Moles and Molar Mass
Name the counted entity and connect grams, moles and particle numbers.
AP Chemistry Topic 1.1 · CED printed p. 30 / PDF p. 37. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Chemical formulas
- Grams and scientific notation
Why the mole is the bridge
A balance reports grams, while chemical reactions rearrange atoms, molecules and ions. We need a bridge between those two scales. One mole contains specified entities. That SI count is exact; for AP calculations, 6.022 × 1023 mol−1 is usually plenty of precision. Always name the entity. A mole of O atoms and a mole of O2 molecules contain the same number of entities, but the latter contains twice as many oxygen atoms.
Use n for amount in moles, m for sample mass in grams, N for the number of specified entities, and NA for Avogadro’s constant in mol−1. Uppercase N and lowercase n do different jobs: count versus amount. Molar mass, M, is mass per mole, in g mol−1. Use to cross from grams to moles, then to cross to entities. Put the units into the setup: grams cancel against grams per mole. Reversing the path means divide particle count by NA, then multiply moles by M.
A formula tells you what to count
For a molecule, add the atomic masses multiplied by their subscripts. CO2 has one C and two O atoms, giving 44.01 g mol−1 using C = 12.01 and O = 16.00. A molecule has an average mass of 44.01 u; a mole has a mass of approximately 44.01 g. The numerical correspondence between u per entity and g per mole is appropriate at AP precision. An ionic solid has no separate CO2-style molecules: for CaCl2, count formula units, one Ca2+ and two Cl− per unit. Subscripts give exact counting factors, so they do not limit significant figures.
Do a quick scale check before you finish. A few grams of a substance with molar mass around 100 g mol−1 should give less than one mole, not hundreds. Equal masses of two different substances generally contain different numbers of entities; the smaller molar mass gives more entities.
Let's work through it
Work it through
A 5.55 g sample of anhydrous CaCl2 has M = 110.98 g mol−1. Find formula units and chloride ions.
- Convert the measured mass: 5.55 g × (1 mol / 110.98 g) = 0.0500 mol CaCl2. Keep unrounded values internally.
- Convert to formula units: (5.55/110.98) mol × 6.022 × 1023 formula units mol−1 = 3.01 × 1022 formula units.
- Use the formula, not the charge, as the counting factor: two chloride ions per formula unit gives 6.02 × 1022 Cl− ions. The count is a composition statement; it does not say that these ions are mobile in the solid.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
What must you specify after saying “one mole”?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
What must you specify after saying “one mole”?
Worked answer and reason
The entity being counted: atoms, molecules, ions, electrons or formula units.
The mole is an amount of specified entities, not a mass unit.
Retrieval 2
Which has more molecules: 10.0 g CO2 or 10.0 g H2O?
Worked answer and reason
H2O, because its molar mass is smaller, so m/M is larger for the same mass.
Entity count is proportional to moles, not directly to grams.
Catch the tempting mistake
- One mole always weighs one gram.
- A mole fixes the entity count; its mass depends on the entity and molar mass.
- CaCl2 contains two calcium ions because calcium has charge 2+.
- The missing subscript on Ca means one calcium ion. Charge and subscript do different jobs.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 1 problem 1 · ap application · symbolic
- Unit 1 problem 2 · ap application · multiple
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For the teacher
- Check that the student names formula units before multiplying by an ionic subscript.
- Ask students to compare equal-mass and equal-mole samples before giving more arithmetic.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 1.1.A
- Calculate quantities of a substance or its relative number of particles using dimensional analysis and the mole concept.
- 1.1.A.1
- One cannot count particles directly while performing laboratory work. Thus, there must be a connection between the masses of substances reacting and the actual number of particles undergoing chemical changes.
- 1.1.A.2
- Avogadro’s number (N_A = 6.022 × 10^23 mol−1) provides the connection between the number of moles in a pure sample of a substance and the number of constituent particles (or formula units) of that substance.
- 1.1.A.3
- Expressing the mass of an individual atom or molecule in atomic mass units (amu) is useful because the average mass in amu of one particle (atom or molecule) or formula unit of a substance will always be numerically equal to the molar mass of that substance in grams. Thus, there is a quantitative connection between the mass of a substance and the number of particles that the substance contains. EQN: n = m/M
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 (supplied source) — Exact topic-numbered learning objectives, essential knowledge, science practices and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
- NIST 2022 CODATA complete constants table — Exact SI Avogadro constant and updated atomic/molar mass correspondence at AP precision.
Glossary and deeper reading · 5 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Ion
An ion is an atom or group of atoms with a net electric charge. Ordinary ion formation changes electron count without changing the element's proton count. For example, a sodium atom losing one electron becomes a sodium ion with charge +1.
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Mole
A mole is an amount of substance containing exactly 6.02214076 × 10²³ specified entities. The entities can be atoms, molecules, ions, or formula units, so the counted entity must be named. For example, one mole of oxygen molecules contains two moles of oxygen atoms.
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Avogadro’s constant
Avogadro’s constant connects a number of specified entities to an amount in moles. Its exact value is 6.02214076 × 10²³ per mole. For example, multiplying two moles of helium atoms by this constant gives their number of atoms.
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Molar mass
Molar mass is the mass of one mole of a specified substance. It is commonly expressed in grams per mole and connects a sample's mass to its amount of substance. For example, water has a molar mass of approximately 18.02 grams per mole.
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Formula unit
A formula unit specifies the simplest whole-number ratio of ions in an ionic compound. It is a counting unit for an extended solid rather than an isolated molecule. For example, one calcium chloride formula unit represents one calcium ion and two chloride ions.