How to Convert Grams to Moles

Most students think the molar mass of a substance is a fixed number they can look up once and reuse, but learning how to convert grams to moles reveals that assumption is wrong. The molar mass changes with every different substance. You must calculate it fresh from the chemical formula each time using the periodic table. Use the by-hand method for homework and exams, applying n = m / M, where n is the amount in moles, m is the mass in grams, and M is the molar mass in g mol⁻¹. Converting grams to moles unlocks every stoichiometry calculation that follows.

OpenStax Chemistry 2e (section 3.1) defines molar mass as the mass of one mole of a substance, numerically equal to the formula mass in daltons but expressed in grams per mole. To find it, sum the atomic masses of every atom in the chemical formula. Use the IUPAC CIAAW Standard Atomic Weights from the current table at ciaaw.org, which are revised annually. For example, hydrogen has a standard atomic weight interval of [1.00784, 1.00828] as of the 2021 IUPAC CIAAW table; for homework, use 1.008 g mol⁻¹ unless your instructor specifies a different value.

Elements: Simple Atomic Masses

For an element like iron (Fe), the conventional atomic weight is 55.845 g mol⁻¹ (2021 IUPAC CIAAW). One mole of iron atoms has a mass of 55.845 g.

Molecular Compounds: Sum the Atomic Masses

For a molecule like carbon dioxide (CO₂), carbon (C) is 12.011 g mol⁻¹ and oxygen (O) is 15.999 g mol⁻¹. Multiply oxygen's value by two and add carbon: 12.011 + (2 × 15.999) = 44.009 g mol⁻¹. For water (H₂O), the molar mass is 18.015 g mol⁻¹.

Ionic Compounds: Formula Unit Mass

Sodium chloride (NaCl) has sodium at 22.98976928 g mol⁻¹ and chlorine at 35.45 g mol⁻¹. Summing gives 58.44 g mol⁻¹. For calcium carbonate (CaCO₃), calcium is 40.078 g mol⁻¹, carbon is 12.011 g mol⁻¹, and three oxygens are 47.997 g mol⁻¹, for a total of 100.086 g mol⁻¹.

With the molar mass known, apply the equation: moles = mass (g) / molar mass (g mol⁻¹). Dimensional analysis ensures the units cancel correctly. Write the conversion factor as (1 mol / M g) and multiply it by the mass in grams. For example, 36.0 g of water divided by 18.015 g mol⁻¹ gives 1.998 mol. The grams cancel, leaving moles.

The number of moles you report must match the least precise measurement. If the mass is given as 36.0 g (three significant figures) and the molar mass is 18.015 g mol⁻¹ (five significant figures), the answer should have three significant figures: 2.00 mol. Round only at the final step, never on intermediate values. A common failure is reporting 1.9978 mol instead of 2.00 mol.

The expression n = m / M is the direct way to find moles from mass. It works because the molar mass acts as a conversion factor between the measurable mass and the count of particles. One mole always contains exactly 6.02214076 × 10²³ particles (Avogadro's constant, as defined by the 2019 SI redefinition published in the BIPM SI Brochure 9th edition). For a sample of 88.0 g of CO₂, the calculation is 88.0 g / 44.009 g mol⁻¹ = 2.00 mol.

Each example demonstrates the same three steps: find molar mass, divide mass by molar mass, round to correct significant figures.

Example 1: Element (Iron)

Mass of iron = 27.9 g. Molar mass of Fe = 55.845 g mol⁻¹. Moles = 27.9 g / 55.845 g mol⁻¹ = 0.500 mol (three significant figures).

Example 2: Molecular Compound (Glucose)

Mass of C₆H₁₂O₆ = 180.0 g. Molar mass: carbon (6 × 12.011 = 72.066), hydrogen (12 × 1.008 = 12.096), oxygen (6 × 15.999 = 95.994), total = 180.156 g mol⁻¹. Moles = 180.0 g / 180.156 g mol⁻¹ = 0.999 mol (three significant figures).

Example 3: Ionic Compound (Sodium Hydroxide)

Mass of NaOH = 20.0 g. Molar mass: sodium (22.98976928), oxygen (15.999), hydrogen (1.008), total = 39.997 g mol⁻¹. Moles = 20.0 g / 39.997 g mol⁻¹ = 0.500 mol (three significant figures).

Example 4: Hydrate (Copper(II) Sulfate Pentahydrate)

Mass of CuSO₄·5H₂O = 50.0 g. Molar mass: copper (63.546), sulfur (32.06), oxygen (4 × 15.999 = 63.996), plus five water molecules (5 × 18.015 = 90.075), total = 249.677 g mol⁻¹. Moles = 50.0 g / 249.677 g mol⁻¹ = 0.200 mol (three significant figures). Forgetting the five water molecules would give a lower molar mass and a wrong answer.

Check your work against these frequent errors before submitting an answer.

Using atomic number instead of atomic mass. Carbon's atomic number is 6; its atomic mass is 12.011 g mol⁻¹. Confusing the two gives a molar mass of 6 g mol⁻¹, which is wrong by a factor of about two.

Forgetting subscripts. Oxygen gas is O₂, not O. Using 15.999 g mol⁻¹ instead of 31.998 g mol⁻¹ halves the molar mass and doubles the calculated moles.

Ignoring unit prefixes. A mass given in kilograms must be converted to grams: multiply by 1000. A 0.500 kg sample of NaCl is 500 g.

Applying the wrong formula. The grams-to-moles equation is n = m / M. The reverse conversion (moles to grams) uses m = n × M. Using the wrong direction is a common exam mistake.

Use this table to verify your calculations for common substances. All molar masses come from IUPAC CIAAW standard atomic weights and are rounded to five significant figures for homework accuracy.

Substance	Formula	Molar Mass (g mol⁻¹)	Mass (g)	Moles (mol)
Water	H₂O	18.015	36.0	2.00
Carbon dioxide	CO₂	44.009	88.0	2.00
Glucose	C₆H₁₂O₆	180.156	180.0	0.999
Sodium chloride	NaCl	58.44	29.2	0.500
Iron	Fe	55.845	27.9	0.500
Ammonia	NH₃	17.031	34.1	2.00

The single most frequent error in grams-to-moles conversions is using the molar mass of the element instead of the compound. A student given 64.0 g of oxygen gas (O₂) who uses 16.00 g mol⁻¹ instead of 32.00 g mol⁻¹ will calculate 4.00 mol instead of 2.00 mol. Always confirm the chemical formula includes subscripts before summing atomic masses.