Slide presentation
Mole and Avogadro’s Number
General Chemistry • Chemical Compounds
Topic 1 · Chemical counting
Mole and Avogadro’s Number
The mole is the bridge between the invisible particle scale and the measurable laboratory scale. It lets chemists count atoms, molecules, and formula units by measuring an amount of substance.
Learning target
By the end, you should be able to explain why \(1\ \text{mol}\) always means \(6.022 \times 10^{23}\) counted entities and use that idea to solve particle-counting problems.
particles per mole
Why it matters
Chemistry needs a counting unit larger than a dozen.
Atoms and molecules are far too small to count one by one in the laboratory. The mole makes a practical connection between a sample you can weigh and the number of particles inside it.
Laboratory measurements
You can measure mass with a balance, but chemical reactions happen particle by particle. The mole links those two worlds.
Reaction ratios
Balanced equations compare particles. Moles allow those ratios to be used with real samples.
Chemical formulas
One mole of H2O contains one mole of water molecules, two moles of H atoms, and one mole of O atoms.
Core concept
A mole is a counting unit, not a type of substance.
A dozen always means 12 items. A mole always means \(6.022 \times 10^{23}\) items. The item being counted depends on the substance: atoms, molecules, ions, or formula units.
Choose the entity
Carbon is counted as C atoms. Oxygen gas is counted as O2 molecules. Sodium chloride is counted as NaCl formula units.
Use the mole
\(1\ \text{mol}\) means one Avogadro’s number of the chosen entity.
Interpret the count
Convert between a macroscopic amount and the number of microscopic particles.
Vocabulary
Know what is being counted before you convert.
The most common error in mole problems is using the right number but counting the wrong entity. The words atom, molecule, and formula unit describe what the mole is counting.
| Term or symbol | Meaning | Typical unit | Example |
|---|---|---|---|
| \(n\) | Amount of substance | mol | \(2.50\ \text{mol}\) CO2 |
| \(N\) | Number of counted particles | particles | \(3.01 \times 10^{23}\) molecules |
| \(N_A\) | Avogadro’s number | particles/mol | \(6.022 \times 10^{23}\ \text{particles/mol}\) |
| Formula unit | Smallest whole-number ratio in an ionic compound | formula units | NaCl, MgO, CaF2 |
| Molecule | A neutral group of atoms bonded together | molecules | H2O, CO2, O2 |
Main relationship
Avogadro’s number is the conversion factor.
The relationship between moles and particles is direct: more moles means proportionally more particles.
\(N\) is the number of particles, \(n\) is the amount in moles, and \(N_A\) is \(6.022 \times 10^{23}\ \text{particles/mol}\).
Moles to particles
Multiply by Avogadro’s number.
particles = moles × \(6.022 \times 10^{23}\)
Particles to moles
Divide by Avogadro’s number.
moles = particles ÷ \(6.022 \times 10^{23}\)
Interactive simulation
Change the moles and watch the particle count scale.
The dots are a simplified model. Each visible dot represents a very large group of real particles, because the true count is astronomically large.
Particle counter
Calculated particle count
6.022 × 10²³ atoms
Model scale: one displayed dot represents a large bundle of particles.
Static fallback model
Without JavaScript, use the formula \(N=nN_A\). For \(1.00\ \text{mol}\), \(N=6.022 \times 10^{23}\) particles.
Dynamic relationship
The graph is a straight line through the origin.
Because \(N=nN_A\), doubling the number of moles doubles the number of particles. The slope of the graph is Avogadro’s number.
The entity label changes, but the numerical relationship stays the same: one mole contains one Avogadro’s number of the selected entity.
Worked example
How many molecules are in \(2.50\ \text{mol}\) of CO2?
Start by identifying the counted entity. CO2 is a molecular compound, so the particles are CO2 molecules.
Write the relationship
\(N=nN_A\)
Substitute the values
\(N=(2.50\ \text{mol})(6.022 \times 10^{23}\ \text{molecules/mol})\)
Calculate and label the answer
\(N=1.51 \times 10^{24}\) CO2 molecules.
Final answer: \(2.50\ \text{mol}\) CO2 contains \(1.51 \times 10^{24}\) CO2 molecules.
Common mistake
Do not confuse molecules with atoms inside the molecules.
A mole of molecules is not always a mole of atoms. The chemical formula tells you how many atoms are inside each molecule or formula unit.
Incorrect reasoning
“\(1\ \text{mol}\) H2O contains \(6.022 \times 10^{23}\) total atoms.”
This counts water molecules correctly, but it forgets that each molecule has 3 atoms.
Correct reasoning
\(1\ \text{mol}\) H2O contains \(6.022 \times 10^{23}\) water molecules.
Each H2O molecule contains 3 atoms, so it contains \(3(6.022 \times 10^{23})=1.807 \times 10^{24}\) total atoms.
Practice check
Try a particles-to-moles conversion.
Question: A sample contains \(9.033 \times 10^{23}\) atoms of copper. How many moles of Cu atoms are present?
Show answer
Choose the conversion
Particles to moles means divide by Avogadro’s number.
Calculate
\(n=\frac{9.033 \times 10^{23}\ \text{atoms}}{6.022 \times 10^{23}\ \text{atoms/mol}}=1.500\ \text{mol}\)
Final answer
The sample contains \(1.500\ \text{mol}\) Cu atoms.
Reasonableness check
\(9.033 \times 10^{23}\) is larger than \(6.022 \times 10^{23}\), so the answer should be larger than \(1\ \text{mol}\). The result \(1.500\ \text{mol}\) makes sense.
Continue learning
Use the mole as a bridge in future chemistry problems.
Most quantitative chemistry problems use the mole as a middle step. After you can move between particles and moles, you are ready to connect moles to mass, formulas, and balanced equations.
Open the calculator
Practice conversions between moles and particles with guided numerical support.
Try related questions
Check whether you can identify the counted entity and choose the correct conversion.
Particles
atoms, molecules, ions, or formula units
Moles
central counting amount
Mass or reactions
grams, formulas, stoichiometry
Final summary
The mole turns particle counting into practical chemistry.
One mole is a fixed count.
\(1\ \text{mol}=6.022 \times 10^{23}\) counted entities.
The entity matters.
Decide whether you are counting atoms, molecules, ions, or formula units.
Moles to particles: multiply.
Use \(N=nN_A\) when the amount in moles is given.
Particles to moles: divide.
Use \(n=\frac{N}{N_A}\) when the particle count is given.
Key idea: Avogadro’s number is not just a large number. It is the conversion factor that connects microscopic particles to measurable chemical amounts.