule of thumb, always use the value rounded to two digits after the decimal point.

Example 2: One periodic table lists the molar mass of Chlorine to be $$35.453$$ grams per mole. Round this to the correct number of digits.

Solution: Use only two digits after the decimal point, making the value that would be used in calculations $$35.45$$.

If by chance you find a periodic table that has less than two digits after the decimal point, you either have an element where the exact precision is unknown (including many metals with high atomic numbers) or a periodic table that lacks precision. In the former case, the real-world scenarios where the non-precise molar masses must be used will be uncommon. In the latter case, find another periodic table.

### Molar Masses of Elements

The molar mass of an individual element is just a number on the periodic table.

Example 3: Use a periodic table to find the molar mass of Cadmium (Cd).

Solution: To two digits after the decimal point, a periodic table will tell you that the molar mass of Cadmium is 112.41 grams per mole.

For all molar mass computations, the state of matter of the chemical is irrelevant; the molar mass stays the same even as the substance changes its state of matter.

### Molar Mass Computations for Molecules

Most substances, of course, are comprised of more than one type of atom. In that case, just add the molar mass of each atom (after rounding) to get the total molar mass.

Example 4: What is the molar mass of Rubidium Bromide?

Solution: Add up each individual molar mass: $$85.47 + 79.90 = 165.37$$ grams per mole.

If there is more than one of an atom in a molecule, then multiply the individual molar mass by the coefficient for each type of atom and then add those values.

Example 5: Find the molar mass of elemental Chlorine, $$Cl_2$$.

Solution: The molar mass of one Chlorine atom is $$35.45$$ grams per mole (rounded). Since there are two atoms, multiply this by $$2$$ to get a molar mass of $$70.90$$ grams per mole.

The next example is slightly more complicated, but is still the same concept in action.

Example 6: Find the molar mass of Cobalt Oxide, $$CoO$$.

Solution: Round the individual molar masses of each element and then add them: $$58.93 + 16.00 = 74.93$$ grams per mole.

The next two examples also progress in difficulty slightly, so just keep the algebra under control, and always remember to round.

Example 7: Find the molar mass of Tungsten Sulfide, $$WS_3$$.

Solution: Combine the mass of each atom in the correct ratio (one Tungsten and three Sulfide) to get $$183.85 + 3(32.07) = 280.06$$ grams per mole.

Example 8: Find the molar mass of Strontium Chlorate, $$Sr(ClO_3)_2$$.

Solution: As a rule of thumb for ionic compounds, when calculating molar masses, find the cation molar mass and the anion molar mass separately, then add them.

Cation: One Strontium atom: $$87.62$$ grams per mole Anion: Three Chlorine atoms and six Oxygen atoms: $$3(35.45) + 6(16.00) = 202.35$$

Add these together: $$289.97$$ grams per mole

The last example in this section involves the reverse process; instead of using a chemical formula to find the molar mass, we use the molar mass to find the chemical.

Example 9: A diatomic element is an element whose stable elemental form has two atoms of the element bonded together. What diatomic molecule has a molar mass of $$32.00 \; g$$?

Solution: Since two atoms of this element have a combined molar mass of $$32.00 \; g$$, one atom of the element has half of that molar mass, $$16.00 \; g$$. We search the periodic table to find an element with this molar mass, and notice that oxygen has a molar mass of $$16.00 \; g$$, so that is our answer. The chemical formula of elemental oxygen is $$O_2$$.

### Molar Mass Conversions

Okay, so now that you know how to find the molar mass of any chemical that exists, the question arises: what are molar mass conversions used for? Since the unit is grams per mole, the molar mass can be used as a conversion factor.

In conversion problems, two different molar mass conversions can be used.

If $$M$$ is the magnitude of the molar mass, use one of two conversions:

A. If converting from grams to moles, use the conversion $$\frac{1}{M}$$ moles per gram.

B. If converting from moles to grams, use the conversion $$\frac{M}{1}$$ grams per mole.

Example 10: How many moles of Rhenium metal are in 352 grams of it?

Solution: From the periodic table, the molar mass of Rhenium is 101.07 grams per mole. Convert grams to moles as follows:

$$352 g Rh \times \frac{1 mol Rh}{101.07 g Rh} = 3.48 mol Rh$$

Example 11: A sample of water has a mass of 34.0 kilograms. How many moles are present?

Solution: This problem has an extra step. Since molar mass conversions involve grams and moles, the kilograms must first be converted to grams:

$$34.0 kg H_2O \times \frac{1000 g H_2O}{1 kg H_2O} = 34000 g H_2O$$

Now find the molar mass of water (this is something you may eventually have memorized, as it is a common substance in real-world applications):

$$2(1.01) + 16.00 = 18.02$$

This is, as usual, in grams per mole. Now convert the mass of water to moles:

$$34000 g H_2O \times \frac{1 mol H_2O}{18.02 g H_2O} = 1900 mol H_2O$$

In the previous example, it would also have been perfectly valid to begin by finding the molar mass of water and converting that to kilograms per mole. Then you could use that to convert the mass of water in kilograms directly to moles.

The final example contains a real-world scenario, but the calculations still follow the same format.

Example 12: A geologist unearths a large sample of cryolite, $$Na_3AlF_6$$. He takes it back to his lab and measures its mass. His scale gives a reading of $$12.4$$ kilograms. How many moles of cryolite did he unearth?

Solution: A molar mass conversion converts from grams to moles, or moles to grams, but our mass is in kilograms, so in order to use a molar mass conversion, we must convert the mass to grams:

$$12.4 \; kg \; Na_3AlF_6 \times \frac{1000 \; g \; Na_3AlF_6}{1 \; kg \; Na_3AlF_6} = 1240 \; g \; Na_3AlF_6$$

Now we must find the molar mass of cryolite so we can use the molar mass conversion:

$$(22.99(3) + 26.98 + 6(19.00))\;g = 209.95 \; g$$

We can use this molar mass to convert the mass of cryolite in the sample to moles:

$$1240 \; g \; Na_3AlF_6 \times \frac{1 \; mol \; Na_3AlF_6}{209.95 \; g \; Na_3AlF_6} = 5.91 \; mol \; Na_3AlF_6$$

Reference, courtesy of

"Chemical Principles The Quest for Insight" 2nd Edition

Atkins, Peter and Jones, Loretta