Chemistry 2e · Composition of Substances and Solutions
Formula Mass and the Mole Concept
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Atoms and molecules are far too small to count one by one, yet chemists constantly need to know exactly how many are present. The solution is to weigh: the mole The SI unit for amount of substance: 6.022 × 10²³ particles. Full entry → is the chemist's counting unit, and molar mass Mass in grams of one mole of a substance (g/mol). Full entry → converts between the mass you can measure on a balance and the number of particles you cannot see. The formula mass Sum of average atomic masses of atoms in a formula, in amu. Full entry → of a compound is the sum of the average atomic masses of its atoms (in atomic mass units, amu), and the molar mass is the same number expressed in grams per mole.
Why this matters
Every quantitative recipe in chemistry — stoichiometry, solution preparation, reaction yields, gas calculations — begins with converting between mass, moles, and particles. In pharmacy, a dose of medication is measured in milligrams, but the number of molecules that dose delivers is what matters biologically; molar mass is the bridge. Fertilizer analysis, fuel efficiency, water-treatment dosing, and laboratory reagent preparation all rely on the same conversion. The mole concept is also the single most heavily tested calculation skill in general chemistry, so mastering it here pays off in every later chapter.
The college version
Core Concepts
Formula mass in atomic mass units
The formula mass is the sum of the average atomic masses of all atoms in a formula unit. For water, H₂O:
2(1.008) + 16.00 = 18.02 amu
For sodium chloride, NaCl: 22.99 + 35.45 = 58.44 amu. The term molecular mass Formula mass of a molecular compound. Full entry → is used for molecular compounds and formula mass for ionic compounds; both are computed the same way. One amu is defined as one-twelfth the mass of a carbon-12 atom, equal to 1.6605 × 10⁻²⁴ g.
The mole and Avogadro's number
A mole is an amount of substance containing exactly 6.022 × 10²³ particles — Avogadro's number 6.022 × 10²³, the number of particles in one mole. Full entry → (NA). The particles may be atoms, molecules, ions, electrons, or formula units; you must say which. Think of the mole as a very large dozen: one mole of eggs and one mole of donuts contain the same number of items, but the two piles have very different masses. One mole of carbon atoms has a mass of 12.01 g; one mole of water molecules has a mass of 18.02 g; both contain 6.022 × 10²³ particles.
Molar mass: grams per mole
The molar mass (M) of a substance is its formula mass expressed in grams per mole, so the two numbers are numerically equal but have different units: H₂O has formula mass 18.02 amu and molar mass 18.02 g/mol. To find the molar mass of a compound, sum the molar masses of its atoms multiplied by their subscripts. For glucose, C₆H₁₂O₆:
6(12.01) + 12(1.008) + 6(16.00) = 72.06 + 12.10 + 96.00 = 180.16 g/mol
Converting between mass, moles, and particles
Three quantities are connected by two conversion factors. Molar mass converts mass ↔ moles: grams × (1 mol / M g) gives moles; moles × (M g / 1 mol) gives grams. Avogadro's number converts moles ↔ particles: moles × (6.022 × 10²³ particles / 1 mol) gives particles. dimensional analysis Solving problems by multiplying by conversion factors so units cancel. Full entry → keeps the path clear — write every factor so the unwanted unit cancels, and check that the remaining unit is the one you want.
Mass of a single particle
Because one mole contains NA particles, the mass of one particle is the molar mass divided by Avogadro's number:
m = MNA
For water: 18.02 g/mol ÷ 6.022 × 10²³ mol⁻¹ = 2.99 × 10⁻²³ g per molecule. The same logic gives 1 amu = 1.6605 × 10⁻²⁴ g.
How It Works / Step-by-Step Process
- Write the chemical formula.
- Compute the formula mass: sum (atomic mass × subscript); record it in amu, then reuse it as the molar mass in g/mol.
- Identify the given quantity and its unit (grams, moles, or particles) and the desired quantity.
- Choose conversion factors: molar mass (g ↔ mol) and Avogadro's number (mol ↔ particles).
- Multiply through so units cancel, calculate, and report the answer with the correct unit and significant figures.
Common Confusions
| Do not confuse | With | Difference |
|---|---|---|
| formula mass | molar mass | Numerically equal, but amu per particle vs grams per mole. |
| "mole is a mass" | mole is a count | 1 mol is always 6.022 × 10²³ particles; masses differ by substance. |
| "one mole of anything weighs the same" | molar masses differ | 1 mol C = 12.01 g; 1 mol H₂O = 18.02 g — same count, different weights. |
| Avogadro's number applies only to atoms | it applies to any particle | Molecules, ions, formula units, even electrons. |
| molar mass of H₂O = mass of H + mass of O | sum with subscripts | 2(1.008) + 16.00 — forgetting the 2 is the most common error. |
| moles and molecules are interchangeable | they differ by a factor of NA | 1 mol = 6.022 × 10²³ molecules; never equate the two numbers. |
Eli explains
The same idea, in plain words
Explain it like I’m 10
You can't count every grain of rice in a bag, but you can weigh the bag and figure out the count because you know the average mass of one grain. Chemists do exactly this with atoms: the mole is a fixed-size counting group — about 6 × 10²³ items, a number so big it would take trillions of years to count aloud — and the molar mass is the weight of one such group. Weigh the sample, divide by the weight of one group, and you know how many groups (moles) you have.
Worked example
Example 1: Grams to moles
How many moles are in 25.0 g of water?
First write the relationship:
n = mM
The molar mass of H₂O is 2(1.008) + 16.00 = 18.02 g/mol. Substitute:
n = 25.0 g × 1 mol18.02 g = 1.39 mol
The grams cancel, leaving moles. (Formula before numbers — always.)
Example 2: Moles to particles
How many water molecules are in 25.0 g of water?
Chain the conversions: g → mol → molecules.
25.0 g × 1 mol18.02 g × 6.022 × 1023 molecules1 mol = 8.35 × 1023 molecules
Each factor is written so the unit on top cancels the unit on the bottom of the previous factor.
Example 3: Moles to grams
What mass of CO₂ is present in 0.750 mol?
m = n × M = 0.750 mol × 44.01 g/mol = 33.0 g
M(CO₂) = 12.01 + 2(16.00) = 44.01 g/mol; the mol units cancel, leaving grams.
Example 4: Mass of a single molecule
What is the mass of one molecule of water?
m = MNA = 18.02 g/mol6.022 × 1023 mol-1 = 2.99 × 10-23 g
A single water molecule weighs about 30 billion-trillionths of a gram — which is exactly why chemists count by the mole instead.
Example 5: Counting ions in a formula
How many moles of Na⁺ ions are in 0.500 mol of Na₂SO₄?
Each formula unit contains 2 sodium ions, so:
0.500 mol Na2SO4 × 2 mol Na+1 mol Na2SO4 = 1.00 mol Na+
Key takeaways
- 1 mole = 6.022 × 10²³ particles (Avogadro's number); always specify the particle (atoms, molecules, ions, formula units).
- Molar mass (g/mol) is numerically equal to formula mass (amu).
- Molar mass of a compound = sum of (atomic mass × subscript) over all atoms.
- Conversion chain: mass ÷ M → moles; moles × NA → particles; reverse to go back; units must cancel.
- One mole of different substances has the same particle count but different masses.
- Mass of one particle = M / NA (e.g., one H₂O molecule ≈ 2.99 × 10⁻²³ g).
- Safety: molar quantities guide safe reagent amounts in the lab — use the calculated amount, never more, and follow your instructor's procedures.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
How many atoms are in exactly 1.00 mol of helium gas?
Show answer
6.022 × 10²³ atoms (one mole of any element contains Avogadro's number of atoms).
What is the molar mass of calcium carbonate, CaCO₃?
Show answer
100.09 g/mol: 40.08 + 12.01 + 3(16.00).
How many moles are in 58.44 g of NaCl?
Show answer
1.00 mol: 58.44 g × (1 mol / 58.44 g).
How many total atoms are in 1.00 mol of CO₂ molecules?
Show answer
3 × 6.022 × 10²³ = 1.81 × 10²⁴ atoms (1 C + 2 O per molecule).
What mass of methane (CH₄) is in 2.50 mol?
Show answer
40.1 g: 2.50 mol × 16.04 g/mol (M = 12.01 + 4(1.008)).
Which contains more particles: 1.00 mol of water or 1.00 mol of oxygen gas?
Show answer
Neither — both contain exactly 6.022 × 10²³ particles; the masses differ (18.02 g vs 32.00 g).
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- mole
- The SI unit for amount of substance: 6.022 × 10²³ particles.
- Avogadro's number
- 6.022 × 10²³, the number of particles in one mole.
- formula mass
- Sum of average atomic masses of atoms in a formula, in amu.
- molar mass
- Mass in grams of one mole of a substance (g/mol).
- molecular mass
- Formula mass of a molecular compound.
- conversion factor
- A ratio equal to 1 that changes units (e.g., 1 mol / 18.02 g).
- dimensional analysis
- Solving problems by multiplying by conversion factors so units cancel.
Sources & references
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