What is a mole?
The mole (mol) is the SI base unit chemists use to count atoms, molecules, ions, or formula units, the same way "dozen" counts eggs. A dozen always means 12 items no matter what the items are. A mole always means 6.022 × 10²³ items no matter what the items are. Chemists need a unit this large because atoms and molecules are far too small to weigh or count one at a time, and a single gram of almost anything contains a huge number of them.
Same number, different mass
One mole of any substance always contains the same NUMBER of particles. What changes from substance to substance is the MASS of that one mole. One mole of H₂ and one mole of Fe both hold 6.022 × 10²³ particles, but the iron weighs far more.
Avogadro's number
Avogadro's number, Nₐ = 6.022 × 10²³, is the number of particles in exactly one mole of anything. It is named for Amedeo Avogadro, though the value itself was measured experimentally later. The "particles" being counted can be atoms, molecules, formula units, or ions, so always name what you're counting alongside the number.
| Sample | Number of particles |
|---|---|
| 1 mol of carbon atoms | 6.022 × 10²³ C atoms |
| 1 mol of H₂O molecules | 6.022 × 10²³ H₂O molecules |
| 1 mol of NaCl formula units | 6.022 × 10²³ NaCl formula units |
| 1 mol of electrons | 6.022 × 10²³ electrons |
Always name the particle
Writing "6.022 × 10²³ H₂O" leaves out what's being counted. Write "6.022 × 10²³ molecules of H₂O" or "6.022 × 10²³ formula units of NaCl" so the type of particle is clear. Ionic compounds are counted in formula units, not molecules, since they don't form true molecules.
Molar mass from the periodic table
The molar mass of a substance is the mass, in grams, of exactly one mole of that substance, with units of g/mol. For a single element, the molar mass is just the atomic mass printed on the periodic table, read in grams per mole instead of atomic mass units. For a compound, add up the atomic masses of every atom in the formula, multiplying each atomic mass by its subscript.
| Element | Atomic mass (g/mol) |
|---|---|
| H | 1.01 |
| C | 12.01 |
| N | 14.01 |
| O | 16.00 |
| Na | 22.99 |
| S | 32.07 |
| Cl | 35.45 |
| Ca | 40.08 |
| Compound | Calculation | Molar mass |
|---|---|---|
| H₂O | 2(1.01) + 16.00 | 18.02 g/mol |
| CO₂ | 12.01 + 2(16.00) | 44.01 g/mol |
| NaCl | 22.99 + 35.45 | 58.44 g/mol |
| C₆H₁₂O₆ | 6(12.01) + 12(1.01) + 6(16.00) | 180.18 g/mol |
| CaCO₃ | 40.08 + 12.01 + 3(16.00) | 100.09 g/mol |
Parentheses multiply through
In a formula like Ca(OH)₂, the subscript 2 outside the parentheses applies to everything inside it, so there are 2 oxygen atoms AND 2 hydrogen atoms. Molar mass = 40.08 + 2(16.00) + 2(1.01) = 74.10 g/mol.
Converting between grams and moles
Molar mass is the bridge between grams, what a scale measures, and moles, what a balanced equation counts. Divide grams by molar mass to get moles. Multiply moles by molar mass to get grams. Example: How many moles are in 117 g of NaCl (molar mass 58.44 g/mol)? mol = g ÷ M = 117 g ÷ 58.44 g/mol = 2.00 mol NaCl Example: What is the mass of 3.50 mol of CO₂ (molar mass 44.01 g/mol)? g = mol × M = 3.50 mol × 44.01 g/mol = 154 g CO₂
Let the units guide you
Write molar mass as a fraction so the unwanted unit cancels. To go grams to moles, multiply by (1 mol ÷ molar mass in grams) so the gram units cancel out and moles are left over.
Converting between moles and particles
Avogadro's number is the bridge between moles, what a balanced equation counts, and particles, individual atoms, molecules, or ions. Multiply moles by 6.022 × 10²³ to get particles. Divide particles by 6.022 × 10²³ to get moles. Example: How many formula units are in 2.00 mol of NaCl? particles = mol × Nₐ = 2.00 mol × 6.022 × 10²³ = 1.20 × 10²⁴ formula units of NaCl (2.00 mol carries three significant figures, so the answer is rounded to three: 1.20 × 10²⁴.) Example: A sample contains 3.011 × 10²³ molecules of CO₂. How many moles is that? mol = particles ÷ Nₐ = 3.011 × 10²³ ÷ 6.022 × 10²³ = 0.5000 mol CO₂
Watch your sig figs
The rounded value 6.022 × 10²³ carries four significant figures. For multiplication and division, round the final answer to the fewest significant figures among the measured quantities in the problem. So if a mass is given to three significant figures, the answer keeps three.
Putting it together: the mole road map
Grams and particles never convert directly into each other. Moles sit in the middle of every conversion, so a two step trip through moles is required whenever a problem starts in grams and asks for particles, or starts in particles and asks for grams.
| Convert | Operation | Formula |
|---|---|---|
| grams → moles | divide by molar mass | mol = g ÷ M |
| moles → grams | multiply by molar mass | g = mol × M |
| moles → particles | multiply by 6.022 × 10²³ | particles = mol × Nₐ |
| particles → moles | divide by 6.022 × 10²³ | mol = particles ÷ Nₐ |
Example: How many oxygen atoms are in 10.0 g of H₂O (molar mass 18.02 g/mol)? Step 1, grams to moles of H₂O: 10.0 g ÷ 18.02 g/mol = 0.555 mol H₂O Step 2, moles of H₂O to molecules of H₂O: 0.555 mol × 6.022 × 10²³ = 3.34 × 10²³ molecules H₂O Step 3, molecules of H₂O to atoms of O: each H₂O molecule holds 1 oxygen atom, so 3.34 × 10²³ molecules H₂O × 1 O atom per molecule = 3.34 × 10²³ O atoms
Draw the road map
Sketch grams on the left, moles in the middle, and particles on the right. Label the left arrow with molar mass and the right arrow with Avogadro's number. Every gram to particle problem is just two hops across that map, and every particle to gram problem is the same two hops in reverse.
Try it yourself
mole-molar-mass-samples.csvDownload mole-molar-mass-samples.csv: https://restedteacher.com/practice-files/chemistry/mole-molar-mass-samples.csv
Five lab samples, each a measured mass of a different compound.
Open it as a spreadsheet
Open mole-molar-mass-samples.csv in Google Sheets or Excel. Add a molar-mass column and a moles column, then fill both down for all five samples at once.
Using the values in the file, answer these. Atomic masses (g/mol): Al 26.98, O 16.00, Mg 24.31, Cl 35.45, K 39.10, Mn 54.94, N 14.01, H 1.01, S 32.07, C 12.01. Round moles to 3 significant figures. 1. Calculate the molar mass of (NH₄)₂SO₄, then find how many moles are in the trial 4 sample. 2. How many formula units of KMnO₄ are in the trial 3 sample? (particles = mol × 6.022 × 10²³) 3. Which of the five samples contains the greatest number of moles?