# What's keeping us from simply redefining Avogadro's Number / the Mole as a definite integer?

This might be a question to ask in a Chemistry site, but because there is a lot of talk about redefining many units of measurements in terms of Avogadro's Number / the Mole, I was wondering why we don't just redefine the Mole to infinite precision, since it is basically inherently an integer.

This might be the only unit/physical constant that can be defined to infinite precision. The only unit that is an "integer".

I guess it's not really a physical constant, per se, in that it is not a property of nature. But then we can easily create a definition of the Kilogram that doesn't change over time as exactly something-something moles worth of Carbon-12.

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Firstly, you need an experiment to count the number atoms precise to 23 significant figures to know that definite integer... – KennyTM Nov 23 '10 at 6:46

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I'm asking why we can't just go the other way around...specify an exact integer to infinite precision and make the definition of 12 grams equal to the mass of that amount of Carbon-12 atoms. – Justin L. Nov 23 '10 at 6:58

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@Justin: Then the values in the past would all become wrong, if that exact number turns out doesn't fall within the error bound of the previous definition. – KennyTM Nov 23 '10 at 7:53

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@KennyTM: No this proposal has been seriously envisaged by metrologists. Your argument would also have applied to previous redefinitions of the second and metre. – Frédéric Grosshans Nov 23 '10 at 10:16

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– hwlau Nov 23 '10 at 10:48
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## 6 Answers

There was a proposal in 2006 trying to define NA as an exact number[1,2]: $$N_A^* = 84\;446\;888^3 = 6.022\;141\;410\;704\;090\;840\;990\;72 \times 10^{23}$$ the problem? This value is incorrect, as the currently most accurate result is[3] $$N_A = 6.022\;140\;84(18) \times 10^{23}$$ i.e. $N_A^*$ is now 3 s.d. away from $N_A$. As I have commented, if we randomly pick a number within the current error bound and call it $N_A$, we risk the problem that a better experiment for the old definition will invalidate the proposed value. To be safe about the validity of that number, you need to produce an equally accurate experiment to show that it is actually valid (like the 299792458 m/s in the definition of meter, and 9192631770 Hz in the definition of second.)

Also, the rationale for redefinition of SI base unit always involve that the current one isn't accurate enough or hard to realize:

• second (1967):

• the definition ... is inadequate for the present needs of metrology
• meter (1960):

• the international Prototype does not define the metre with an accuracy adequate for the present needs of metrology,
• it is moreover desirable to adopt a natural and indestructible standard,
• meter (1983):

• the present definition does not allow a sufficiently precise realization of the metre for all requirements
• candela (1979):

• the time has come to give the candela a definition that will allow an improvement in both the ease of realization and the precision of photometric standards, ...

Do the current experiments which reduces to NA = 12 gram of carbon-12 atoms not accurate enough or hard to realize? I don't think so; 9 significant figures are already very accurate. However, the redefinition of mole would be put on board on 2011 (24th CGPM). One proposal is to define[4] $$N_A \overset{\underset{\mathrm{def}}{}}{=} 6.022\;141\;5 \times 10^{23} \mathrm{mol}^{-1},$$ to decouple kilogram from the definition of mole. So if this path is taken, the only thing that keep us from defining it as a definite number to 10 significant figures is because "the conference haven't started yet".

But infinite precision? That would be a long way before we can reach and need that.

Ref:

1. Ronald Fox and Theodore Hill, A Proposed Exact Integer Value for Avogadro's Number. http://arxiv.org/abs/physics/0612087
2. Ronald Fox and Theodore Hill, An Exact Value for Avogadro's Number. http://www.americanscientist.org/issues/pub/2007/2/an-exact-value-for-avogadros-number/3
3. B. Andreas, Y. Azuma, G. Bartl, et. al., An accurate determination of the Avogadro constant by counting the atoms in a 28Si crystal http://arxiv.org/abs/1010.2317
4. Ian M Mills, Peter J Mohr, Terry J Quinn, et. al., Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005). http://iopscience.iop.org/0026-1394/43/3/006
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-1: This is ridiculous--- the definition is a definition. If you redefine the kilogram, it becomes correct. – Ron Maimon Oct 22 '11 at 6:15
@RonMaimon If you adopt a "wrong" value as the definition you introduce a new error in every measurement that went before. Certainly few of those earlier measurements had enough precision for this to matter, but there were some. For continuities sake you should (indeed, must) insure that your new definition agrees with the old one to the highest available precision. – dmckee♦ Jul 16 '12 at 14:04

The problem is that you want your unit definitions to be realizable - so specifying "1 mol is long number molecules, 1 gram is 1/12 of the mass of one mol of $C_{12}$" is nice for your thought process, but as long as there is no practical way to count molecules at such scales to a precision of better than $10^{-9}$ (which I think is the precision of the kilogram standard), there is no operational advantage to it.

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There is the advantage that you don't have to rely on Paris for your system of units. – Ron Maimon Oct 22 '11 at 6:16

Basically, you are proposing to redefine the kilogram, and your approach has been proposed and recently (in october 2010) abandoned ( http://en.wikipedia.org/wiki/Kilogram#Carbon-12 ). I think the reason why the Watt-balance approach has been preferred for the future definition of the kilogramme was mainly technological : it is more precise and would allow more practical realization of the kilogramme.

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Basically, there's no reason why we couldn't redefine the mole as as simple integer number of atoms or molecules. In fact, as other users have mentioned, there's a lot of people who'd like to do that.

On the other hand, that's not how chemists actually use the mole in practice. You simply can't count 6×10^23 atoms or molecules, nor do you need to. What is important for chemists is to know (for example) that there are the same number of atoms in 58 grams of iron as in 12 grams of carbon, and so on for all the other elements. It's not important to know exactly what that number is, just that it's the same number, and, for much of the history of chemistry, we had absolutely no idea what the number was.

I should point out as well that the mole is not the only unit which is an "integer". If you take the coulomb as a unit of electric charge, that should be equal to an integer number of elementary charges, shouldn't it? Actually, it's not, for historical reasons, and there doesn't seem to be much enthusiasm for making it an integer number of elementary charges either.

You can find my paper discussing this in more technical terms at http://precedings.nature.com/documents/5138/version/1

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No one can prove with 100% certainty that there are will be no benefits. In every discipline acquiring a higher degree of precision is advancement. Unless there is an uncertainty principal for a more precise definition, then the idea of striving for a higher precision should be encouraged. The fact that no one at the moment knows how to achieve a higher precision makes the task a perfect Phd project!

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In 2007, I submitted a letter-to-the-editors (AmSci, May/Jun2007, Vol. 95 Issue 3, p195). I suggested that the "half-life" decay of a mole of radioactive element should end with a whole atom; thus 20=1. Going in reverse, the current value of Avogadro’s Number is approximated by 279 = 604 462 909 807 314 587 353 088.

In a 1996 copyrighted pamphlet, “Mole, Bits, and Cubes” (TXu000593728), I submitted that this Binary definition should be the value of Avogadro’s Number. It is invariant, free of dimensionality, and free of all the physical measurements currently being used to “hone in” on a value that seems far too prejudiced considering it is all tangled up with a chunk of metal that needs periodic cleaning that removes few bits of matter in the process and is subject to experimental errors in measurements (80 parts in a billion? and at what accuracy).

With No = 279, the kilogram is as good as measurements can determine the purity, number, and atomic mass of the units of whatever material (e.g., the silicon-28 sphere that is being proffered) is being measured and the standard on which the standards folks make the reference point. Thus, a binary mole of absolutely pure carbon-12 would currently weight precisely 12.0· grams and always be so until they changed the reference point from C-12. At least Avogadro’s “Number” would finally be a “constant” – one and the same.

What I see is a great effort (by those who will be making a decision) not to alter the massive weights and measurements structure that is in place throughout the world of commerce. In that realm, Avogadro’s Number/constant is not a factor - only the size of the “king’s foot”; in this case “Le Gran K” or an article representing it. Science takes second place in this realm; but, then it is scientists who are doing the "defining"!

See http://pages.swcp.com/~jmw-mcw/binary_mole.htm for definition of the binary mole.

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