Calculating the molar mass of chemical compounds lesson

Key points at a glance

• Molar mass is the mass of one mole of a substance, measured in grams per mole (g mol^-1).
• To find it, add up the relative atomic masses of every atom in the formula. Nothing more complicated than that is ever required.
• A_r is the relative atomic mass of a single element. M_r is the relative formula mass of a whole compound. Both are just numbers; molar mass is the same number with the unit g mol^-1 attached.
• A subscript multiplies only the symbol before it, and a number outside a bracket multiplies everything inside the bracket.
• The relationship you will use constantly is moles = mass ÷ M_r.
• Use the A_r values printed on the periodic table you are given. Chlorine is 35.5 and copper is 63.5 – do not round them to whole numbers.

Molar mass is the bridge between the grams you can weigh out on a balance and the number of particles actually reacting. Almost every calculation in chemistry – reacting masses, concentrations, titrations, percentage yield – starts by working one out, so it is worth being quick and reliable at it.

What is molar mass?

The mass of one mole of any substance is its molar mass. Molar mass is measured in grams per mole (g mol^-1) or kilograms per mole (kg mol^-1).

A mole is simply a fixed number of particles – a counting unit, in the same way that "a dozen" is a counting unit. One mole of any substance contains the same number of particles as one mole of any other. What changes from substance to substance is how much that many particles weigh, and that is exactly what molar mass tells you.

A_r, M_r and molar mass

These three terms describe almost the same thing, and mixing them up is the commonest source of confusion in this topic.

Term	Stands for	Applies to	Unit	Example
Ar	Relative atomic mass	One element	None – it is a ratio	Ar of oxygen = 16
Mr	Relative formula mass	A compound or molecule	None – it is a ratio	Mr of water = 18
Molar mass	Mass of one mole	Either	g mol-1	Molar mass of water = 18 g mol-1

The convenient part is that the numbers are identical. Once you have worked out that the M_r of water is 18, the molar mass is 18 g mol^-1 – no conversion needed. Some books use "relative molecular mass" for molecules and "relative formula mass" for ionic compounds; relative formula mass is the safer term because it works for both.

Relative atomic masses are not whole numbers because most elements exist as a mixture of isotopes, and A_r is the weighted average across that mixture. That is why chlorine is 35.5 rather than 35 or 36.

How to calculate molar mass of compounds?

The molar mass of an element or compound can be calculated if its formula is known, because the molar mass of a compound is the sum of the molar masses of all the atoms in it. Work through it in four steps:

1. Write out the formula and list every element in it.
2. Count the atoms of each element. A subscript applies only to the symbol immediately before it; a number outside a bracket multiplies everything inside.
3. Look up each A_r on the periodic table you are given.
4. Multiply and add. Multiply each A_r by the number of those atoms, then total the results.

Molar mass of several elements in a table

Element	Symbol	Molar Mass (g/mol)
Hydrogen	H	1.008
Helium	He	4.003
Lithium	Li	6.941
Carbon	C	12.011
Nitrogen	N	14.007
Oxygen	O	15.999
Fluorine	F	18.998
Sodium	Na	22.990
Magnesium	Mg	24.305
Aluminium	Al	26.982
Silicon	Si	28.086
Chlorine	Cl	35.453
Potassium	K	39.098
Calcium	Ca	40.078
Iron	Fe	55.845
Copper	Cu	63.546
Zinc	Zn	65.38
Bromine	Br	79.904
Silver	Ag	107.868
Iodine	I	126.904
Gold	Au	196.967

In GCSE and IGCSE questions these values are normally rounded, so you would use H = 1, C = 12, N = 14, O = 16, Na = 23, Cl = 35.5 and so on. The worked examples below use the rounded values, which is what the periodic table in an exam gives you. Always use the values on the paper in front of you rather than remembered ones.

Worked examples: calculating molar mass

Molar mass of water

A water molecule is made up of two hydrogen atoms (H) and one oxygen atom (O). The molar mass of water (H₂O) is therefore the sum of the masses of two hydrogen atoms and one oxygen atom.

1. Formula: H₂O – two hydrogen atoms, one oxygen atom.
2. Hydrogen: 2 × 1 = 2
3. Oxygen: 1 × 16 = 16
4. Total: 2 + 16 = 18, so the molar mass of water is 18 g mol^-1.

Molar mass of HCl

1. Formula: HCl – one hydrogen atom, one chlorine atom.
2. Hydrogen: 1 × 1 = 1
3. Chlorine: 1 × 35.5 = 35.5
4. Total: 1 + 35.5 = 36.5 g mol^-1. Note the half – rounding chlorine to 35 here is a very common way to lose marks.

Molar mass of O₂

1. Formula: O₂ – oxygen gas exists as diatomic molecules.
2. Oxygen: 2 × 16 = 32 g mol^-1.

Watch this one carefully. One mole of oxygen atoms has a mass of 16 g, but one mole of oxygen molecules has a mass of 32 g. If a question says "oxygen gas", it means O₂.

Molar mass of NaCl

1. Formula: NaCl – one sodium ion, one chloride ion.
2. Sodium: 1 × 23 = 23
3. Chlorine: 1 × 35.5 = 35.5
4. Total: 58.5 g mol^-1.

Sodium chloride is ionic, so there is no such thing as an NaCl molecule. The 58.5 is the mass of one mole of NaCl formula units, which is why "relative formula mass" is the more accurate name.

Molar mass of NaOH

1. Formula: NaOH – one sodium, one oxygen, one hydrogen.
2. Sodium: 23; oxygen: 16; hydrogen: 1
3. Total: 23 + 16 + 1 = 40 g mol^-1.

Molar mass of ethanol

Ethanol is written C₂H₅OH, which is the same as C₂H₆O. Count the hydrogens carefully: five in the C₂H₅ part and one more in the OH group, making six in total.

1. Carbon: 2 × 12 = 24
2. Hydrogen: 6 × 1 = 6
3. Oxygen: 1 × 16 = 16
4. Total: 24 + 6 + 16 = 46 g mol^-1.

Using the unrounded values from the table above (C = 12.011, H = 1.008, O = 15.999) gives 46.07 g mol^-1, which agrees to the nearest whole number.

Molar mass of CO₂

1. Formula: CO₂ – one carbon atom, two oxygen atoms.
2. Carbon: 1 × 12 = 12
3. Oxygen: 2 × 16 = 32
4. Total: 12 + 32 = 44 g mol^-1.

Molar mass of NH₃

1. Formula: NH₃ – one nitrogen atom, three hydrogen atoms.
2. Nitrogen: 1 × 14 = 14
3. Hydrogen: 3 × 1 = 3
4. Total: 14 + 3 = 17 g mol^-1.

Brackets and water of crystallisation

Two formats catch people out. Both follow the same rule – multiply everything inside by the number outside.

A formula with brackets: calcium nitrate, Ca(NO₃)₂

1. Work out the mass of one nitrate group first: N (14) + 3 × O (16) = 14 + 48 = 62.
2. There are two nitrate groups: 2 × 62 = 124.
3. Add the calcium: 40 + 124 = 164 g mol^-1.

A hydrated salt: copper(II) sulfate crystals, CuSO₄·5H₂O

The dot does not mean multiply – it means that five water molecules are locked into the crystal for every one CuSO₄. This is called water of crystallisation, and its mass must be included.

1. CuSO₄: 63.5 + 32 + (4 × 16) = 63.5 + 32 + 64 = 159.5
2. 5H₂O: 5 × 18 = 90
3. Total: 159.5 + 90 = 249.5 g mol^-1.

Using molar mass: the mole equation

Once you have a molar mass, one relationship does the rest of the work:

moles = mass (g) ÷ M_r

Rearranged, that gives mass = moles × M_r and M_r = mass ÷ moles. Many students draw it as a triangle with mass on top and moles and M_r underneath: cover the quantity you want and the triangle shows you what to do with the other two. There is more on rearranging expressions like this in our guide to rearranging formulas.

Worked example: how many moles?

Calculate the number of moles in 25 g of calcium carbonate, CaCO₃.

1. M_r of CaCO₃ = 40 + 12 + (3 × 16) = 40 + 12 + 48 = 100
2. moles = mass ÷ M_r = 25 ÷ 100
3. = 0.25 mol

Worked example: what mass?

What is the mass of 2.0 mol of carbon dioxide?

1. M_r of CO₂ = 44
2. mass = moles × M_r = 2.0 × 44
3. = 88 g

Finding the molar mass of an unknown acid by titration

Titration is the standard laboratory method for finding the molar mass of an acid you cannot identify. You measure out a known mass of it, find out how many moles that turned out to be, and divide one by the other. Our separate lesson on acid-base titration covers the practical technique in detail.

The method

1. Weigh out an accurately known mass of the unknown acid.
2. Dissolve it in distilled water and make the solution up to a known volume in a volumetric flask – typically 250 cm³. You now know the mass per cubic decimetre, but not yet the concentration in moles.
3. Pipette a measured portion, usually 25.0 cm³, into a conical flask and add a few drops of indicator.
4. Titrate with a standard solution of sodium hydroxide of accurately known concentration, adding it from a burette until the indicator changes colour.
5. Repeat until you have concordant titres, and take the mean of those.

The calculation, worked through

2.40 g of a monoprotic acid HA was dissolved and made up to 250 cm³. A 25.0 cm³ portion needed 20.0 cm³ of 0.100 mol dm^-3 sodium hydroxide. Find the molar mass of the acid.

1. Moles of NaOH used: moles = concentration × volume in dm³ = 0.100 × (20.0 ÷ 1000) = 0.00200 mol.
2. Moles of acid in the 25 cm³ portion: the equation is HA + NaOH → NaA + H₂O, a 1:1 ratio, so this is also 0.00200 mol.
3. Moles of acid in the whole 250 cm³: the portion was one tenth of the flask, so 0.00200 × 10 = 0.0200 mol.
4. Molar mass: M_r = mass ÷ moles = 2.40 ÷ 0.0200 = 120 g mol^-1.

One warning about step 2. The 1:1 ratio only holds for a monoprotic acid – one that releases a single H⁺ ion per molecule, such as hydrochloric or ethanoic acid. A diprotic acid such as sulfuric acid releases two, so it reacts with twice as much alkali, and the moles of acid would be half the moles of NaOH. Read the equation before you divide.

Practice questions

1. Calculate the M_r of magnesium oxide, MgO.
2. Calculate the M_r of sulfuric acid, H₂SO₄.
3. Calculate the M_r of magnesium hydroxide, Mg(OH)₂.
4. How many moles are there in 8.0 g of sodium hydroxide, NaOH?
5. What is the mass of 0.50 mol of glucose, C₆H₁₂O₆?

Answers: 1. 24 + 16 = 40.   2. (2 × 1) + 32 + (4 × 16) = 2 + 32 + 64 = 98.   3. 24 + 2 × (16 + 1) = 24 + 34 = 58.   4. M_r = 40, so moles = 8.0 ÷ 40 = 0.20 mol.   5. M_r = (6 × 12) + (12 × 1) + (6 × 16) = 72 + 12 + 96 = 180, so mass = 0.50 × 180 = 90 g.

Exam tips

• Use the A_r values on the periodic table you are given. Chlorine is 35.5 and copper is 63.5; rounding them to whole numbers throws the final answer out.
• Work out the contents of a bracket first, then multiply. Ca(OH)₂ contains two oxygens and two hydrogens, not one of each.
• Remember that hydrogen, nitrogen, oxygen and the halogens exist as diatomic molecules when they are elements. The M_r of oxygen gas is 32, not 16.
• Include the water of crystallisation. The M_r of CuSO₄·5H₂O is 249.5, not 159.5.
• Show every line of your working. Method marks are available even when the final number is wrong, but only if the examiner can see what you did.
• Give molar mass the unit g mol^-1. M_r and A_r themselves have no units, because they are ratios.

Frequently asked questions about molar mass

How do you calculate the molar mass of a compound?

Write out the formula, count how many atoms of each element it contains, look up each relative atomic mass on the periodic table, multiply each A_r by the number of those atoms, and add the results. The answer is in grams per mole.

What is the difference between A_r and M_r?

A_r is the relative atomic mass of a single element, such as 16 for oxygen. M_r is the relative formula mass of a whole compound, found by adding up the A_r values of every atom in the formula, such as 18 for water.

Is molar mass the same as relative formula mass?

They are the same number, but not quite the same quantity. M_r is a ratio and has no units; molar mass is a mass per mole and carries the unit g mol^-1. If the M_r of carbon dioxide is 44, its molar mass is 44 g mol^-1.

Why is the molar mass of chlorine 35.5 and not a whole number?

Because chlorine exists naturally as a mixture of two isotopes with different masses, and the relative atomic mass is the weighted average across that mixture. Most elements have several isotopes, which is why their A_r values are rarely exact whole numbers.

What is the molar mass of water?

18 g mol^-1. Water is H₂O, so it contains two hydrogen atoms at 1 each and one oxygen atom at 16, giving 2 + 16 = 18.

How do you work out molar mass when the formula has brackets?

Calculate the mass of everything inside the bracket first, then multiply by the number outside it. For Ca(NO₃)₂, one nitrate group is 14 + 48 = 62, two of them are 124, and adding calcium gives 164.

What does the dot mean in CuSO₄·5H₂O?

It shows water of crystallisation – five water molecules built into the crystal for each CuSO₄ unit. Their mass counts towards the molar mass, adding 5 × 18 = 90 to give 249.5 g mol^-1.

How do you convert grams to moles?

Divide the mass in grams by the molar mass: moles = mass ÷ M_r. For example, 25 g of calcium carbonate with an M_r of 100 gives 25 ÷ 100 = 0.25 mol.

How can a titration give the molar mass of an unknown acid?

You weigh out a known mass of the acid, titrate a measured portion against an alkali of known concentration, and use the titre to find how many moles of acid you had. Dividing the mass by the number of moles gives the molar mass. Check the equation first, because a diprotic acid reacts with twice as much alkali as a monoprotic one.