Unit 1 · Topic 1.1 Beta

Moles and Molar Mass

Chemists count particles in moles of 6.022 × 10²³.

Practice 1: Models and RepresentationsPractice 5: Mathematical Routines

Question set for this topic

Part 1 · Hook

Why this matters

A bakery buys eggs by the dozen and a print shop buys paper by the ream, because counting one at a time is slow. Atoms are far too small to count at all: a single drop of water holds about 10²¹ molecules. Chemists count them by weighing, using a counting unit called the mole.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. Which setup changes 4.50 g into kilograms?

  1. 4.50 g × (1 kg / 1000 g)
  2. 4.50 g × (1000 g / 1 kg)
  3. 4.50 g × (1 kg / 100 g)
  4. 4.50 g ÷ (1 kg / 1000 g)
Show the answer

Put grams on the bottom so they cancel: 4.50 g × (1 kg / 1000 g) = 0.00450 kg.

  • Correct: 4.50 g × (1 kg / 1000 g):
  • 4.50 g × (1000 g / 1 kg):
  • 4.50 g × (1 kg / 100 g):
  • 4.50 g ÷ (1 kg / 1000 g):

2. What is (2.0 × 10³) × (3.0 × 10²⁰)?

  1. 6.0 × 10²³
  2. 6.0 × 10⁶⁰
  3. 5.0 × 10²³
  4. 6.0 × 10¹⁷
Show the answer

Multiply the coefficients (2.0 × 3.0 = 6.0) and add the exponents (3 + 20 = 23).

  • Correct: 6.0 × 10²³:
  • 6.0 × 10⁶⁰:
  • 5.0 × 10²³:
  • 6.0 × 10¹⁷:

3. How many significant figures does 0.0250 mol have?

  1. 3
  2. 4
  3. 2
  4. 5
Show the answer

Leading zeros do not count; the 2, the 5 and the trailing zero after the decimal point do.

  • Correct: 3:
  • 4:
  • 2:
  • 5:

Part 4 · See it

See it first

Mass in grams, amount in moles and number of particles in a row: divide by the molar mass to go from grams to moles, multiply by 6.022 × 10²³ to go from moles to particles, and reverse each step to go back.
The path between a measured mass and a number of particles always goes through moles: molar mass links grams and moles, and Avogadro's number links moles and particles. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Atoms and molecules are far too small to count one by onechemists count them in groups of 6.022 × 10²³, called a mole
  2. The mole is defined so that the mass of one particle in amu matches the mass of a mole in gramsthe atomic mass on the periodic table is also the molar mass in g/mol
  3. A balance measures grams, and molar mass is grams per moledividing a mass by the molar mass gives the amount in moles
  4. Each mole holds Avogadro's number of particlesmultiplying moles by 6.022 × 10²³ gives the number of particles

Part 6 · Key ideas

Key ideas

  • One mole is 6.022 × 10²³ particles (Avogadro's number). Always say which particles: one mole of water molecules holds three moles of atoms.
  • Molar mass (g/mol) = the sum of the atomic masses of every atom in one particle. Water: 2(1.008) + 16.00 = 18.02 g/mol.
  • grams ÷ molar mass = moles; moles × 6.022 × 10²³ = particles. Always go through moles.
  • Equal masses of different substances hold different numbers of particles: lighter particles, more of them.

Part 7 · Misconception

A common mistake

The wrong idea: Equal masses of two substances contain equal numbers of molecules.

What actually happens: Molecules of different substances have different masses, so the same mass holds different numbers of them. 1.0 g of H₂ has about 16 times as many molecules as 1.0 g of O₂. Compare amounts in moles, not grams.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

1. What does one mole of a substance contain?

  1. One gram of the substance, whatever it is made of
  2. The number of atoms in one molecule of the substance
  3. 6.022 × 10²³ of the particles named, such as atoms or molecules
  4. Enough of the substance to fill a 1-liter container
Show the answer

One mole is Avogadro's number, 6.022 × 10²³, of whatever particles you name.

  • One gram of the substance, whatever it is made of: A mole is a count, not a mass. One mole of different substances has different masses.
  • The number of atoms in one molecule of the substance: That number is in the formula and is usually small, such as 3 for water.
  • Correct: 6.022 × 10²³ of the particles named, such as atoms or molecules: Right: a mole is a counting unit, like a dozen, for 6.022 × 10²³ things.
  • Enough of the substance to fill a 1-liter container: A mole is a count of particles, not a volume.

Data table

Five samples on a balance

A student weighs five pure samples and looks up each molar mass.

Mass and molar mass of each sample
SampleSubstanceFormulaMass (g)Molar mass (g/mol)
1Aluminum foilAl13.526.98
2Copper wireCu12763.55
3WaterH₂O45.018.02
4EthanolC₂H₆O23.046.07
5Table sugar (sucrose)C₁₂H₂₂O₁₁85.6342.30

2. How many moles of aluminum atoms are in Sample 1?

Type a number and its unit.

Show the answer

13.5 g × (1 mol / 26.98 g) = 0.5004 mol, which is 0.500 mol to the three significant figures of the mass.

  • Answer: 0.500 mol

3. Which sample contains the greatest number of atoms in total?

  1. Sample 3, the water
  2. Sample 2, the copper
  3. Sample 4, the ethanol
  4. Sample 5, the sucrose
Show the answer

Moles of atoms = moles of particles × atoms per particle. Sucrose: 0.250 × 45 = 11.3 mol; water 2.50 × 3 = 7.49 mol; copper 2.00 mol; ethanol 4.49 mol; aluminum 0.500 mol.

  • Sample 3, the water: Water has the most molecules (2.50 mol), but only 3 atoms each, so 7.49 mol of atoms.
  • Sample 2, the copper: The largest mass, but copper atoms are heavy: 127 g ÷ 63.55 g/mol = 2.00 mol of atoms.
  • Sample 4, the ethanol: 0.499 mol of molecules × 9 atoms each = 4.49 mol of atoms, less than sucrose or water.
  • Correct: Sample 5, the sucrose: Right: 85.6 g ÷ 342.30 g/mol = 0.250 mol of molecules, and each molecule has 45 atoms, so 11.3 mol of atoms.

4. How many hydrogen atoms are in Sample 4?

Type a number in hydrogen atoms.

Show the answer

23.0 g ÷ 46.07 g/mol = 0.4992 mol of ethanol molecules. Each has 6 H atoms: 0.4992 × 6 = 2.995 mol of H atoms. × 6.022 × 10²³ = 1.80 × 10²⁴ H atoms.

  • Answer: 1.80 × 1024 hydrogen atoms

5. What is the molar mass of calcium carbonate, CaCO₃? Use Ca 40.08, C 12.01, O 16.00.

Type a number and its unit.

Show the answer

Add the atomic masses of every atom in one formula: 40.08 + 12.01 + 3(16.00) = 100.09 g/mol.

  • Answer: 100.09 g/mol

6. What is the mass of 0.0250 mol of glucose, C₆H₁₂O₆ (molar mass 180.16 g/mol)?

Type a number and its unit.

Show the answer

0.0250 mol × (180.16 g / 1 mol) = 4.504 g, which is 4.50 g to three significant figures.

  • Answer: 4.50 g

7. One molecule of ethanol has a mass of 46.07 amu. What is the mass of one mole of ethanol molecules?

  1. 46.07 amu
  2. 46.07 × 6.022 × 10²³ g
  3. 46.07 ÷ 6.022 × 10²³ g
  4. 46.07 g
Show the answer

The number is the same at both scales: 46.07 amu per molecule and 46.07 g per mole. That is why the mole was defined as it was.

  • 46.07 amu: That is the mass of one molecule, not of 6.022 × 10²³ of them.
  • 46.07 × 6.022 × 10²³ g: This multiplies twice: the g/mol number already counts a whole mole.
  • 46.07 ÷ 6.022 × 10²³ g: Dividing gives the mass of one molecule in grams, not of a mole.
  • Correct: 46.07 g: Right: the mole is defined so that amu per particle equals grams per mole.

Part 9 · Summary

Summary

Chemists count particles in moles of 6.022 × 10²³. The molar mass, the sum of the atomic masses in one particle, has the same number in g/mol as one particle's mass in amu, so it converts a measured mass into moles. Avogadro's number converts moles into particles. Equal masses of different substances hold different numbers of particles.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections