Chemguide: Support for CIE A level Chemistry
Learning outcome 2.1
Relative masses of atoms and molecules
Learning outcome 2.1.1
This statement just wants you to know what is meant by a unified atomic mass unit which has often in the past just been called an atomic mass unit.
The masses of atoms are all measured relative to the mass of a carbon-12 isotope on a scale where this isotope has a mass of exactly 12 unified atomic mass units.
That means that an atomic mass unit is one-twelfth of the mass of an atom of the carbon-12 isotope.
We commonly talk about the masses of atoms, ions, molecules and so on as being measured on the C-12 scale. There is more about this in the next section.
Learning outcome 2.1.2
This statement wants you to be able to define various various important mass terms in chemistry.
Relative isotopic mass
This isn't the first term on the syllabus list, but it makes sense to talk about it first.
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, there are two isotopes of chlorine: Cl-35 and Cl-37. The Cl-37 hast two more neutrons than Cl-35.
On the C-12 scale, the C-12 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 Mg-24 is twice as heavy as an atom of C-12, and so is given a relative isotopic mass of 24.
Note: When we talk about Cl-35 or Mg-24, the numbers quoted are strictly speaking the mass numbers and count the numbers of protons + neutrons. To a reasonable approximation neutrons and protons have a mass of 1 atomic mass unit, but they are not exactly 1, and neither are their masses exactly the same.
For A level purposes, we make the assumption that their masses are both exactly 1 on the C-12 scale, and so when you work out a relative isotopic mass, you can just count the number of protons plus neutrons.
Relative atomic mass, Ar
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 Cl-35 for every 1 of Cl-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.
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
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.
The relative formula mass of NaCl = 23 + 35.5 = 58.5
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 . . .
The "formula unit" is just the formula as you have written it - for example, NaCl or CuSO4.5H2O or CO2 or Cl2 or whatever.
© Jim Clark 2019