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I-07: Moles, molar mass and isotopes

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Module I-07 · Recommended before: Before molecular formulas and stoichiometry

Moles, molar mass and isotopes

The mole connects microscopic particles and measurable mass. Isotopic masses must be averaged by fractional abundance, not simple averaging.

Learn the method

n = m/M; average isotope mass = Σ(fraction × isotope mass)

  1. Find molar mass from atomic masses.
  2. Use n = mass / molar mass.
  3. Convert to particles using Avogadro’s constant when needed.
  4. For isotopes, multiply each mass by its fractional abundance and add.

Common mistake: Use a compound’s molar mass, not an atomic mass of one component.

Worked example

Problem: How many moles are in 36.04 g of water, using 18.02 g/mol?

Step-by-step solution: n = 36.04 g / (18.02 g/mol) = 2.000 mol.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Isotope weighted averages

An element has two isotopes: 10.0 u (20%) and 11.0 u (80%). Average mass = 0.20×10.0 + 0.80×11.0 = 10.8 u.

Moles to particles

For 0.250 mol of a substance, entities = 0.250×6.022×10²³ = 1.51×10²³ entities.

Counting atoms and ion charge

For ²³Na⁺, sodium has 11 protons, 23−11=12 neutrons, and 11−1=10 electrons.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. How many moles of H₂O are in 45.05 g? Use 18.02 g/mol.
Hint for question 1

Divide mass by molar mass.

Question 2. How many moles of H₂O are in 54.06 g? Use 18.02 g/mol.
Hint for question 2

Divide mass by molar mass.

Question 3. How many moles of H₂O are in 63.07 g? Use 18.02 g/mol.
Hint for question 3

Divide mass by molar mass.

Question 4. How many moles of H₂O are in 72.08 g? Use 18.02 g/mol.
Hint for question 4

Divide mass by molar mass.

Question 5. How many moles of H₂O are in 81.09 g? Use 18.02 g/mol.
Hint for question 5

Divide mass by molar mass.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

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