Follow the map, and cancel the units.
A lab scale reads in grams. A chemical equation counts in moles. How do you convert between what you can weigh and what the atoms need? Use a conversion map and dimensional analysis. Set up the fractions so the units cancel, and the math works out. By the end, you can convert between grams and moles with any molar mass.
Core Claims
- Dimensional analysis: Write a fraction of equal values in different units. Multiply by it to change units safely.
- Diagonal cancellation: Set up the grid so the starting unit cancels and the target unit is left.
- Conversion values: Molar mass (g/mol) converts grams to moles. Avogadro's number converts moles to particles.
Dimensional analysis setup
Retrieval Checklist
- Set up a dimensional analysis grid with matching units.
- Convert mass to moles, and moles to particle counts.
The mole is always the central hub.
Follow one rule when you convert quantities in the lab: always convert through the mole. The mole links the count of particles to the mass on the scale.
This gives you the mole map. Molar mass is the bridge. It converts mass in grams to an amount in moles, or moles back to grams.
This lesson focuses on the grams ↔ moles spoke. The moles ↔ particles spoke uses Avogadro's number (6.022 × 10²³) instead of molar mass. Grams never skip the mole.
Converting grams straight to particles. Grams and particles never connect directly. Convert grams to moles first, then moles to particles.
Let the units do the work.
Do not memorize when to multiply or divide. Use dimensional analysis (the factor-label method). Units behave like variables in algebra. The same unit on top and bottom cancels, and only the unit you want is left.
A conversion factor is a fraction. One mole of water (H₂O) equals 18.02 grams, so you can write two fractions that both equal 1:
To convert 36.04 grams of water to moles, choose the fraction placing grams in the denominator. This cancels the starting unit:
The starting unit (g H₂O) cancels against the denominator, and you are left with mol H₂O. The units prove the setup is correct before you touch a calculator.
Putting the starting unit in the numerator. Grams times grams per mole gives g² per mole, which is not moles. Flip the fraction so the unit you want to cancel sits in the denominator.
Set up the math. Watch the units cancel.
Choose the conversion factor card that cancels the starting unit. Then check that the math works.
Which conversion factor cancels the starting unit?
Problem 1 of 5
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Look for the card that puts the starting unit in the denominator, so the units cancel.
- Hydrogen atom
- Oxygen atom
- Carbon atom
- Sodium ion
- Chloride ion
- No factor chosen yet
- The units cancel
- The units do not cancel
Determining empirical and molecular formulas.
This section covers empirical and molecular formulas. Core exams do not assess it. It deepens how you use mole relationships and formulas.
An empirical formula gives the smallest whole-number mole ratio of the elements in a compound (for example CH₂O). A molecular formula gives the actual number of atoms in one molecule. Glucose is C₆H₁₂O₆, which is (CH₂O)₆.
The four-step empirical formula method
- Percent to mass: Assume a 100.0 g sample, so each percentage becomes grams (40.0% C is 40.0 g C).
- Mass to moles: Divide each element's mass by its atomic mass.
- Divide by the smallest: Divide every mole value by the smallest one to get the mole ratio.
- Multiply until whole: If a ratio is a decimal (1.5, 1.33, 1.25), multiply every number by 2, 3 or 4 to get whole numbers.
Molecular formula: Divide the true molar mass by the empirical formula mass to get n. Then multiply each empirical subscript by n.
Which empirical formula fits these percentages?
Predict the scale reading.
Fill the blanks from memory.
Type each blank from memory, then press Check. Press Show answers after your first check if you are stuck.
Using fractions to cancel units is called . The central hub of every mole conversion is the . A fraction with equal amounts in different units on top and bottom is a . To cancel a unit on the starting value, the conversion factor puts that unit in the .
Explain why treating units like variables stops you from multiplying when you should divide.
Writing it out forces your brain to organize the idea. Write your answer first, then peek and compare.
Units act like variables, so you can see whether they cancel. A correct setup puts the unwanted unit in the denominator, and it cancels. A wrong setup does not cancel. For example, grams times grams per mole gives g² per mole, which is not moles. Tracking the cancellation guarantees that the unit left over is the one you want, so you never multiply when you should divide.
Write your answer first. Then grade yourself.
Give yourself 1 mark for each idea you wrote down.
A recipe needs exactly 126.02 grams of sodium bicarbonate (NaHCO3, molar mass 84.01 g/mol). Calculate the moles of NaHCO3 required. Show your dimensional analysis setup with every unit and every cancellation written out.
- Start (1 mark): You write the starting value with units: 126.02 g NaHCO₃.
- Setup (1 mark): You put grams in the denominator and show them cancelling.
- Answer (1 mark): You get 1.500 mol NaHCO₃. An answer of 1.50 mol is accepted.
Carbon capture needs exact mole conversions. Scrubbers pull carbon dioxide out of exhaust gas. Engineers use factor-label conversions to find the mass of liquid amine that absorbs a given number of CO₂ molecules.
Adaptive Competency Practice: HS-PS1-7
Practice dimensional analysis, mole-mass conversions, and particle count calculations with live feedback. Earn an authenticated competency certificate upon completing the adaptive sequence.