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## AP®︎/College Chemistry

### Course: AP®︎/College Chemistry>Unit 1

Lesson 1: Moles and molar mass

# Average atomic mass

The average atomic mass (sometimes called atomic weight) of an element is the weighted average mass of the atoms in a naturally occurring sample of the element. Average masses are generally expressed in unified atomic mass units (u), where 1 u is equal to exactly one-twelfth the mass of a neutral atom of carbon-12. Created by Sal Khan.

## Want to join the conversation?

• So the atomic mass unit is 1/12th the mass of carbon-12. And the average atomic mass of hydrogen is approximately 1 relative to this value. So, wouldn't one atom of hydrogen be more ideal for the amu, especially when finding the relative atomic mass? So I'm just wondering why it had to be 1/12th of carbon??
• Good question that requires a kind of long explanation!

A long time ago, the standard for measuring average atomic mass was actually based on oxygen, and scientists thought all oxygen was oxygen-16 (8 protons, 8 neutrons). But after isotopes were discovered (oxygen-17, oxygen-18, etc), everything got really confusing, so scientists agreed to use carbon-12.

The average atomic mass for hydrogen is actually around 1.008 amu. Protium is by far the must abundant isotope of hydrogen, and it only contains 1 proton, and no neutrons. The relative abundance of Deutrium (1 proton, 1 neutron) is so small that it is barely accounted for when calculating the average atomic mass. So the mass of a proton is around 1.008 amu, not 1. Following this logic, the carbon-12 atom's atomic mass should actually be 12.09 amu; however, the mass is exactly 12 amu. Why?

The missing mass is called mass defect, and it represents the binding energy. Since the nucleus is full of protons, which has positive charge, they would repel and the nucleus would fly apart. Binding energy is the energy that holds the nucleus together. Because of energy-mass equivalence (E = mc^2), we know that energy and mass are interchangeable. Some of the mass of the atom gets converted into binding energy, so the mass of the entire nucleus would actually be less than the mass of each individual proton and neutron added together. This is why the mass of carbon-12 is 12 amu, not 12.09.

Scientists used carbon-12 because no other atom has exact whole-number masses in the amu scale. Also, scientists needed a pure isotope to base the system on.
• What does it mean to say Carbon-12's neutron has 1.008amu? Since an amu is 1.660540*10^-27, does that mean that C-12's neutron is equal to 1.008*1.660540*10^-12? I don't really understand the math.
• I don’t think that’s how you should be thinking about this. A carbon-12 atom has a mass of exactly 12 unified atomic mass units.
Protons and neutrons in an atom have less mass than if they are unbound, the difference is called mass defect.
• Hi! Here are some brief notes that I took in the video. If I got anything wrong, feel free to comment below (I would appreciate it)!

Atomic mass unit (or "amu") - also known as "u", or "unified atomic mass unit".
★ u = 1.660540*10^-27kg (I know... what a number!)

Proton - about 1 u (more closely, 1.007)
Neutron - 1 u (more closely, 1.008)
Electron - almost one two thousandth of a proton or neutron (in other words, really small!)

★ The number under the elements in the periodic table (for example, the "1.008" in Hydrogen) is the "aam", or average atomic mass.

Average atomic mass - weighted average of various versions of the element (ex. 1.008 is the aam of Hydrogen).

Isotopes - same element w/ different # of neutrons.

My question: How many "versions" are there for each element? Is there an infinite # of versions? And if so, how do you calculate that average (aam)?
Edit: Actually, the next video goes into calculating the aam. But I'm still wondering about how many versions there can be for an element.

I hope this helps! Wherever you are in the world, I wish you luck in chemistry and whatever courses you will be taking in the future!
• I am assuming that when you say versions, you mean the various isotopes of an element? In that case, there aren't an infinite amount of versions; there is a set amount. I'm pretty sure there are some elements with ~36 isotopes, and there probably is more to discover. But there definitely isn't an infinite amount. As for the average atomic mass, we only are able to calculate it based on the isotopes that we know. Hopefully this helps and if I missed anything, feel free to add :)
• It's very useful to have the average masses of atoms on the periodic table, but how did we actually measure the mass of a neutron or a proton?
• A proton's mass can be measured in a mass spectrometer which accelerates a proton through an electric field where it is deflected by a perpendicular magnetic field. The amount of deflection determines the mass of the charged particle. The more a particle is deflected, the less mass it has. We also use this method to determine the masses of molecules. Mass spectrometry only works on charged particles so only the proton's mass can be determined directly using this method since the neutron has no charge.

For the neutron, an indirect method using mass spectrometry is utilized. A proton's mass can be determined, as can a deuterium's mass using mass spec. Deuterium is one of the less abundant isotopes of hydrogen which contains only 1 proton and 1 neutron. You can essentially find the difference in mass between the deuterium and proton to find the mass of the neutron. Hope that helps.
• At you said that a proton's mass is 1.007 u_ but when you showed the periodic table, the mass of Hydrogen was 1.008 _u. Isn't 1.008 u_ the mass of neutron? But Hydrogen doesn't have a neutron. Then why is the mass of Hydrogen 1.008 when the mass of a protonis 1.007 _u?
• The mass on the periodic table is the average mass of a hydrogen atom, taking into account its three natural isotopes.
You can’t say “hydrogen doesn’t have a neutron” because two of its natural isotopes do, this pushes the average mass up ever so slightly.
• I have a question. How was the atomic mass unit actually calculated and how was the specific 1.66×10^-27 kg number discovered. Also, how was the proton and neutron found to be close to this number? Thanks!
• Initially, the atomic mass was calculated taking 1 a.m.u. to be the mass of one hydrogen atom. But this method was not giving values as whole numbers or simple decimal numbers, extending to many decimal places which complicated calculations. Oxygen was used for a very brief period in place of hydrogen. Carbon was used since its abundantly available and gave whole numbers when used in place of hydrogen.
• How can 80%(5AU) + 205(6AU) be equal to 5.2 AUs?
• Because it's a weighted average. If 80% of the atoms are 5U and 20% of the atoms are 6U, in a sample of 100 atoms, roughly 80 of them will be 5U, and roughly 20 of them will be 6U. If you take the average of all those atoms (80*5 + 20*5)/100, you get 5.2.
• Why is the average `5.2` instead of `5.5`?
• It we wanted the arithmetic average then it would be 5.5 because (5+6)/2 = 5.5. But for average atomic mass we're calculating a weighted average. The difference between the two types of averages is that an arithmetic average are of equal importance, but a weighted average takes into account the importance of some values over others. For average atomic mass, the isotopes of an element are found in difference abundances or amounts in nature. This means that certain isotope's atomic masses contribute more to the element's average mass than other isotopes.

For the hypothetical element Sal is describing, 80% of the element's atoms have an atomic mass of 5 amu, while only 20% have an atomic mass of 6. For this calculation we multiply the masses by their percentages and sum them up to find the weighted average. Keep in mind for percentages to be used in a calculation like this they need to be in decimal form. So 80% is 0.80 and 20% is 0.20. This means the calculation is: 5(0.80) + 6(0.20) = 5.2 amu.

Hope that helps.
• Hello! I'm wondering why neutron's are larger than protons? Because protons are positive while neutrons are neutral, shouldn't protons be larger? I'm most likely thinking about this the wrong way, but does anyone know why they equal the amount that they do?