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## Chemistry library

### Course: Chemistry library>Unit 1

Lesson 1: Introduction to the atom

# Worked example: Atomic weight calculation

How to calculate atomic weight from atomic mass and percent abundance of carbon isotopes. Created by Sal Khan.

## Want to join the conversation?

• If Carbon-12 has an atomic mass of 12 amu, why does Carbon-13 have 13.0034 amu? Why isn't 13 amu? •   It's because of something called binding energy.
Carbon-12 has a mass of 12 amu by definition. Theoretically, this would mean that each proton and each neutron has a mass of one amu, but this turns out not to be so. The actual mass of a proton is about 1.007 amu, and the mass of a neutron is about 1.008 amu. If you add the masses of six protons and six neutrons, you get 12.09. So why does C-12 have less mass than the sum of its components? The extra mass is converted to energy (E = mc2), which is released. This energy is called binding energy. Because of this energy being released, a carbon-12 nucleus is more stable than six protons and six neutrons are by themselves. If you put the energy back in, then the nucleus would fly apart.
Anyway, back to carbon-13. Now, it seems like carbon-13 should have a mass of 13, because it seems like all of the extra mass from the neutrons and protons turns into binding energy, right? Nope! In this case, we don't need to lose the whole 0.008 amu worth of energy to keep that extra neutron bound in place. In fact, we only need to convert 0.0046 amu into energy. The rest of it stays, and that is why carbon-13 has a mass of 13.0034 amu.
Hope this helps!
• Just wondering: can an atom be an isotope and an ion at the same time? •   All atoms are isotopes. All ions are atoms.
• why is only carbon-12 and carbon-13 used to find the atomic weight, aren't you supposed add the total weight of all carbon to find the atomic weight? i'm really confused about this? •   Do you mean why don't we also include other isotopes in our calculations, such as carbon-14? Only carbon-12 and carbon-13 are present in significant amounts, so it's okay to include just these two in our calculations. Of course, very precise calculations would need to include all isotopes, even those that are very rare.
• How do they determine the amount of each elements' different isotopes there are on the planet? Even if we could accurately measure this, wouldn't it fluctuate and change the average constantly? •  I would guess that somebody went around and took enough samples to have statistically significance. They then checked the samples to find the ratios. The interesting thing is that if the samples are taken on say Venus it would be different. Thus the periodic table on Venus would have different atomic weight values.
• Carbon-12 is exactly 12 amu as definition and it has 6 protons and 6 neutron (neglecting electrons) then 1 proton or neutron should also equal 1 amu exactly?? I asked it before and carried to binding energy but it is confusing... plz explain briefly. •  The mass of a neutral Carbon-12 atom is exactly 12 u, which means it includes the bound mass of protons and neutrons, as well as the mass of the electrons.

The binding energy that holds the protons and neutrons together comes from some amount of mass such that E=mc^2. If you change the number of bound neutrons or protons, you also change the energy required to bind them together, thus the total mass changes. This is also why individual, unbound protons or neutrons have a mass more than 1 u.
• This question is for both 12C and 13C. Where is the 98.89% and the 1.110% derived from?
I was under the impression 12C and 13C are both different isotopes for Carbon.

Secondly, I wanted to ask what is the reasoning for adjusting the decimal to the left?

Thank you! • If you hypothetically take a bag of 1000 carbon atoms on earth, you find that on average ~989 of them are carbon-12 and ~11 are carbon-13. If you repeat that a billion times you'll get the odd atom of carbon-14 here and there too, but still basically the same amount of carbon-12 to carbon-13, about 98.9% to 1.1%. The percentages of these isotope can be measured by using a special mass spectrometer.

He's adjusting the decimal because he is trying to calculate the average mass of one random carbon atom on earth. It's easier to use decimals in a calculator than percentages. To convert a percentage to a decimal you divide by 100, which is the same as moving the decimal point two places to the left.
• I'm confused, if this is an average, why 12.01 was not divided by 2? is it not suppose that the average of something is the sum of its parts and then divided by that same number? • If each isotope was in equal proportions (eg. each made up 50%) that would work, but that isn't the case here. One isotope makes up ~99% of all carbon, the other makes up ~1%. Clearly the isotope that makes up 99% needs to be given more importance.

There is more than one way to take an average. What you generally think of when you hear average is called the arithmetic mean, this average is called the weighted mean.
• It's so cool that math is involved in chemistry!! Maybe chemistry won't be so bad next year :)

I kind of asked this question last video, but more specifically, can there be 11C, with 6 protons and 5 neutrons? I get how 12C and 13C can get the atomic weight of 12.01, but are there more versions of carbon like 11C or... 15C? I don't get how the aam can be 12.01 unless only 12C and 13C exist (or other numbers that can reach that average).

*Edit: NOW I understand! The percentages explain how much carbon in the world has an atomic weight of ___.*

Now I'm wondering how people know about the percentages? How do people know how 12C is 98.89% and 13C is 1.110% in the world? • Currently isotopes of carbon from carbon-8 to carbon-23 have been observed. Most carbon atoms are carbon-12 which is why the average atomic mass of carbon is dominated by the atomic mass of carbon-12.

We use a technique called mass spectrometry is essentially sort the isotopes of a particular element and to know the abundance of each isotope in a sample. To get the average atomic mass of an element which can be used worldwide, we take samples of the element from multiple places around Earth and average all these samples.

Hope that helps.
• does that mean that the atomic weights are only related to Earth not as a whole universe?? • I know that different isotopes of a same element have same chemical properties. So, does the difference in number of neutrons have any effect on isotopes? I mean, are there any cases when different isotopes show different properties? 