Moles Practice- Converting Between Units

What the Mole Actually Is

A mole isn't an animal you dig out of your yard. In chemistry, it's a counting unit—like a dozen, but astronomically bigger.

One mole equals 6.02 × 10²³ things. These things can be atoms, molecules, ions, electrons—whatever particle you're tracking.

Chemists call this number Avogadro's number (Nₐ). You'll use it constantly, so memorize it or keep it on your formula sheet.

The mole exists because atoms are impossibly small. You can't count them individually. So you count them in enormous groups instead.

Why Molar Mass Matters

Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol).

For any element, the molar mass is the number sitting under the element on the periodic table. That's not a coincidence—it's by design.

For compounds, you add up the molar masses of every element, multiplied by how many atoms of each element are present.

Quick Example: Water (H₂O)

• Hydrogen: 1.01 g/mol × 2 = 2.02 g/mol
• Oxygen: 16.00 g/mol × 1 = 16.00 g/mol
• Total molar mass of H₂O = 18.02 g/mol

That's it. Add, multiply, done.

The Three Conversions You Must Know

Every mole calculation in basic chemistry boils down to three conversions:

• Grams ↔ Moles (using molar mass)
• Moles ↔ Particles (using Avogadro's number)
• Moles ↔ Liters (using molar volume at STP)

Master these three, and you've mastered moles.

How To: Converting Grams to Moles

Formula: moles = grams ÷ molar mass

Example: You have 36 grams of water. How many moles is that?

36 g ÷ 18.02 g/mol = 2.0 moles H₂O

Just divide. The units cancel out the way they should. Grams divided by g/mol gives you moles.

How To: Converting Moles to Grams

Formula: grams = moles × molar mass

Example: You have 0.5 moles of sodium chloride (NaCl). What's the mass?

Molar mass of NaCl: 22.99 + 35.45 = 58.44 g/mol

0.5 mol × 58.44 g/mol = 29.22 grams

Multiplying this time. Moles times g/mol cancels down to grams.

How To: Converting Moles to Particles

Formula: particles = moles × 6.02 × 10²³

Example: How many atoms are in 3 moles of carbon?

3 mol × 6.02 × 10²³ atoms/mol = 1.81 × 10²⁴ atoms

The mole number is huge. Your answers will always be in scientific notation unless the number of moles is absurdly large.

How To: Converting Particles to Moles

Formula: moles = particles ÷ 6.02 × 10²³

Example: You have 1.5 × 10²⁴ molecules of CO₂. How many moles is that?

1.5 × 10²⁴ ÷ 6.02 × 10²³ = 2.49 moles CO₂

Flip the operation. Divide instead of multiply.

How To: Converting Moles to Liters (Gas at STP)

At standard temperature and pressure (STP), one mole of any gas occupies 22.4 liters. This is molar volume.

Formula: liters = moles × 22.4 L/mol

Example: How much space does 2 moles of oxygen gas take up at STP?

2 mol × 22.4 L/mol = 44.8 liters

How To: Converting Liters to Moles (Gas at STP)

Formula: moles = liters ÷ 22.4 L/mol

Example: You have 56 liters of nitrogen gas at STP. How many moles?

56 L ÷ 22.4 L/mol = 2.5 moles N₂

Again—just flip the operation.

Conversion Cheat Sheet

Practice Problems

Try these without looking at the answers first.

Problem 1

Calculate the moles in 98 grams of sulfuric acid (H₂SO₄).

Molar mass of H₂SO₄: (1.01×2) + 32.07 + (16×4) = 98.09 g/mol

98 g ÷ 98.09 g/mol = 1.0 mol

Problem 2

How many atoms are in 0.75 moles of gold?

0.75 mol × 6.02 × 10²³ = 4.52 × 10²³ atoms

Problem 3

What volume does 5 moles of methane (CH₄) occupy at STP?

5 mol × 22.4 L/mol = 112 liters

Problem 4

You have 3.01 × 10²³ molecules of ammonia (NH₃). How many moles?

3.01 × 10²³ ÷ 6.02 × 10²³ = 0.5 moles

Common Mistakes to Avoid

• Forgetting to find molar mass first. You can't convert grams to moles without knowing the molar mass. Always check the periodic table first.
• Confusing molar mass with molecular mass. Same number, different units. Molecular mass is in atomic mass units (amu), molar mass is in grams per mole (g/mol).
• Using 22.4 for non-STP conditions. That number only applies at standard temperature and pressure. Different conditions require the ideal gas law.
• Screwing up the Avogadro's number calculation. 6.02 × 10²³ is the number. Write it down. Don't approximate it as 6 unless your teacher allows it.
• Forgetting to balance equations first. If you're finding moles of a specific reactant or product, the balanced equation tells you the mole ratio. Skip this step, and your answer will be wrong.

The Bottom Line

Mole conversions aren't complicated. They're arithmetic with specific conversion factors.

Grams to moles? Divide by molar mass. Moles to particles? Multiply by Avogadro's number. Liters of gas? Use 22.4 at STP.

That's the entire skill. Memorize the three conversion factors, and every problem becomes simple multiplication or division.

No shortcuts exist. You just have to practice until the process is automatic.