Molecular weight:
adding up atomic masses from a formula

The sum rule

A molecule of water is far too light to weigh directly, so chemists use a relative scale. Molecular weight tells you the mass of one molecule relative to one-twelfth of a carbon-12 atom, and numerically it equals the mass in grams of one mole of that substance. Water comes out at 18.015: one mole of water weighs 18.015 g.

Strictly, the same figure is called molar mass when written in g/mol, and formula mass or formula weight for ionic compounds such as sodium chloride that do not form discrete molecules. In everyday chemistry the terms are used almost interchangeably.

An atom without a written subscript counts as one. Atomic masses on the periodic table are weighted averages of the isotopes found in nature, so they are not whole numbers.

Worked examples: water and glucose

A larger molecule works the same way, just with more lines. Glucose is C₆H₁₂O₆.

Brackets and hydrates

Brackets multiply everything inside them by the subscript outside. Calcium hydroxide, Ca(OH)₂, holds one calcium and two OH groups, so it has 1 Ca, 2 O and 2 H.

A hydrate such as CuSO₄·5H₂O is calculated in two parts: the salt itself, plus five times the mass of water, 5 × 18.015 = 90.075. The dot means the water is part of the formula, so it counts.

How many decimal places to carry

Use the atomic masses to the precision of the periodic table you have, and round only at the end. A school problem usually wants the answer to one or two decimals; analytical work may need four. The accepted values are revised by the standards body from time to time, so a published table from a recent year is the safer source than a memorised number.

• Rounding C, H and O to 12, 1 and 16 gives 180 for glucose, close enough for a quick estimate.
• Rounding Cl to 35.5 gives 58.5 for table salt, a common convention in textbooks.
• Use the full values when preparing standard solutions or reporting a result.

From formula to percentage composition

Once the total molecular weight is known, each element's share is its contribution divided by the total. For water, hydrogen contributes 2.016 of 18.015, or 11.19%, and oxygen 15.999 of 18.015, or 88.81%. The two shares add to 100%, which is a handy check that the arithmetic holds.

The same approach identifies how much of an element a sample contains. A 50 g sample of glucose holds 50 × 72.066 ÷ 180.156 = 20.0 g of carbon. Fertiliser labels, mineral analyses and nutritional data all lean on this share-of-total idea.

Going the other way, percentage composition lets you recover an empirical formula by dividing each element's percentage by its atomic mass and comparing the ratios of the results.

Molecular weight, formula mass and isotopes

A true molecule has a definite number of atoms, but sodium chloride is a lattice of ions with no discrete NaCl molecule. For such substances the quantity is called formula mass or formula weight. The arithmetic is unchanged; the name reflects what the formula represents.

Mass spectrometers measure individual molecules, so they see the isotopes separately. Chlorine, for example, is about three parts chlorine-35 to one part chlorine-37, so a molecule containing one chlorine atom appears at two masses two units apart. The standard atomic weight of 35.45 is the abundance-weighted average of those, and it is the right number for bulk chemistry where a gram of material contains vast numbers of molecules.

• Monoisotopic mass uses the most abundant isotope of each element and is what mass spectrometry often reports.
• Average molecular weight uses standard atomic weights and is what balances and stoichiometry need.
• Some elements have a published range of atomic weights because natural abundances vary slightly by source.

Reading organic formulas and checking the sum

Organic formulas are often written as condensed structures, such as CH₃CH₂OH for ethanol. Count the atoms of each element across the whole string before multiplying: that is two carbons, six hydrogens and one oxygen, or C₂H₆O, giving 2 × 12.011 + 6 × 1.008 + 15.999 = 46.069 g/mol. Brackets that hold repeating units, as in (CH₂)ₙ, are handled by multiplying by n.

A few sanity checks catch most mistakes. The total should be larger than the largest single atomic mass in the formula. Oxygen-rich compounds should land in a plausible range for their size. If you have calculated the same compound twice by two routes, for example by summing atoms and by summing functional groups, both answers should agree to the last decimal.

Many chemistry courses give atomic masses to one or two decimals, and answers are marked to the same precision, so check which table your question expects.

Slips that cost marks

• Attaching a subscript to the wrong element, such as reading the 2 in CO₂ as belonging to carbon.
• Forgetting the multiplier outside brackets.
• Dropping the water in a hydrate.
• Mixing up the unit: relative molecular mass is a pure number, while molar mass has units of g/mol.