# $1.7\cdot 10^{-24}$ mole apples a day

As the title suggests I was wondering why the International Bureau of Weights and Measures decided a mole to be a standard (SI-)unit. After some research I found I was not alone with this problem.

The core of my question is:

1. How is the unit “mole” necessary as a standard unit?
2. If mole is the standard unit, why wouldn't I have a give all numbers in mole?

Of course a mole is a convenient unit but I can't see how it is as fundamental as i.e. a meter, as it is clearly based on the concept of counting the atoms.

EDIT: Due to the first answer I got I realized my question is probably misleading: by fundamental I do not mean dictated by nature but considered a base unit. The need of units is obvious in the case of meters and seconds: no matter how you want to measure time or length, you will necessarily have to compare it to some standard (in this case meter and seconds, independently of how they are defined). In the case of "number of particles" this is not needed, instead one could say they are compared to "1". This is normally not considered a unit. Is this difference only a personal opinion?

• Feb 4 '14 at 15:58
• In the case of "number of particles" this is not needed, instead one could say they are compared to "1". You are correct, but comparing it to $6.023\times 10^{23}$ is a more convenient thing to do as it brings the resultant comparisons to easily manageable scales and values. Feb 4 '14 at 16:15

A unit like the mole is obviously convenient for chemists because you can make simple statements like two moles of hydrogen react with one mole of oxygen to produce one mole of water. Any unit that was not a multiple of atoms would conceal the simplicity of the reaction.

Given that you want your unit to be convenient for everyday use it makes sense to choose a value that is easy to count. A mole is 12g of carbon, or 1g of hydrogen and so on, and for chemists weighing out their reagents this makes it an easy unit to work with.

That's why the mole became a popular unit. Whether it's a necessary unit is debatable and depends on exactly how you define necessary.

## Now re your question 2:

Consider the second. Is the definition of the second any more fundamental than the definition of the mole? It's not obvious to me that the number $9.192631770 \times 10^9$ is any more fundamental than $6.023 \times 10^{23}$. Yet we all use seconds because it's a convenient unit like the mole.

But we don't give all times in seconds. I count my age in years not seconds because the year is a far more convenient unit to use for large time intervals. Likewise I count my apples in ones (or possibly dozens) not moles, again because it's a far more convenient unit when dealing with small numbers.

That's why you shouldn't give all numbers in moles, but instead choose the one, dozen, gross or whatever unit makes life easiest.

## And finally:

Just for the record, the metre isn't a fundamental unit. It's derived from the definition of the second and the speed of light.

And also for the record, the mole (well, Avagadro's number) is being promoted as a way of defining the kilogram.

• Wouldn't expressing an exact quantity (like the number of apples) in moles introduce a high imprecision, since the conversion factor is not exact? Feb 4 '14 at 15:51
• The mole is defined to about one part in $10^7$. I wouldn't say that was a high imprecision. I'd be quite happy to know the number of apples I have to one part in 10 million. Feb 4 '14 at 15:55
• As I don't feel like you answered the question I was thinking about I introduced an edit. Feb 4 '14 at 15:55
• And: at least where I live, the law requires i.e. companies to label there products using SI-units. Thus the appropriate unit for eggs would be mole... Feb 4 '14 at 16:01
• The mole is the SI unit for amount of substance. It's not a unit for the number of things. It would only be appropriate for eggs when the quantity of eggs was so great that it was effectively infinitely divisible. I doubt your local companies will be prosecuted for not labelling their packs of eggs in moles. Feb 4 '14 at 16:25

This question got me thinking, but luckily the guys who defined the mole thought about the implications of a fixed unit for all kinds of amounts (the number of things). Interestingly, this is connected to the question why people are required by law in some places to use the meter as a length unit, but are not required to give temperatures (e.g. in the forecast) in Kelvin.

If you look at the brochure published by the International Bureau of Weights and Measures on page 114 (page 22 in the PDF) you will see a section called 'Unit of amount of substance (mole)'

It states (emphasis mine)

2.1.1.6 Unit of amount of substance (mole)

[...] It is important to always give a precise specification of the entity involved (as emphasized in the second sentence of the definition of the mole); this should preferably be done by giving the empirical chemical formula of the material involved. Although the word “amount” has a more general dictionary definition, this abbreviation of the full name “amount of substance” may be used for brevity. [...]

So to answer your question: People are not obliged to sell apples and eggs in moles, because it's not an SI unit for amount, but for amount of a (chemical) substance.

Regarding the temperature you also see

2.1.1.5 Unit of thermodynamic temperature (kelvin)

[...] Because of the manner in which temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol T, in terms of its difference from the reference temperature $T_0 =273.15\;\text K$ , the ice point. This difference is called the Celsius temperature [...]

So besides clearly referring to the Celsius temperature, the definition of the Kelvin deals with thermodynamic temperatures, which in my opinion not necessarily include the weather forecast or cooking.

The kilogram is the only kg-m-sec physical standard: a 35 mm film can-sized cylinder of Pt-Ir alloy whose mass measurably drifts (possibly trace atmospheric hydrogen chemistry) at different rates for the primary standard and its secondary standards. A silicon-28 single crystal solid sphere machined precise to a couple of atoms thickness is a superior standard kilogram - by exactly defining the mole.

Unless you can provide a purely theoretical relationship for the kilogram that can be reduced to practice at will, the mole is fundamentally important to the engineering of civilization.