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I learning basic chemistry and i have a doubt.

I have this definitions

Molar mass: Is the mass of $6.022\times10^{23}$ atoms of a chemical element and its unit of measurement is $\mathrm{g/mol}$.

In the periodic table, for example, beryllium has two numbers: $4$ and $9.0122$. I know that $4$ is the number of protons, but I have the doubt with $9.0122$.

I know that $9.0122$ is given in $\mathrm{g/mol}$, therefore $9.0122$ is the mass of $6.022\times10^{23}$ atoms of beryllium, and is given by the average of the mass of one mole of each isotope of the beryllium.

But I know that is the mass number and is the amount of protons + neutrons. (And how is possible that is not an integer number?)

So, what is this number really? the mass of one mole of the element or the sum of protons + neutrons?

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Atomic mass is not exactly proportional to the mass number of the nucleus. Let's look at all the complicated factors that appear in one little atomic mass value:

  • Particles: Protons and neutrons do not have exactly the same mass
  • Binding Energy: The mass of a nucleus is less than the sum of the individual protons and neutrons because energy is lost (so mass is lost, $E=mc^2$) when the nucleons bind together.
  • Averaging over isotopes: On top of that there are isotopes, and they have different numbers of neutrons therefore different atomic masses; when we see a single number it's usually averaged among all the atoms of a typical sample, usually as the element occurs on Earth.
  • And in light of all those things, whatever unit we define for atomic mass. (I believe it is now a gram divided by a defined value for Avogadro's number.)

With all those factors in play, you're basically not going to get a whole number for atomic mass in the Periodic Table.

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So, what is this number really? the mass of one mol of the element or the sum of protons + neutrons?

The number is the molar mass expressed in g/mol, i.e. stripped off these units. (The molar mass is the mass of a sample of the element divided by its amount of substance. This explains why the units are g/mol.) Alternatively, you can also say the number is the relative atomic mass (historically known as standard atomic weight). The way the two are defined results in the same numeric value when the molar mass is given in g/mol (the relative atomic mass is dimensionless, so it has no units at all).

Elements with a single stable isotope

In the periodic table, for example the beryllium have two numbers: 4 and 9.0122. I know that 4 is the number of protons, but i have the doubt with 9.0122

Beryllium has a single stable isotope, $^9\ce{Be}$, with 4 protons and 5 neutrons. The mass number of this isotope is 9, and the molar mass is 9.0122 g/mol. The molar mass is not exactly 9 g/mol because the molar mass of protons and neutrons is not exactly 1 g/mol, and because there is a mass defect related to the famous $E = m c^2$ relationship.

Elements with more than one stable isotope

Take boron, for example. The two stable isotopes are $^{10}\ce{B}$ and $^{11}\ce{B}$. You get the molar mass of terrestrial boron by a weighted average of the molar masses of these two isotopes (or more practically by measure the mass and getting the amount of a fairly pure sample of boron).

https://upload.wikimedia.org/wikipedia/commons/9/92/NuclideMap.PNG Source: https://upload.wikimedia.org/wikipedia/commons/9/92/NuclideMap.PNG

See also: https://chemistry.stackexchange.com/a/114484/72973

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