Why is Avogadro's number such a strange value instead of a round number?

It was not chosen to be pretty; it was chosen so the numbers on the periodic table do double duty. The mole was defined so that one mole of carbon-12 has a mass of exactly 12 grams, which makes the atomic mass in amu numerically equal to the molar mass in g/mol for every element. That convenience is worth an awkward-looking constant. Since 2019 the value has been fixed by definition at exactly 6.02214076 × 10^23 particles per mole, and 6.022 × 10^23 is the rounded version used in class.

Is molar mass the same thing as molecular mass?

They are numerically the same but describe different amounts and use different units. Molecular mass is the mass of one molecule in amu; molar mass is the mass of one mole of those molecules in grams per mole. Water is 18.02 amu per molecule and 18.02 g/mol. For ionic compounds the term formula mass replaces molecular mass, because NaCl is a lattice ratio rather than a discrete molecule.

Do I include the coefficient in front of a formula when finding molar mass?

No. In 3\,H_2O, the 3 tells you how much water you have; it does not change what water is. Molar mass is a property of the substance, so water is 18.02 g/mol regardless of the coefficient. Coefficients become important in stoichiometry later in this unit, where they set the mole ratios between reactants and products.

How many decimal places should I keep for atomic masses?

Follow whatever your teacher's periodic table shows, and stay consistent — two decimal places is standard for most classes. Because you are adding, the sum should be reported to the same decimal position as the least precise value you used. Do not round intermediate products; round only the final total, or small errors accumulate in compounds with many atoms.

CHEM-6.1

The Mole & Molar Mass

Learn what a mole really counts, why Avogadro's number is 6.022 × 10²³, and how to build molar mass from any chemical formula step by step.

What you'll do in this lesson

A voice-first session with the Crimsora tutor on The Mole & Molar Mass, then targeted practice and FRQs — with the tutor adapting to where you get stuck.

Start The Mole & Molar Mass free

What this lesson covers

Atoms are far too small to count one at a time, yet chemistry is all about counting: how many atoms of oxygen react with how many atoms of hydrogen. Chemists solved this problem by inventing a counting word — the mole — that links a number of particles you can never see to a mass you can actually weigh on a balance.

In this lesson you will learn exactly what the mole counts, why Avogadro's number has the value it does, and how to read a chemical formula and the periodic table together to compute a molar mass in grams per mole. Molar mass is the bridge you will cross in every remaining lesson of this unit — mole conversions, percent composition, stoichiometry, and limiting reactants all begin with a correct molar mass. Getting fluent here makes everything after it easier.

The Mole Is a Counting Word, Not a Mass

A mole is a specific quantity of things, exactly the way a dozen is a specific quantity of things. One dozen is 12 of something; one mole is

6.022 \times 10^{23}

of something. That number is called Avogadro's number, symbol

N_A

Counting word	How many	Typical use
pair	2	shoes
dozen	12	eggs
ream	500	sheets of paper
mole	$6.022 \times 10^{23}$	atoms, molecules, ions

The mole is enormous because atoms are tiny. A single copper atom has a mass of roughly

1.05 \times 10^{-22}

grams, so you need hundreds of sextillions of them before the pile is big enough to see, let alone weigh. Avogadro's number was chosen so that one mole of atoms has a mass in grams that matches the atomic mass on the periodic table. One mole of carbon-12 atoms has a mass of exactly 12 grams.

Be careful about what the mole is counting. "One mole of oxygen" is ambiguous — one mole of oxygen atoms (

\mathrm{O}

) contains

6.022 \times 10^{23}

atoms, but one mole of oxygen gas (

\mathrm{O_2}

) contains

6.022 \times 10^{23}

molecules, which is

1.204 \times 10^{24}

atoms. Always name the particle: atoms, molecules, formula units, ions, or electrons.

A common misconception is that a mole is a mass or a volume. It is neither. It is a count. Different substances have wildly different masses per mole precisely because their particles have different masses, even though the count is always the same.

From Atomic Mass to Molar Mass

Every box on the periodic table lists an atomic mass — a weighted average of the masses of that element's naturally occurring isotopes, expressed in atomic mass units (amu). Carbon shows 12.01 amu, not exactly 12, because about 1.1 percent of natural carbon is carbon-13.

The powerful part is the numerical coincidence built into the definition of the mole: the atomic mass in amu equals the molar mass in grams per mole. Carbon is 12.01 amu per atom and 12.01 g/mol. Iron is 55.85 amu per atom and 55.85 g/mol. You do not calculate this — you read it off the table and change the units.

Element	Atomic mass (amu, one atom)	Molar mass (g/mol, $6.022 \times 10^{23}$ atoms)
H	1.008	1.008
He	4.003	4.003
Na	22.99	22.99
Fe	55.85	55.85

So one mole of helium (4.003 g) and one mole of iron (55.85 g) contain the identical number of atoms. Iron's mole is heavier only because each iron nucleus carries far more protons and neutrons.

One wrinkle: for elements that exist as diatomic molecules in their standard state —

\mathrm{H_2}

\mathrm{N_2}

\mathrm{O_2}

\mathrm{F_2}

\mathrm{Cl_2}

\mathrm{Br_2}

\mathrm{I_2}

— the molar mass of the molecule is twice the atomic mass. Nitrogen gas is 28.02 g/mol, not 14.01 g/mol. Students lose track of this constantly in gas problems later in the unit, so decide up front whether the formula in front of you is

\mathrm{N}

\mathrm{N_2}

Building the Molar Mass of a Compound

Molar mass of a compound is the sum of the molar masses of every atom in one formula unit. The procedure never changes:

First, expand the formula so you know how many of each atom are present. Subscripts multiply the atom immediately before them; a subscript outside parentheses multiplies everything inside. In

\mathrm{Ca(NO_3)_2}

there is 1 Ca, 2 N, and 6 O — the 2 outside multiplies both the N and the 3 O's.

Second, look up each element's molar mass. Third, multiply each by its count. Fourth, add. Keep at least two decimal places in the intermediate steps so rounding does not creep into the total.

For

\mathrm{Ca(NO_3)_2}

1(40.08) + 2(14.01) + 6(16.00) = 40.08 + 28.02 + 96.00 = 164.10 \text{ g/mol}

Hydrates use a raised dot, as in

\mathrm{CuSO_4 \cdot 5H_2O}

. The dot means "plus," and the coefficient 5 multiplies the entire water molecule: 5 O and 10 H in addition to the sulfate's atoms. That compound comes to 249.7 g/mol; ignoring the water gives 159.6 g/mol and every later calculation is wrong.

The most frequent errors are mechanical, not conceptual. Students distribute a subscript to only the first atom inside parentheses, drop a zero when multiplying oxygen, or use the atomic number from the top of the periodic table box instead of the atomic mass. Before you accept an answer, do a rough sanity check:

\mathrm{Ca(NO_3)_2}

contains six oxygens alone, so a total under 100 g/mol is impossible.

Units, Significant Figures, and Reading the Answer

Molar mass always carries units of grams per mole, written

\mathrm{g/mol}

\mathrm{g \cdot mol^{-1}}

. Writing a bare number like "164.10" is an incomplete answer, because the whole point of molar mass is that it is a conversion factor between grams and moles. In the next lesson you will use it as

\frac{164.10 \text{ g}}{1 \text{ mol}}

or its reciprocal, and the units are what tell you which way to flip it.

For significant figures, treat the subscripts in a formula as exact counting numbers — they never limit precision. The precision comes from the periodic table values you used. If you use masses to two decimal places (40.08, 14.01, 16.00), report the sum to two decimal places. When adding, line up decimal places rather than counting total digits, since the addition rule for significant figures is about decimal position.

Some vocabulary distinctions your teacher may ask about:

Term	Applies to	Example
atomic mass	one atom, in amu	Cl = 35.45 amu
molecular mass	one covalent molecule, in amu	$\mathrm{H_2O}$ = 18.02 amu
formula mass	one ionic formula unit, in amu	NaCl = 58.44 amu
molar mass	one mole of any of these, in g/mol	NaCl = 58.44 g/mol

All four numbers are numerically identical for a given substance; only the unit and the amount described change. Ionic compounds get the phrase "formula unit" rather than "molecule" because

\mathrm{NaCl}

describes the smallest whole-number ratio in a crystal lattice, not a discrete two-atom particle floating around.

Estimating and Checking Your Work

Molar mass calculations are easy to check if you build a habit of estimating first. Round each element to the nearest whole number, add mentally, and compare to your calculator result. For

\mathrm{H_2SO_4}

: about

2 + 32 + 64 = 98

. If your calculator says 9.8 or 980, you mis-keyed something.

A second check is the oxygen count. Oxygen is 16.00 g/mol, so every oxygen in the formula adds 16 to the total. Compounds loaded with oxygen — nitrates, sulfates, phosphates, carbonates — always come out heavy.

\mathrm{Al_2(SO_4)_3}

has twelve oxygens contributing 192.00 g/mol all by themselves.

A third check is comparative reasoning. If two compounds differ by one atom, their molar masses should differ by that atom's mass.

\mathrm{CO}

is 28.01 g/mol and

\mathrm{CO_2}

is 44.01 g/mol — a difference of exactly 16.00, one oxygen. If your two answers do not differ sensibly, one of them is wrong.

Finally, watch for coefficients versus subscripts. In the expression

3\,\mathrm{H_2O}

, the 3 is a coefficient describing how many molecules you have; it does not change the molar mass of water. Water is 18.02 g/mol whether you have one molecule or three moles of them. Coefficients matter in stoichiometry later in this unit, but they never appear inside a molar mass calculation. Students who multiply 18.02 by 3 while computing molar mass have confused an amount with a per-mole property.

Key terms

Mole (mol).: The SI unit for amount of substance; one mole contains exactly $6.022 \times 10^{23}$ elementary particles such as atoms, molecules, ions, or formula units.
Avogadro's number.: The value $6.022 \times 10^{23}$ particles per mole, symbol $N_A$ ; the fixed count that defines the mole.
Atomic mass.: The weighted average mass of an element's naturally occurring isotopes, listed on the periodic table in atomic mass units (amu).
Molar mass.: The mass in grams of one mole of a substance, with units of g/mol; numerically equal to the atomic, molecular, or formula mass in amu.
Formula unit.: The smallest whole-number ratio of ions in an ionic compound, such as NaCl; used instead of "molecule" because ionic solids form lattices.
Molecular mass.: The sum of the atomic masses of all atoms in one covalent molecule, expressed in amu.
Hydrate.: A compound with water molecules built into its crystal structure, written with a raised dot as in $\mathrm{CuSO_4 \cdot 5H_2O}$ ; the water counts toward the molar mass.
Subscript.: The small number after an atom or a set of parentheses in a formula, showing how many of that atom or group appear in one formula unit.

Worked example

Calculate the molar mass of aluminum sulfate,

\mathrm{Al_2(SO_4)_3}

. Use atomic masses Al = 26.98, S = 32.06, O = 16.00.

Step 1 — Expand the formula. The subscript 3 sits outside the parentheses, so it multiplies everything inside: both the S and the four O's. Aluminum has its own subscript of 2, unaffected by the parentheses.

Al: 2 atoms. S:

1 \times 3 = 3

atoms. O:

4 \times 3 = 12

atoms. Total of 17 atoms in one formula unit.

Step 2 — Multiply each count by its molar mass.

Aluminum:

2 \times 26.98 = 53.96

g/mol

Sulfur:

3 \times 32.06 = 96.18

g/mol

Oxygen:

12 \times 16.00 = 192.00

g/mol

Step 3 — Add the contributions.

53.96 + 96.18 + 192.00 = 342.14 \text{ g/mol}

Step 4 — Check. Rough estimate:

2(27) + 3(32) + 12(16) = 54 + 96 + 192 = 342

. That matches. Notice that oxygen alone supplies 192 of the 342 g/mol, more than half the mass — typical for a polyatomic-ion compound.

Answer: 342.14 g/mol. Because every atomic mass was used to two decimal places, the sum is reported to two decimal places, and the units g/mol must be written.

The most common wrong answer here is 214.14 g/mol, which comes from applying the 3 to the sulfur but forgetting to also triple the four oxygens. Expanding the formula in Step 1 before touching a calculator prevents that.

Practice questions

What is the molar mass of magnesium hydroxide,

\mathrm{Mg(OH)_2}

? (Mg = 24.31, O = 16.00, H = 1.008)

41.32 g/mol
42.33 g/mol
58.33 g/mol
74.33 g/mol

Answer: 58.33 g/mol

The subscript 2 outside the parentheses applies to both the O and the H, giving 1 Mg, 2 O, and 2 H. So

24.31 + 2(16.00) + 2(1.008) = 24.31 + 32.00 + 2.02 = 58.33

g/mol. The answer 41.32 g/mol comes from counting only one O and one H; 42.33 g/mol comes from doubling the H but not the O. Expanding the formula into an atom count before calculating is what prevents both errors.

A student weighs out 4.003 g of helium gas and 55.85 g of iron filings. Explain why these two very different masses contain the same number of atoms, and state what that number is.

Answer: Both samples contain one mole of atoms, which is $6.022 \times 10^{23}$ atoms. The mole is defined as a fixed count, and molar mass is set so that one mole of any element has a mass in grams equal to its atomic mass in amu. Helium's mole is lighter because each helium atom has only 2 protons and 2 neutrons, while each iron atom has 26 protons and about 30 neutrons — roughly 14 times more mass per atom.

The key idea is separating count from mass. Students often assume a heavier sample must contain more particles, but particle mass varies enormously across the periodic table. Since

55.85 / 4.003 \approx 14

, the per-atom mass ratio exactly accounts for the sample mass ratio while the count stays identical at

N_A

Rank these three substances from smallest to largest molar mass and show the calculation for each:

\mathrm{N_2}

\mathrm{CO_2}

\mathrm{H_2SO_4}

. Use N = 14.01, C = 12.01, O = 16.00, H = 1.008, S = 32.06.

Answer: $\mathrm{N_2} = 2(14.01) = 28.02$ g/mol; $\mathrm{CO_2} = 12.01 + 2(16.00) = 44.01$ g/mol; $\mathrm{H_2SO_4} = 2(1.008) + 32.06 + 4(16.00) = 2.02 + 32.06 + 64.00 = 98.08$ g/mol. Order from smallest to largest: $\mathrm{N_2} < \mathrm{CO_2} < \mathrm{H_2SO_4}$ .

Nitrogen gas is diatomic, so its molar mass is twice the periodic-table value — writing 14.01 g/mol for

\mathrm{N_2}

is one of the most common slips in this unit. Sulfuric acid ends up heaviest largely because its four oxygens contribute 64.00 g/mol on their own, a useful reminder that oxygen-rich formulas are almost always the heavy ones.

FAQ

Why is Avogadro's number such a strange value instead of a round number?: It was not chosen to be pretty; it was chosen so the numbers on the periodic table do double duty. The mole was defined so that one mole of carbon-12 has a mass of exactly 12 grams, which makes the atomic mass in amu numerically equal to the molar mass in g/mol for every element. That convenience is worth an awkward-looking constant. Since 2019 the value has been fixed by definition at exactly $6.02214076 \times 10^{23}$ particles per mole, and $6.022 \times 10^{23}$ is the rounded version used in class.
Is molar mass the same thing as molecular mass?: They are numerically the same but describe different amounts and use different units. Molecular mass is the mass of one molecule in amu; molar mass is the mass of one mole of those molecules in grams per mole. Water is 18.02 amu per molecule and 18.02 g/mol. For ionic compounds the term formula mass replaces molecular mass, because $\mathrm{NaCl}$ is a lattice ratio rather than a discrete molecule.
Do I include the coefficient in front of a formula when finding molar mass?: No. In $3\,\mathrm{H_2O}$ , the 3 tells you how much water you have; it does not change what water is. Molar mass is a property of the substance, so water is 18.02 g/mol regardless of the coefficient. Coefficients become important in stoichiometry later in this unit, where they set the mole ratios between reactants and products.
How many decimal places should I keep for atomic masses?: Follow whatever your teacher's periodic table shows, and stay consistent — two decimal places is standard for most classes. Because you are adding, the sum should be reported to the same decimal position as the least precise value you used. Do not round intermediate products; round only the final total, or small errors accumulate in compounds with many atoms.

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