How to count atoms by weighing them: moles and stoichiometry
HESI A2 topic: Stoichiometry
- One mole is 6.022 × 10²³ particles.
- Molar mass is the sum of atomic masses, in g/mol.
- Moles = grams ÷ molar mass; grams = moles × molar mass.
- Coefficients are mole ratios, never gram ratios.
- The limiting reactant runs out first and caps the product.
Key facts
- One mole contains 6.022 × 10²³ particles (Avogadro's number).
- Molar mass in g/mol is numerically equal to the formula mass in amu; add up the atomic masses of every atom in the formula.
- Moles = grams ÷ molar mass; grams = moles × molar mass.
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- The coefficients in a balanced equation give mole ratios, not mass ratios.
- Grams-to-grams problems take three steps: grams A → moles A → moles B → grams B.
- The limiting reactant runs out first and sets the maximum amount of product; the other reactant is in excess and some is left over.
Quick check1 question · 2 more at the end
What is the molar mass of carbon dioxide, CO₂? (Use C = 12 g/mol and O = 16 g/mol.)
Correct answer: C.
Molar mass is the sum of the atomic masses of every atom in the formula. CO₂ has one carbon and two oxygens: 12 + (2 × 16) = 44 g/mol. Always multiply each atomic mass by its subscript before adding.
A One hundred ninety-two multiplies the atomic masses together (12 × 16) instead of adding them.
B Thirty-two counts the two oxygens but leaves out the carbon atom.
C Correct: 12 + 2(16) = 44 g/mol.
D Twenty-eight counts only one oxygen atom (12 + 16), which is the molar mass of CO, not CO₂.
Full lesson
Each part starts with its main idea. Open a part when you want the details.
The short answer: A mole is 6.022 × 10²³ particles, and a substance's molar mass (in g/mol) is the sum of its atomic masses from the periodic table. Stoichiometry uses the coefficients of a balanced equation as mole ratios: convert grams to moles, use the ratio, then convert moles back to grams. The reactant that runs out first is the limiting reactant.
1 What is a mole?A mole is a counting unit, like a dozen, but for particles far too small to count one by one. 1 min
A mole is a counting unit, like a dozen, but for particles far too small to count one by one. One mole is 6.022 × 10²³ particles, a value called Avogadro's number. The particles can be atoms, molecules or ions.
Chemists use the mole because it links the invisible world to a balance. One mole of a substance has a mass in grams equal to its formula mass in atomic mass units. A mole of carbon-12 atoms has a mass of 12 grams.
2 How do you find molar mass from the periodic table?Molar mass is the sum of the atomic masses of every atom in the formula, in grams per mole (g/mol). 1 min
Molar mass is the sum of the atomic masses of every atom in the formula, in grams per mole (g/mol). Read each element's atomic mass from the periodic table, multiply by its subscript, and add.
| Substance | Work | Molar mass |
|---|---|---|
| Water, H₂O | 2(1.008) + 16.00 | 18.02 g/mol |
| Sodium chloride, NaCl | 22.99 + 35.45 | 58.44 g/mol |
| Carbon dioxide, CO₂ | 12.01 + 2(16.00) | 44.01 g/mol |
For hand calculations, problems often tell you to use rounded values such as H = 1, C = 12 and O = 16. Then water is 18 g/mol and CO₂ is 44 g/mol.
3 How do you convert between grams and moles?Molar mass is the bridge between grams and moles. 1 min
Molar mass is the bridge between grams and moles. Use it as a conversion factor:
- Grams → moles: divide by molar mass. 36 g of water ÷ 18 g/mol = 2 mol.
- Moles → grams: multiply by molar mass. 0.5 mol of CO₂ × 44 g/mol = 22 g.
4 What does a balanced equation tell you about amounts?The coefficients in a balanced equation are mole ratios. 1 min
The coefficients in a balanced equation are mole ratios. In N₂ + 3H₂ → 2NH₃, 1 mol of nitrogen reacts with 3 mol of hydrogen to make 2 mol of ammonia. The ratio holds whether you count single molecules or moles, but never for grams, because each substance has a different molar mass.
Using these ratios to calculate amounts is called stoichiometry.
5 How do you go from grams of one substance to grams of another?Every grams-to-grams problem follows the same three-step path. 1 min
Every grams-to-grams problem follows the same three-step path. Example: how many grams of water form from 4 g of hydrogen gas? Use 2H₂ + O₂ → 2H₂O, with H = 1 and O = 16.
- Grams to moles of what you have. H₂ is 2 g/mol, so 4 g ÷ 2 g/mol = 2 mol H₂.
- Mole ratio. The equation shows 2 mol H₂ → 2 mol H₂O, a 1:1 ratio, so 2 mol H₂O forms.
- Moles to grams of what you want. 2 mol × 18 g/mol = 36 g of water.
6 What is a limiting reactant?The limiting reactant is the one that runs out first, and it caps how much product can form. 1 min
The limiting reactant is the one that runs out first, and it caps how much product can form. Think of building bicycles that each need 2 wheels and 1 frame. With 10 wheels and 3 frames, you can build only 3 bikes; the frames are limiting and 4 wheels are left over.
Chemistry works the same way. Suppose you have 4 mol H₂ and 3 mol O₂ for 2H₂ + O₂ → 2H₂O. The 4 mol H₂ needs only 2 mol O₂, so hydrogen runs out first. Hydrogen is limiting, 4 mol of water forms, and 1 mol of O₂ is left over as the excess reactant.
Common mistakes
The traps students fall into most. Read these before you practice.
Watch out: Coefficients compare moles, not grams; 2H₂ + O₂ → 2H₂O does not mean 2 g of hydrogen reacts with 1 g of oxygen.
Watch out: Multiply each atomic mass by its subscript; CO₂ is 12 + 2 × 16 = 44 g/mol, not 12 + 16 = 28.
Watch out: The reactant with fewer moles is not automatically the limiting one; compare what you have to what the ratio requires.
Watch out: To get moles you divide grams by molar mass, not multiply.
How to remember it
Memory hook: "Grams can't talk to grams; they have to go through moles." Every route between two substances passes through the mole ratio in the middle.
Self-check:
- Find the molar mass of CH₄ using C = 12 and H = 1.
- How many moles are in 88 g of CO₂?
- For N₂ + 3H₂ → 2NH₃ with 1 mol N₂ and 6 mol H₂, which reactant is limiting?
Show answers
- 16 g/mol.
- One carbon: 12.
- Four hydrogens: 4 × 1 = 4.
- Add: 12 + 4 = 16 g/mol.
- 2 mol.
- CO₂ is 12 + 2 × 16 = 44 g/mol.
- Divide grams by molar mass: 88 g ÷ 44 g/mol = 2 mol.
- N₂ is limiting.
- The ratio is 1 mol N₂ to 3 mol H₂.
- 1 mol N₂ needs only 3 mol H₂, and you have 6 mol.
- N₂ runs out first. It makes 2 mol NH₃, and 3 mol H₂ is left over.