Chemguide: Core Chemistry 14 - 16

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Relative atomic mass, relative molecular mass and relative formula mass

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This page explains the atomic mass scale based on the mass of an atom of the C-12 isotope.

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The importance of the C-12 isotope in chemistry calculations

A brief revision of isotopes

The number of neutrons in an atom can vary within small limits. For example, there are three kinds of carbon atom 12C, 13C and 14C. They all have the same number of protons, but the number of neutrons varies.

 protons neutrons mass number carbon-12 6 6 12 carbon-13 6 7 13 carbon-14 6 8 14

These different atoms of carbon are called isotopes. The fact that they have varying numbers of neutrons makes no difference whatsoever to the chemical reactions of the carbon.

Isotopes are atoms which have the same atomic number but different mass numbers. They have the same number of protons but different numbers of neutrons.

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The C-12 scale

The masses of atoms are measured relative to the mass of a C-12 atom.

You can't use a familiar mass unit like a gram because atoms are so small. For example, it would take about 6 x 1023 hydrogen atoms to weigh 1 g.

That's 600,000,000,000,000,000,000,000 atoms. Weighing atoms in a standard mass unit like grams would be daft!

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Relative isotopic mass

Most people start with relative atomic mass but it makes sense to talk about relative isotopic mass first.

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

There is an alternative phrasing for this which some people find easier to understand.

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

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.

Use whichever seems more obvious to you while you are trying to understand this, but for exam purposes learn whichever is in your syllabus.

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Isotopes and relative atomic mass

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

(I'm using the version of the definition which I find easier!)

Relative atomic mass is given the symbol Ar.

"Weighted average" is also called "weighted mean". An example shows how this works.

An example using chlorine

This is an example where the numbers are so easy that you might well be expected to remember them.

Chlorine has two isotopes, Cl-35 and Cl-37, and ordinary chlorine contains these in the ratio of 3 atoms of Cl-35 to every 1 atom of Cl-37 (to a good-enough approximation for our purposes).

If you have a sample of chlorine it will contain unbelievably vast numbers of chlorine atoms, and it is useful to be able to give an average value for the mass of a chlorine atom. An average of 35 and 37 is 36, but that doesn't allow for the fact that there are three times as many Cl-35 atoms as Cl-37.

Relative atomic mass is a weighted average (often called a weighted mean) of the masses of the isotopes. That is an average which takes account of the different proportions of the various isotopes.

Suppose you had four typical chlorine atoms - 3 atoms of Cl-35 and 1 atom of Cl-37.

The total mass of the four atoms would be

(3 x 35) + (1 x 37) = 142

The "average" mass of one atom is therefore

142/4 = 35.5

If you look at the Periodic Table you will find that 35.5 is the figure quoted as the relative atomic mass of chlorine.

In case you are wondering about the units of relative atomic mass - there aren't any! It is a value which is measured relative to the mass of the C-12 isotope.

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Looking up relative atomic masses

Most Periodic Tables include relative atomic masses, and if you need them in exams, you will always be given any values necessary - either on a Periodic Table or in the question.

If you don't have a paper copy of a Periodic Table with relative atomic masses on, you can download and print one from this site.

Most Periodic Tables have two numbers against each atom - the atomic number and the relative atomic mass. The relative atomic mass is always the bigger one.

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Working out relative atomic masses from percentages

Suppose you had to work out the relative atomic mass of boron, given the following data.

A sample of boron contains

B-10    18.7%

B-11    81.3%

If you had 100 typical atoms, 18.7 would be B-10 and 81.3 would be B-11.

Note:  If it bothers you to have 0.7 or 0.3 of an atom, you could always take 1000 atoms instead, but that just involves more thought! The answer will be the same either way.

Total mass of 100 atoms = (18.7 x 10) + (81.3 x 11) = 1081.3

So relative atomic mass = 1081.3/100 = 10.8 to 3 significant figures.

Note:  You can't quote your answer to more than 3 significant figures because that is all the percentages are quoted to. You might argue that the mass numbers are only quoted to 2 significant figures, but in fact these are totally precise numbers. The mass numbers count the numbers of protons and neutrons in the atom. There is no error in this.

You mustn't quote answers more accurately than your least accurate input number.

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Relative molecular mass and relative formula mass, Mr

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.

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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

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Defining the relative molecular mass

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

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.

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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

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.

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

The "formula unit" is just the formula as you have written it - for example, NaCl or CuSO4.5H2O or CO2 or Cl2 or whatever.

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