Chemguide: Support for CIE A level Chemistry


Learning outcome 1.1(a)

This statement deals with the definitions of relative isotopic mass, relative atomic mass, relative molecular mass and relative formula mass.

Before you go on, you should find and read the statement in your copy of the syllabus.


Relative isotopic mass

Isotopes are atoms of the same element (and so with the same number of protons and electrons), but with different masses due to having different numbers of neutrons.

So, for example, chlorine has two different sorts of atoms each of which has 17 protons and 17 electrons. However, one of these atoms has 18 neutrons whereas the other has 20. All the chemical properties of the atoms are the same because they have the same numbers of protons and electrons, but they have different masses.

The mass of an atom is incredibly small, and it doesn't make sense to use standard units like grams to measure it. Instead masses are measured on a scale based on the mass of an atom of the 12C isotope.

On the 12C scale, the 12C isotope is given a mass of exactly 12 units, and the masses of all other isotopes are measured on the same scale.

For example, an atom of 24Mg is twice as heavy as an atom of 12C, and so is given a relative isotopic mass of 24. An atom of the 1H isotope is only 1/12 of the mass of the 12C isotope and so is given a relative isotopic mass of 1.


Note:  Actually, measured accurately, the hydrogen-1 isotope has a relative isotopic mass of about 1.008. At A level, for simplicity, the hydrogen value is just rounded off. That's true of quite a lot of other atoms as well.


There are two equivalent ways in which you can define relative isotopic mass. They mean exactly the same thing.

Either:

  • The relative isotopic mass of an isotope is the mass of the isotope on a scale on which a carbon-12 atom has a mass of exactly 12 units.

Or:

  • The relative isotopic mass of an isotope is the mass of the isotope relative to 1/12 of the mass of a carbon-12 atom.

Learn whichever of these you have been taught.


Relative atomic mass, Ar

Similarly, relative atomic mass can be defined in two exactly equivalent ways:

Either:

  • The relative atomic mass of an element is the weighted average of the masses of its isotopes on a scale on which a carbon-12 atom has a mass of exactly 12 units.

Or:

  • The relative atomic mass of an element is the weighted average of the masses of its isotopes relative to 1/12 of the mass of a carbon-12 atom.

Again, learn whichever of these you have been taught.


A "weighted average" allows for the fact that there won't be equal amounts of the various isotopes. This example should make that clear:

In chlorine, there are 3 atoms of chlorine-35 for every 1 of chlorine-37.

Suppose you had 4 typical atoms of chlorine.

The total mass of these would be (3 x 35) + (1 x 37) = 142

The average mass of these 4 atoms would be 142 / 4 = 35.5.

35.5 is the relative atomic mass of chlorine.

Notice the effect of the "weighted" average. A simple average of 35 and 37 is, of course, 36. Our answer of 35.5 allows for the fact that there are more of the lighter isotope of chlorine - and so the "weighted" average ought to be closer to that.

You can always find the relative atomic mass of an element from a Periodic Table.

But take care to choose the right number! Look at the key for the table, but, in any case, the relative atomic mass will always be the larger number given. Look at the Periodic Table provided by CIE for exam use, which you will find towards the end of the syllabus.


Relative molecular mass, Mr

You have to be careful with this term, because it should only be applied to substances which actually exist as molecules. A molecule consists of a fixed number of atoms joined together by covalent bonds. (Actually, in the case of the noble gases, a molecule can also be a single atom.)

You shouldn't use the term for things, like sodium chloride, which are ionically bonded.


Working out the relative molecular mass

You work out the relative molecular mass of a substance by adding up the relative atomic masses of the atoms it consists of. So, for example, to work out the relative molecular mass of water, H2O, you add the relative atomic masses of two hydrogens and one oxygen.

Mr of H2O = (2 x 1) + 16 = 18

To work out the relative molecular mass of CHCl3:

Mr of CHCl3 = 12 + 1 + (3 x 35.5) = 119.5


Defining the relative molecular mass

Either:

  • The relative molecular mass of a substance is the weighted average of the masses of the molecules on a scale on which a carbon-12 atom has a mass of exactly 12 units.

Or:

  • The relative molecular mass of a substance is the weighted average of the masses of the molecules relative to 1/12 of the mass of a carbon-12 atom.


Note:  You may find that many sources miss out the bit about weighted averages, but this should be included unless you are thinking about the mass of a particular molecule with a particular combination of isotopes of the various atoms.

For example, taking the example of CHCl3 above:

There is no single molecule of CHCl3 which has a mass of 119.5. The problem is that an average sample of these molecules will contain isotopes of both chlorine-35 and chlorine-37. That means that individual molecules can have the following masses:

12 + 1 + (3 x 35) = 118

12 + 1 + (2 x 35) + 37 = 120

12 + 1 + 35 + (2 x 37) = 122

12 + 1 + (3 x 37) = 124

The weighted average takes account of the proportions of each of these molecules in an average sample of the substance.

Don't get too worried about all this! It is far more likely that you will have to work out a relative molecular mass by adding up the relative atomic masses than that you will have to define it.




Relative formula mass, Mr

Notice that relative formula mass is given exactly the same symbol, Mr, as relative molecular mass.

In fact, relative formula mass is a much more useful term than relative molecular mass because it includes everything, whatever the bonding. It works just as well for ionic substances as for covalent substances.

I strongly recommend that you use this term all the time, and only talk about relative molecular mass if you are specifically asked about it in an exam.


Working out the relative formula mass

Write down the formula, and then add up all the relative atomic masses of the atoms it contains.

Example 1

The relative formula mass of NaCl = 23 + 35.5 = 58.5

Example 2

The relative formula mass of copper(II) sulfate crystals, CuSO4.5H2O:

Mr of CuSO4.5H2O = 63.5 + 32 + (4 x 16) + 5 x [(2 x 1) + 16] = 249.5


Note:  The relative atomic mass of copper is often quoted as 64. I am using 63.5 here because that is the figure that comes from the CIE Periodic Table.


Be careful with things which contain water of crystallisation like the copper(II) sulfate crystals in this example. Add the water up first and then multiply it by 5 (or whatever other number you need). If you try to do it as hydrogen and oxygen separately, you stand a good chance of getting it wrong. Students usually remember to multiply the 2 hydrogens by 5, but forget to multiply the oxygen by 5. If you add the water up as a whole, that can't happen.


Defining the relative formula mass

I find it hard to imagine an exam question in which you were asked to define relative formula mass rather then just work it out, but just in case . . .

Either:

  • The relative formula mass of a substance is the weighted average of the masses of the formula units on a scale on which a carbon-12 atom has a mass of exactly 12 units.

Or:

  • The relative formula mass of a substance is the weighted average of the masses of the formula units relative to 1/12 of the mass of a carbon-12 atom.


The "formula unit" is just the formula as you have written it.



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© Jim Clark 2010 (last modified March 2014)