# I need some clarifications about the mole, please

by yhPscis
Tags: clarifications, mole
 P: 17 1 mole of a substance equals the amount of grams needed for that substance to have 6.0221413e+23 (Avogadro's number) atoms in it, isn't it? In order to determine how many grams one mole of a substance is, I've learned that you just need to check the atomic mass number on your periodic table, take that number and put "gram" at the end. The thing I don't understand is, how come it's that simple? The atomic mass number is the number of protons and electrons (nucleons) in the atom, right? So how come 6.0221413e+23 times the mass of all nucleons ALWAYS amounts to the number of nucleons in grams for any substance? For example, carbon has an atomic mass number of 12 so 1 mole of carbon equals 12 grams of carbon. Hydrogen has an atomic mass number of 1 so 1 mole of carbon equals 1 gram of hydrogen. Is this some great coincidence? Or is there a link that I'm not seeing? I'm not sure I understood what a mole is and my research on it just confuses me, so there's why I'm asking. Thank you for reading and (hopefully) helping!
P: 23,363
 Quote by yhPscis The thing I don't understand is, how come it's that simple?
Because we selected amu value to be so.
P: 17
 Quote by Borek Because we selected amu value to be so.
Can you please explain how they did?

1 amu is the mass of 1 nucleon. The mass of a nucleon can't be chosen, it's fixed, it's a fact of nature that we can merely observe.

This source explains that scientists couldn't directly measure the mass of a nucleon so they created the relationship:

1 amu = 1/6.0221415 x 10^23 grams

I understand that 1 mole of 12 amu equals 12 grams following this relationship

6.0221415 x 10^23 = N = 1 mole

1 amu = 1/N g

N x 12 x 1 amu = N x 12 x 1/N g

<=> N x 12 x 1 amu = 12 x 1 g

<=> N x 12 amu = 12 g

But what I still don't get is, how did they know that the mass of a nucleon was equal to 1/6.0221415 x 10^23 grams ?

The gram is a fixed quantity too, so they couldn't just arbitrarily choose that relationship to fit their needs, right?

P: 395
I need some clarifications about the mole, please

 Quote by yhPscis 1 mole of a substance equals the amount of grams needed for that substance to have 6.0221413e+23 (Avogadro's number) atoms in it, isn't it? In order to determine how many grams one mole of a substance is, I've learned that you just need to check the atomic mass number on your periodic table, take that number and put "gram" at the end. The thing I don't understand is, how come it's that simple? The atomic mass number is the number of protons and electrons (nucleons) in the atom, right? So how come 6.0221413e+23 times the mass of all nucleons ALWAYS amounts to the number of nucleons in grams for any substance? For example, carbon has an atomic mass number of 12 so 1 mole of carbon equals 12 grams of carbon. Hydrogen has an atomic mass number of 1 so 1 mole of carbon equals 1 gram of hydrogen. Is this some great coincidence? Or is there a link that I'm not seeing? I'm not sure I understood what a mole is and my research on it just confuses me, so there's why I'm asking. Thank you for reading and (hopefully) helping!

Welcome to PF
You are a critical thinker, and your question is a nice one and it proves that you don't just take knowledge as constant information but a "why" question always pops in your mind Avogadro's is a selected number, it's not a coincidence at all that the mass of Avogadro's number is equal to the mass number, Avogadro's was precisely selected because they certainly knew that the mass of his number for any element atoms will be equal to its mass number, how come? That seems so weird!! But it's actually very simple, let's do some math to get to the bottom of this.
But first lets just point to some impotent things
Atoms consist of protons, neutrons and electrons
1 - protons and neutrons roughly have equal masses
2 - electrons' mass is negligible

So the mass of an atom = mass of neutrons + mass of protons = a.m.u x Mass number
Mass of "n" atoms = a.m.u x mass number x n
If n = the reciprocal of a.m.u then Mass of " n " atoms = Mass number
bingo !!! That reciprocal is Avogadro's number, Avogadro's number = 1/a.m.u
So mass of Avogadro's number of atoms = mass of proton or neutron x mass number x Avogadro's number = a.m.u x mass number x 1/a.m.u = mass number
So it's not a coincidence, Avogadro's number was selected to be the mass of one a.m.u reciprocal so that one mole of any substance becomes equal to its mass number, thanks to Avogadro, chemical calculations are very Simple.
P: 23,363
 Quote by ElmorshedyDr So the mass of an atom = mass of neutrons + mass of protons = a.m.u x Mass number
That's not true.

Mass of neutron is 1.674927351×10-27 kg

Mass of proton is 1.672621777×10-27 kg

Mass of alpha particle (helium nucleus) is 6.64465675×10-27 kg

Alpha particle is two neutrons and two protons, so its mass should be

2*1.674927351×10-27 + 2*1.672621777×10-27 = 6.695098256×10-27

Where is the missing 0.050441506×10-27 kg?
P: 17
 Quote by ElmorshedyDr Welcome to PF
Thank you.

 Quote by ElmorshedyDr So the mass of an atom = mass of neutrons + mass of protons = a.m.u x Mass number Mass of "n" atoms = a.m.u x mass number x n If n = the reciprocal of a.m.u then Mass of " n " atoms = Mass number bingo !!! That reciprocal is Avogadro's number, Avogadro's number = 1/a.m.u So mass of Avogadro's number of atoms = mass of proton or neutron x mass number x Avogadro's number = a.m.u x mass number x 1/a.m.u = mass number So it's not a coincidence, Avogadro's number was selected to be the mass of one a.m.u reciprocal so that one mole of any substance becomes equal to its mass number, thanks to Avogadro, chemical calculations are very Simple.
I think I understand the logic behind it:

Having n times the mass of an atom is practical in that it enables us to cancel out the number of nucleons in the equation (they're equal to 1)

mass of Avogadro's number of atoms = mass of proton or neutron x mass number x Avogadro's number

My only issue now is that this should be correct:

Avogadro's number = 1/mass of proton or neutron

But it isn't by my calculations

mass of proton = 1.6726×10^-24 g (according to wiki)
avogadro's number = 6.0221413x10^23 (according to google)

6.0221413x10^23 != 1/1.6726×10^-24

(the answer to 1/1.6726×10^-24 is 5.9787157718...x10^23 , going by my calculator).

Did I make a mistake in my calculations? Or did I actually not understand the logic that you explained?
 P: 395 My reply is not accurate 100%
P: 23,363
 Quote by yhPscis how did they know that the mass of a nucleon was equal to 1/6.0221415 x 10^23 grams ?
They didn't KNEW it, they DEFINED it as 1g/NA.

What they really did was they defined first 1 mole to be the number of atoms in exactly 12 grams of C-12. Selection of C-12 and 12 is arbitrary (actually in the past it was O-16 and 16 g). That allowed them to determine NA. Once they had NA, they calculated amu value - and this way it was guaranteed to work the way it does.
P: 395
 Quote by yhPscis Thank you. I think I understand the logic behind it: Having n times the mass of an atom is practical in that it enables us to cancel out the number of nucleons in the equation (they're equal to 1) mass of Avogadro's number of atoms = mass of proton or neutron x mass number x Avogadro's number My only issue now is that this should be correct: Avogadro's number = 1/mass of proton or neutron But it isn't by my calculations mass of proton = 1.6726×10^-24 g (according to wiki) avogadro's number = 6.0221413x10^23 (according to google) 6.0221413x10^23 != 1/1.6726×10^-24 (the answer to 1/1.6726×10^-24 is 5.9787157718...x10^23 , going by my calculator). Did I make a mistake in my calculations? Or did I actually not understand the logic that you explained?
I was thinking about that too, and I also did some calculations and I find out that there something going wrong, as I said before my reply isn't accurate 100% but it got the main logical idea I hope someone on the forum could edit a correction, I did my best
 Admin P: 23,363 Simple summation won't work for two reasons, First, mass of the nucleus is lower than the sum of masses of all nucleons by so called binging energy. Second, molar mass is the weighed average of masses of all isotopes present. That's why it was important to choose an isotope (C-12) and not an element (C) for the definition.
P: 17
 Quote by Borek They didn't KNEW it, they DEFINED it as 1g/NA. What they really did was they defined first 1 mole to be the number of atoms in exactly 12 grams of C-12. Selection of C-12 and 12 is arbitrary (actually in the past it was O-16 and 16 g). That allowed them to determine NA. Once they had NA, they calculated amu value - and this way it was guaranteed to work the way it does.
EDITED POST

So you're contradicting ElmorshedyDr's logic?

You're saying that they came up with Avogadro's number first and then calculated the amu value?
So the number of Avogadro isn't actually the reciprocal of the mass of a nucleon (chosen to make the mass of the nucleon cancel out in the equations so that the atomic number would remain)?

If that's correct, then how come their arbitrary choice (of the number of atoms in 12 grams of C-12) causes the mass of the atom to equal the atomic number in grams?

I'm sorry, I'm really doing my best, but I'm not sure I understand what you mean...
P: 23,363
 Quote by yhPscis You're saying that they came up with Avogadro's number first and then calculated the amu value?
Yes.

 So the number of Avogadro isn't actually the reciprocal of the mass of a nucleon
Exactly.

 If that's correct, why did they define Avogadro's number?
They defined mole, not the Avogadro's number. Once they defined mole, it was enough to count atoms in a mole (remember, exactly 12 g of C-12) to determine NA.

There is a plan to redefine the mole, and express it in terms of NA - that is, to define NA as being equal to some arbitrary value. But so far Avogadro's constant is not defined, but determined.
 P: 395 http://science.howstuffworks.com/avogadros-number.htm I really recommend reading this.
P: 17
 Quote by Borek Yes. Exactly. They defined mole, not the Avogadro's number. Once they defined mole, it was enough to count atoms in a mole (remember, exactly 12 g of C-12) to determine NA. There is a plan to redefine the mole, and express it in terms of NA - that is, to define NA as being equal to some arbitrary value. But so far Avogadro's constant is not defined, but determined.
I think you were answering me while I was editing my post, so you didn't see the change, but I'm still confused on:

how come their arbitrary choice (of the number of atoms in 12 grams of C-12) causes the mass of the atom to equal the atomic number in grams? How can something arbitrary fit so perfectly?

I don't understand how they could "define" the mass of a nucleon and not "know" it, given that grams are a fixed quantity of mass and the mass of a nucleon is a fixed quantity in nature that they could merely observe not choose, too...

If you're not seeing my problem, here's an example:

I "define" that the ball I'm holding has a mass of 2 kg. But when I lay it on my balance, it says that it weighs 9.81 newton here on earth. If the acceleration on earth equals 9.81 then the ball must have a mass of 1 kg (regardless of what I "defined"/chose earlier), it's not me who "defines" its mass, its mass is a fact of reality which I "know" because I calculated it.

 Quote by ElmorshedyDr http://science.howstuffworks.com/avogadros-number.htm I really recommend reading this.
I've read it, but it defines avogadro's number as the reciprocal of the mass of a nucleon (on the second page) which our calculations and Borek contradicts. :/
P: 17
 Quote by Borek They didn't KNEW it, they DEFINED it as 1g/NA.
Quote by Borek
 Quote by yhPscis So the number of Avogadro isn't actually the reciprocal of the mass of a nucleon
Exactly.
Wait, if 1 amu equals 1g/Avogadro's number (as defined), then Avogadro's number equals 1g/1 amu, right?
And 1g/1amu is the reciprocal of 1 amu, right?
And 1 amu is 1/12 of the mass of a C-12 atom, so it's the mass of one nucleon.
So that definition does say that Avogadro's number is the reciprocal of the mass of 1 amu, right?

Ugh, this is so confusing :(