The conversion formula: divide grams by molar mass

To change grams into moles, divide the number of grams by the molar mass of the substance. The formula is: moles = grams ÷ molar mass. Molar mass is measured in grams per mole (g/mol) and tells you how much one mole of a substance weighs.

The molar mass of an element is its atomic weight, which you can find on the periodic table. For a compound, add up the atomic weights of all the atoms in the molecule. For example, water (H₂O) has a molar mass of 18 g/mol because hydrogen weighs about 1 g/mol and oxygen weighs about 16 g/mol, so 1 + 1 + 16 = 18.

Key Takeaways

  • Moles = grams divided by molar mass, where molar mass comes from the periodic table and is measured in g/mol.
  • Find molar mass by looking up atomic weights on the periodic table for elements, or by adding atomic weights together for compounds.
  • Always check that your units cancel out: grams in the numerator and grams per mole in the denominator leave you with moles.
  • Round your answer to the same number of significant figures as the measurement you started with.

Finding the molar mass of an element

The periodic table lists the atomic weight of each element, usually shown as a decimal number below the element's symbol. This number is the molar mass in grams per mole. For sodium, the atomic weight is about 23 g/mol. For carbon, it is about 12 g/mol. For chlorine, it is about 35.5 g/mol.

If you are working with an element that exists as a molecule in nature—like oxygen gas (O₂) or nitrogen gas (N₂)—multiply the atomic weight by the number of atoms in the molecule. Oxygen gas has a molar mass of 32 g/mol because each oxygen atom weighs 16 g/mol and there are two atoms per molecule.

Finding the molar mass of a compound

For a compound, write out the chemical formula and look up the atomic weight of each element on the periodic table. Multiply each atomic weight by the number of times that element appears in the formula, then add all the results together.

For sodium chloride (NaCl): sodium is 23 g/mol and chlorine is 35.5 g/mol, so the molar mass is 23 + 35.5 = 58.5 g/mol. For glucose (C₆H₁₂O₆): carbon is 12 g/mol (× 6 = 72), hydrogen is 1 g/mol (× 12 = 12), and oxygen is 16 g/mol (× 6 = 96), so the molar mass is 72 + 12 + 96 = 180 g/mol.

Working through a step-by-step example

Suppose you have 25 grams of sodium chloride and want to know how many moles that is. First, find the molar mass: sodium is 23 g/mol and chlorine is 35.5 g/mol, so NaCl has a molar mass of 58.5 g/mol. Then divide: 25 grams ÷ 58.5 g/mol = 0.427 moles.

Another example: you have 10 grams of water (H₂O). The molar mass is 18 g/mol. So 10 grams ÷ 18 g/mol = 0.556 moles. Notice that in both cases, the grams cancel out and you are left with moles in your answer.

Checking your units and significant figures

Always write out the units as you work through the problem. When you divide grams by grams per mole, the grams cancel and you are left with moles. If your units do not cancel correctly, you have set up the problem wrong.

Round your final answer to match the number of significant figures in your starting measurement. If you measured 25 grams (two significant figures), your answer should have two significant figures. If you measured 25.0 grams (three significant figures), your answer should have three. This keeps your answer honest about how precisely you actually measured the substance.

Converting back from moles to grams

If you need to go the other direction—from moles to grams—use the reverse formula: grams = moles × molar mass. This is useful when a problem tells you how many moles you have and asks how much that weighs.

For example, if you have 2 moles of carbon (atomic weight 12 g/mol), multiply: 2 moles × 12 g/mol = 24 grams. If you have 0.5 moles of water (molar mass 18 g/mol), multiply: 0.5 moles × 18 g/mol = 9 grams.

Frequently Asked Questions

Where do I find the molar mass if it is not on the periodic table?

The periodic table shows atomic weights for elements. For compounds, calculate molar mass by adding the atomic weights of all atoms in the molecule. If you have a complex compound and cannot find the formula, check your textbook, lab manual, or the substance's label.

What if my answer comes out to a very small decimal, like 0.00045 moles?

That is correct. Moles can be very small numbers, especially when you start with a small mass of a heavy substance. You can also express this in scientific notation (4.5 × 10⁻⁴ moles) or in smaller units like millimoles (0.45 mmol) if that is clearer for your work.

Do I need to memorize the periodic table?

No. You should have access to the periodic table during homework, quizzes, and exams unless your instructor specifically forbids it. Memorizing a few common elements (carbon, hydrogen, oxygen, nitrogen) is useful, but looking up values is the normal practice.

What if the problem gives me molar mass instead of asking me to find it?

Use the molar mass provided in the problem. The problem writer may have rounded differently than the periodic table, or may be using a simplified value. Always use the number given in the problem unless you are told to look it up yourself.