In the lab, scales read in grams, but chemical equations "speak" in moles. How do we convert back and forth between what we can weigh and what the atoms require? We use a simple conversion map, and the foolproof method of dimensional analysis. If you set up the fractions so that the units cancel, the math will balance itself.
To convert chemical quantities in the laboratory, you must follow one golden rule: always convert through the mole. The mole is the common counting language of chemistry, connecting the microscopic count to the macroscopic weight.
This relationship forms our Mole Map. If you start with a mass in grams and want to find moles, or if you start with moles and want to find mass, the molar mass is the conversion factor bridge.
This lesson focuses on the grams ↔ moles spoke. The moles ↔ particles spoke uses the same logic with Avogadro's number (6.022 × 10²³) in place of molar mass — you met it back in 2-7a, and it's on the map here as a reminder that the mole is always the hub, never a detour through grams.
Rather than memorizing when to multiply or divide, we use dimensional analysis (the factor-label method). You treat units like algebraic variables: any unit in a numerator divided by the same unit in a denominator cancels out, leaving only the desired unit behind.
A conversion factor is written as a fraction. Because one mole of Water (H₂O) is exactly equal to 18.02 grams, we can write two conversion factor fractions that both equal 1:
1 mol H₂O18.02 g H₂O or 18.02 g H₂O1 mol H₂O
To convert 36.04 grams of water to moles, you choose the fraction that puts the unwanted unit (grams) in the denominator to cancel the starting grams:
36.04 g H₂O × 1 mol H₂O18.02 g H₂O = 2.00 mol H₂O
Because the starting unit (g H₂O) and the denominator unit cancel, you are left with `mol H₂O`. The units prove that the setup is correct before you ever punch the numbers into a calculator.
Select the conversion factor card that correctly cancels the starting unit. Drag or click the card to slot it in, and check if the math balances.
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Click one of the cards below to choose a conversion factor. Look for the card that puts the starting unit in the denominator so they cancel out.
1. Mass of 2.50 moles of water: One mole of water has a mass of 18.02 grams. If you measure out exactly 2.50 moles of water, what will the scale read?
To convert moles to grams, you multiply by the molar mass:
2.50 mol H₂O × (18.02 g H₂O / 1 mol H₂O) = 45.05 g H₂O
The moles units cancel out, leaving grams.
2. Moles in a carbon sample: A sample of pure charcoal contains 36.03 grams of Carbon (molar mass 12.01 g/mol). How many moles of Carbon atoms are in this sample?
To convert grams to moles, you divide by the molar mass:
36.03 g Carbon × (1 mol Carbon / 12.01 g Carbon) = 3.00 mol Carbon
The grams units cancel, leaving moles.
Fill in the blanks to lock in the core terms. Matches are case-insensitive.
Explain how treating units as algebraic variables guarantees that you don't accidentally multiply when you should divide during mole conversions.
Treating units as algebraic variables ensures that you place the conversion units in the correct positions (numerator or denominator) so that unwanted units cancel out. If you set up a conversion incorrectly—for example, multiplying grams by grams/mole instead of mole/grams—the units will not cancel and will instead result in a nonsense unit (like g²/mol). Tracking unit cancelation mathematically guarantees that the final remaining unit is the one you are solving for, preventing calculation direction errors.
Give yourself a point for each idea you actually wrote down. The flag (⚑) marks the critical unit tracking step.
A recipe requires exactly 126.02 grams of sodium bicarbonate (NaHCO3, molar mass 84.01 g/mol). Calculate the moles of NaHCO3 required, showing your complete dimensional analysis setup with all conversion units and unit cancelations clearly written out.
Self-score: 3 = all three points · 2 = calculated 1.5 mol but missing unit cancelation marks in setup · 1 = calculated 1.5 mol with no setup shown.
Carbon capture engineering requires precise molar scaling. Industrial scrubbers capture carbon dioxide from exhaust gas. Chemical engineers must use factor-label conversions to calculate the exact mass of liquid amine required in grams to absorb the targeted number of gaseous CO₂ molecules.