# Can "mole" unit only be integer values?

1. Nov 26, 2015

### pyroknife

I am confused about the concept of a mole. Avogadro's # says that 1 mole has 6.023*10^23 particles.
Does it make sense to talk about moles in a non-integer sense?
For example, can you say that 1/2 mole has 1/2*(6.023*10^23) particles?

2. Nov 26, 2015

### phyzguy

Yes, you can certainly talk about 1/2 mole, which has 3.0115*10^23 particles, or 1/10 mole, which has 6.023*10^22 particles, or 1/1000 mole, which has 6.023*10^20 particles. Perhaps your confusion lies in the fact that you must have an integer number of particles. But Avogadro's number is so huge, that you cannot resolve it down to the level of individual atoms. To do this, you would have to tell the difference between the number:
602,300,000,000,000,000,000,000
and the number:
602,300,000,000,000,000,000,001
No measuring device is that precise. So you are always talking about an approximate number of particles.

3. Nov 26, 2015

### Staff: Mentor

Actually there is a proposal to redefine mole to be an integer number.

Technically it IS an integer number even now, as it is "number of atoms in exactly 12 g of C-12". We are just limited by the accuracy with which we can define and measure mass.

4. Nov 26, 2015

### SteamKing

Staff Emeritus
Now, if you'd like to volunteer to count the number of atoms in 12 g of carbon ...

5. Nov 26, 2015

### Staff: Mentor

Didn't they try to redefine 1kg as a certain and exact amount of atoms?

6. Nov 26, 2015

### SteamKing

Staff Emeritus
That's just one proposed method for defining the kilogram:

https://en.wikipedia.org/wiki/Kilogram

See the section on "Atom Counting"

There are other proposals for defining the kilogram in terms of certain fundamental constants, like Planck's Constant, but no agreement has yet been reached by the international body in charge.

7. Nov 26, 2015

### Staff: Mentor

Thank you. I thought they were closer.

8. Nov 26, 2015

### James Pelezo

Well, by NIST standards Na = (6.0221415 ± 0.0000010) × 1023 units, provided that atomic mass of C-12 remains constant over time... but, of course it does not ... Interesting challenge.

9. Nov 27, 2015

### Staff: Mentor

What do you mean by that? If you are talking about the fact that the mass of the International Prototype Kilogram in Paris changes with time, this has nothing to do with the properties of 12C changing, but is simply related to the imperfections of an actual artifact.

10. Nov 27, 2015

### DrDu

Even the number of particles can be non-integer, e.g. when you talk about statistics, so there is even less problem with the number of moles being non-integer.

11. Nov 27, 2015

### James Pelezo

In this case, I can only reply to what I have read. The note specifically postulates that C-12 has changed with time, but, granted, it does not specify anything relating to properties of C-12 ... Here's the excerpt and reference...

These changes cannot be measured exactly, simply because there is no "perfect" reference against which to measure them—Le Gran K is always exactly one kilogram, by definition. It is estimated that Le Gran K may have changed about 50 micrograms—that is, roughly by about 150 quadrillion (1.5 × 1017) atoms—since it was constructed. This implies that by current measurement conventions, the mass of a single atom of carbon-12 is changing in time, whereas modern theory postulates that it remain constant.
http://www.americanscientist.org/issues/id.368,y.0,no.,content.true,page.1,css.print/issue.aspx

My apologies if I've misunderstood your point of issue.

12. Nov 28, 2015

### Staff: Mentor

The key part of the quote is
The mass is apparently changing because the standard keeps changing as the IPK loses or gain some atoms as it is manipulated.

13. Nov 28, 2015

### Staff: Mentor

This is poorly worded. The mass of an atom is not changing over time. The mass of the kilogram prototype is changing over time. So as the mass of the kilogram changes the number of atoms per kilograms must change in order for the mass to remain constant.

14. Dec 6, 2015

### James Pelezo

I'm confused by the wording of the underlined statement... 'as the mass of the kilogram changes the number of atoms per Kg must change => constant mass'? This sounds like a 'Yogi-ism'... 'If ya come to a fork in the road, take it' ... confusing, huh? That is, how does the number of atoms changing result in a constant mass?

Last edited by a moderator: Dec 7, 2015
15. Dec 7, 2015

### Staff: Mentor

He means "as the mass of the kilogram prototype changes".

16. Dec 8, 2015

### James Pelezo

OK, thanks... that makes more sense.