Mole Conversion Practice- Problems and Solutions

What the Mole Actually Is

Stop overthinking it. A mole is just a number. Specifically, it's 6.02 × 10²³ particles (Avogadro's number). That's it. When chemists say "one mole of carbon," they mean you have 6.02 × 10²³ carbon atoms sitting in front of you.

The mole exists because atoms are impossibly small. You can't count them. So chemists invented a counting unit, the same way you use "dozen" to count 12 eggs.

The Conversion Factors You Actually Need

Every mole problem is really just a unit conversion problem. Memorize these relationships:

• 1 mole = molar mass in grams (found on the periodic table)
• 1 mole = 6.02 × 10²³ particles (atoms, molecules, formula units)
• 1 mole of gas at STP = 22.4 liters

The periodic table gives you molar mass directly. That number under the element symbol? That's grams per mole. Use it.

Mole Conversion Problems and Solutions

Problem 1: Grams → Moles

Question: How many moles are in 36 grams of water (H₂O)?

Step 1: Find the molar mass of H₂O.

• H = 1.01 g/mol × 2 = 2.02 g/mol
• O = 16.00 g/mol
• Total = 18.02 g/mol

Step 2: Set up the conversion.

36 g ÷ 18.02 g/mol = 2.0 moles H₂O

That's it. Divide grams by molar mass when going from mass to moles.

Problem 2: Moles → Number of Particles

Question: How many molecules are in 0.75 moles of CO₂?

Use Avogadro's number as your conversion factor.

0.75 mol × 6.02 × 10²³ molecules/mol = 4.52 × 10²³ CO₂ molecules

Multiply when going from moles to particles. Divide when going the other way.

Problem 3: Moles → Liters of Gas

Question: What volume does 2.5 moles of oxygen gas occupy at STP?

At standard temperature and pressure, 1 mole = 22.4 liters.

2.5 mol × 22.4 L/mol = 56 L O₂

This only works at STP. If the problem doesn't specify STP, you'll need the ideal gas law (PV = nRT), which is a different beast.

Problem 4: Grams → Molecules (Two-Step Conversion)

Question: How many glucose molecules (C₆H₁₂O₆) are in 90 grams?

Step 1: Convert grams to moles.

• Molar mass: (12.01 × 6) + (1.01 × 12) + (16.00 × 6) = 180.18 g/mol
• 90 g ÷ 180.18 g/mol = 0.50 moles

Step 2: Convert moles to molecules.

0.50 mol × 6.02 × 10²³ = 3.01 × 10²³ molecules

Chain your conversions. Grams → Moles → Molecules. Each arrow is one conversion factor.

Problem 5: Particles → Grams

Question: What is the mass of 1 trillion (1 × 10¹²) iron atoms?

Step 1: Convert atoms to moles.

1 × 10¹² atoms ÷ 6.02 × 10²³ atoms/mol = 1.66 × 10⁻¹² moles

Step 2: Convert moles to grams.

Fe molar mass = 55.85 g/mol

1.66 × 10⁻¹² mol × 55.85 g/mol = 9.27 × 10⁻¹¹ grams

That's an absurdly small number. That's why we use moles for anything measurable.

Quick Reference Table

Getting Started with Mole Conversions

Here's the process for any mole conversion problem:

1. Read the problem. Identify what you're starting with and what you need to find.
2. Find the molar mass if you need it. Add up atomic masses from the periodic table.
3. Draw your conversion arrow. Start unit → End unit.
4. Insert conversion factors. Every arrow needs a bridge (molar mass, Avogadro's number, or 22.4 L/mol).
5. Cancel units. If you set it up right, unwanted units disappear.
6. Calculate. Multiply across the top, divide across the bottom.

The mistake most students make is trying to memorize every formula instead of understanding the conversion chain. You don't need formulas. You need one concept: convert through moles as your middleman.