Mole Conversions Made Easy: Grams to Moles, Moles to Molecules, and Every Conversion Between

Every mole conversion uses one of three relationships:

1. Grams ↔ Moles: divide by molar mass (g/mol) to go from grams to moles. Multiply by molar mass to go from moles to grams. Molar mass = the sum of atomic masses from the periodic table.

2. Moles ↔ Particles (molecules, atoms, ions): multiply by Avogadro's number (6.022 × 10²³) to go from moles to particles. Divide by Avogadro's number to go from particles to moles.

3. Moles ↔ Liters of gas (at STP): multiply by 22.4 L/mol to go from moles to liters at STP (0°C, 1 atm). Divide by 22.4 to go from liters to moles.

That is the entire mole conversion toolkit. Every problem — no matter how complicated it looks — is just a chain of these three conversions. Grams to molecules? Convert grams → moles (÷ molar mass), then moles → molecules (× 6.022 × 10²³). Liters of gas to grams? Convert liters → moles (÷ 22.4), then moles → grams (× molar mass).

Snap a photo of any mole conversion problem and ChemistryIQ identifies the starting unit, the target unit, and chains the conversions step by step — showing dimensional analysis at every step.

This content is for educational purposes only and does not constitute medical advice.

The molar mass is the bridge between grams and moles. It tells you how many grams one mole of a substance weighs. You calculate it by adding up the atomic masses of every atom in the formula.

Example: What is the molar mass of water (H₂O)? Hydrogen = 1.008 g/mol × 2 = 2.016. Oxygen = 16.00 g/mol × 1 = 16.00. Molar mass of H₂O = 18.02 g/mol. This means one mole of water weighs 18.02 grams.

Example: What is the molar mass of glucose (C₆H₁₂O₆)? Carbon: 12.01 × 6 = 72.06. Hydrogen: 1.008 × 12 = 12.10. Oxygen: 16.00 × 6 = 96.00. Molar mass = 180.16 g/mol.

Grams → Moles: moles = grams ÷ molar mass. How many moles in 54.06 g of water? 54.06 ÷ 18.02 = 3.00 moles.

Moles → Grams: grams = moles × molar mass. What is the mass of 0.25 moles of glucose? 0.25 × 180.16 = 45.04 grams.

The most common mistake: using the atomic mass of one atom instead of adding up all atoms in the formula. The molar mass of NaCl is NOT 23 (just sodium) — it is 23 + 35.45 = 58.44 g/mol. Always account for every atom, including subscripts and coefficients in hydrates.

ChemistryIQ calculates molar masses automatically when you snap a photo of a formula — no need to look up each atomic mass individually.

Avogadro's number (6.022 × 10²³) is the number of particles in one mole. It works for molecules, atoms, ions, formula units — any type of particle.

Moles → Molecules: molecules = moles × 6.022 × 10²³. How many molecules in 2.5 moles of CO₂? 2.5 × 6.022 × 10²³ = 1.506 × 10²⁴ molecules.

Molecules → Moles: moles = molecules ÷ 6.022 × 10²³. How many moles is 3.01 × 10²³ molecules of O₂? 3.01 × 10²³ ÷ 6.022 × 10²³ = 0.500 moles.

The subtlety that trips students: atoms within molecules. One mole of O₂ contains 6.022 × 10²³ molecules, but 2 × 6.022 × 10²³ = 1.204 × 10²⁴ oxygen ATOMS (because each O₂ molecule has 2 atoms). If the question asks for atoms, multiply by the number of atoms per molecule after converting to molecules.

Example: How many hydrogen atoms in 36.04 g of water? Step 1: grams → moles. 36.04 ÷ 18.02 = 2.00 moles H₂O. Step 2: moles → molecules. 2.00 × 6.022 × 10²³ = 1.204 × 10²⁴ molecules H₂O. Step 3: molecules → hydrogen atoms. Each water has 2 H atoms: 1.204 × 10²⁴ × 2 = 2.409 × 10²⁴ hydrogen atoms.

This three-step chain (grams → moles → molecules → atoms) is the most complex mole conversion you will encounter in gen chem. ChemistryIQ handles chains of any length — it shows each conversion factor and cancels units at every step using dimensional analysis.

At Standard Temperature and Pressure (STP: 0°C, 1 atm), one mole of any ideal gas occupies exactly 22.4 liters. This is the molar volume, and it provides a shortcut for gas problems that avoids the ideal gas law entirely.

Moles → Liters at STP: liters = moles × 22.4. What volume does 0.75 moles of N₂ occupy at STP? 0.75 × 22.4 = 16.8 L.

Liters → Moles at STP: moles = liters ÷ 22.4. How many moles of O₂ in 5.6 L at STP? 5.6 ÷ 22.4 = 0.25 moles.

The critical caveat: 22.4 L/mol ONLY works at STP (0°C, 1 atm). At any other temperature or pressure, you must use the ideal gas law (PV = nRT) instead. If the problem says at STP, use 22.4. If it specifies any other conditions, use PV = nRT. This is the most commonly tested nuance in molar volume problems.

Chain example: What mass of CO₂ occupies 11.2 L at STP? Step 1: liters → moles. 11.2 ÷ 22.4 = 0.500 moles. Step 2: moles → grams. Molar mass of CO₂ = 12.01 + 2(16.00) = 44.01 g/mol. 0.500 × 44.01 = 22.0 grams.

Dimensional analysis keeps you on track: start with the given quantity, multiply by conversion factors that cancel the unwanted units, and end with the desired units. 11.2 L × (1 mol / 22.4 L) × (44.01 g / 1 mol) = 22.0 g. The liters cancel, the moles cancel, and you are left with grams.

ChemistryIQ shows the dimensional analysis setup for every conversion — it writes out the conversion factors with units so you can see exactly what cancels, which is the format most professors require for full credit.