GCSE · Chemistry · Edexcel · Spec 1CH0

Calculating relative atomic mass from isotopic abundances

Picture a bag of 100 chlorine atoms: 75 with a mass of 35, 25 with a mass of 37. What does one atom weigh, on average?

Predict first

Where does the mean land?

Each bag holds 100 atoms of just two isotopes: chlorine-35 (mass 35) and chlorine-37 (mass 37). The tag shows how many are chlorine-35 : chlorine-37. Drag each marker to where you think that bag's mean atomic mass sits, then check.

75:25 — 75 Cl-35 : 25 Cl-37 (this one is real chlorine)50:50 — 50 Cl-35 : 50 Cl-3725:75 — 25 Cl-35 : 75 Cl-37

Don't mix these two up

Mass numbervsRelative atomic mass (Ar)

One is about a single atom. The other is about the whole element.

Focus

What it describes

Mass number

The protons plus neutrons in one atom

Relative atomic mass (Ar)

The mean mass of an element's atoms, taking their abundances into account, compared with 1/12 of a carbon-12 atom

The insight

One atom versus the mean of many atoms. That's the whole difference.

Always a whole number?

Mass number

Yes, always

Relative atomic mass (Ar)

No, not always (chlorine's is 35.5)

Where you meet it

Mass number

In an isotope's name, such as chlorine-37

Relative atomic mass (Ar)

On the periodic table

What isotopes do to it

Mass number

Isotopes of an element differ: same number of protons, different number of neutrons, so different mass numbers

Relative atomic mass (Ar)

One value for the element, averaged across all its isotopes

Which idea sounds like yours?

Why is chlorine 35.5?

Chlorine has two isotopes, chlorine-35 and chlorine-37. Its relative atomic mass is 35.5, not 36.

Which idea is closest to what you think right now?

You just average the two masses: (35 + 37) ÷ 2.Some chlorine atoms really do have a mass of 35.5.It's a mean that counts each isotope by its abundance, so it sits nearer 35.Two isotopes means half the atoms are each.

How sure are you?

I'm sureI think soI'm guessing

You just average the two masses: (35 + 37) ÷ 2.

This is a common misconception

That sum gives 36, not 35.5. A simple average quietly treats the two isotopes as equally common, and they aren't: 75% of chlorine is chlorine-35 and only 25% is chlorine-37.

Some chlorine atoms really do have a mass of 35.5.

This is a common misconception

No chlorine atom does. Each atom is chlorine-35 or chlorine-37, with a whole mass number. 35.5 only exists as an average over all the atoms.

It's a mean that counts each isotope by its abundance, so it sits nearer 35.

This matches the evidence

Exactly. More of the atoms are chlorine-35, so they pull the mean toward 35. That's a weighted mean, and the next block shows how to calculate one.

Two isotopes means half the atoms are each.

This is a common misconception

Not always. Abundances vary from element to element, and chlorine is 75% chlorine-35 and 25% chlorine-37. A half-and-half split would put the mean at 36.

Every atom has a whole mass number, but relative atomic mass is the mean over all the atoms, with each isotope counted by its abundance. That's why 35.5 is real and no atom weighs it.

Chlorine, step by step

Problem

Chlorine is 75% chlorine-35 and 25% chlorine-37. Work out its relative atomic mass.

Your turn

Boron: fill in the gaps

Boron is 19.9% boron-10 and 80.1% boron-11. Calculate its relative atomic mass.

Pair each mass with its own abundance: boron-10 with 19.9, boron-11 with 80.1.
missing step

Which line is step 2?

Add the two masses first: 10 + 11 = 21.Multiply each mass by its abundance: 10 × 19.9 = 199 and 11 × 80.1 = 881.1.Multiply the two abundances together: 19.9 × 80.1.

Check the working

Copper: find the costly line

A student finds the relative atomic mass of copper (copper-63 at 69.2%, copper-65 at 30.8%) to one decimal place. One line costs them the mark. Which one?

A student's answer — which line goes wrong?

Copper-63 has an abundance of 69.2% and copper-65 has an abundance of 30.8%.
Method: multiply masses by abundances, add the results, then divide by the sum of the abundances.
63 × 30.8 = 1940.4 and 65 × 69.2 = 4498, so the total is 6438.4.
The abundances add up to 69.2 + 30.8 = 100.
6438.4 ÷ 100 = 64.384
The relative atomic mass of copper is 64.4 (to one decimal place).

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

What you need to know

Isotopes are atoms of one element with the same number of protons but different numbers of neutrons, so their mass numbers differ.
Abundance is the proportion of an element's atoms that are a particular isotope.
Have a goIn a sample of 200 atoms of an element, 50 are one particular isotope. What is that isotope's abundance as a percentage?
25%
Abundance is the proportion of the atoms that are that isotope: 50 out of 200 is a quarter, which is 25%.
Abundances vary between elements: chlorine is 75% chlorine-35 and 25% chlorine-37, not half of each.
Have a goSam says: "Two isotopes? Easy, 50 of each in a bag of 100 atoms." For chlorine, how many chlorine-35 atoms is Sam short by?
25
Abundances vary from element to element: a bag of 100 chlorine atoms has 75 chlorine-35 atoms, not 50.
Relative atomic mass (Ar) is the mean mass of an element's atoms, taking abundances into account, compared with 1/12 of a carbon-12 atom.
Calculate Ar by multiplying each isotope's relative mass by its abundance, adding, then dividing by the sum of the abundances.
When abundances are percentages, they add up to 100, so you divide by 100.
Have a goMass 4 makes up 90% of an element's atoms and mass 14 makes up 10%. What total do you get from multiplying and adding, before you divide?
500
4 × 90 = 360 and 14 × 10 = 140, which add to 500. Dividing by the sum of the abundances (100) then gives an Ar of 5.
Chlorine's Ar comes out at 35.5, not 36, because three-quarters of its atoms are chlorine-35.
Ar isn't always a whole number because it's a mean; a mass number, counting one atom's protons and neutrons, always is.
Most periodic tables round Ar to a whole number, except chlorine (35.5) and copper (63.5); some quote one decimal place.

The big picture

Relative atomic mass (Ar) is the mean mass of an element's atoms, taking each isotope's abundance into account. So it sits nearer the more abundant isotope and doesn't have to be a whole number. To work it out, multiply each isotope's mass by its percentage abundance, add the results, then divide by the sum of the abundances (100 for percentages).

Key points

1Ar = (sum of each isotope's mass × abundance) ÷ (sum of the abundances).

2With two isotopes, Ar sits nearer the mass of the more abundant one, and only halfway if the abundances are equal.

3Ar needn't be a whole number, but a mass number always is.

4Averaging the isotope masses without using abundances is the classic wrong answer.

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Worked example

Problem

A made-up element has two isotopes: mass 50 at 60% abundance and mass 52 at 40% abundance. Calculate its relative atomic mass.

⚠ Watch out

Dividing by 2 because there are two isotopes. You divide by the sum of the abundances, which is 100 when they're percentages.

🧠

Memory hook

Bigger crowd, bigger pull: the isotope with more atoms drags the mean toward its own mass.

✓

Check yourself

Isotopes of mass 8 (30%) and mass 10 (70%): is Ar nearer 8 or 10? Predict first, then calculate. You should get 9.4.

Flashcards

(11)

What is an isotope?

An atom of an element with the same number of protons but a different mass number, because it has a different number of neutrons.

What is the abundance of an isotope?

The proportion of the atoms of the element that are that isotope.

True or false: an element with two isotopes is always 50% of each.

False. Abundances vary from element to element. Chlorine is 75% chlorine-35 and 25% chlorine-37.

What is relative atomic mass (Ar)?

The mean mass of an element's atoms, taking their abundances into account, compared with 1/12 of the mass of a carbon-12 atom.

Say the method for Ar in words.

Multiply each isotope's relative mass by its percentage abundance, add the results, then divide by the sum of the abundances.

What do percentage abundances add up to?

Always 100, so you divide by 100.

Where does Ar sit between two isotope masses?

Nearer the mass of the more abundant isotope. It is halfway only if the abundances are equal.

Why isn't relative atomic mass always a whole number?

It's a mean that takes account of the different abundances of the isotopes, so it can fall between whole numbers.

How do mass number and relative atomic mass differ?

Mass number counts the protons and neutrons in one atom and is always whole. Relative atomic mass is the mean mass of the element's atoms and isn't always whole.

Why isn't chlorine's Ar the simple average, 36?

A simple average treats both isotopes as equally common. Chlorine is 75% chlorine-35, so the mean sits nearer 35, at 35.5.

Which two elements do most periodic tables not round to a whole number?

Chlorine (35.5) and copper (63.5). Some tables quote relative atomic masses to one decimal place.

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Where does the mean land?

Why is chlorine 35.5?

Boron: fill in the gaps

Copper: find the costly line

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