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We have meter in the SI - we use that to measure length. Other length units like light years can be expressed in meters. But how often do we express amounts or quantities in moles? Mole is a number of things, nut we do not define 1 in terms of mole, or a dozen, or a million. I have never seen anyone stating that a coil has $500/N_A$ moles of turns. It seems that we define none of the everyday counting units in moles.

However, it is included in SI, and it is even proposed to be included in the revisions. Why not just use 1 if we need the reference amount for the system of counting units, and make mole a derived or a non-SI unit used in SI (like liter)?

Inspired by Why is the mol a fundamental physical quantity?

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    $\begingroup$ @AccidentalFourierTransform Are you referencing to the question that I mentioned as inspiration in the very first sentence? That question asks "why is it a physical quantity" and "why is it a fundamental physical quantityy" that are answered there by "it is because it is" and "it isn't fundamental". Neither the question asks nor the answers tell why it's in the SI instead of "1" which seems more fundamental to me (isn't it?). $\endgroup$
    – Džuris
    Mar 23, 2017 at 21:08
  • $\begingroup$ Slightly seriously, physics has its share of anachronistic terms, perhaps consider indulging the chemists in this case :) $\endgroup$
    – user146020
    Mar 23, 2017 at 21:09
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    $\begingroup$ "The mole is never used" is the mark of someone who had never opened a chemistry paper. The SI is for all of science, not just for physics. $\endgroup$ Mar 23, 2017 at 21:14
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    $\begingroup$ More seriously, though: because history, to a large extent (though not completely). The concept of an SI base unit is relatively shaky and getting shakier, even the ampere is in trouble. $\endgroup$ Mar 23, 2017 at 21:20
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    $\begingroup$ I wouldn't call this question a duplicate. The "duplicate" question is about whether mol is a fundamental physical quantity and this one is about why it's included in SI. Some people on stack exchange are very trigger happy about flagging. $\endgroup$ Nov 5, 2020 at 6:58

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Because SI is a system of standards to ensure that different experimental results are reported in compatible formats, not a system of fundamental physical units. Many of the SI "base units" clearly have no fundamental physical significance - for example, for all intents and purposes temperature and energy conceptually have the same units, and the candela is a unit of "luminous intensity," which is specifically calibrated to the human eye, not to any natural physical quantity.

My advice: if you're doing experiments, stick to SI. If you doing theory (including classroom-type learning), stick to any other system.

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    $\begingroup$ Many experimenters use non-SI units like parsecs or inverse centimeters. Many experimenters use non-mole units of quantity like "1" or "50". And using "50" is not even considered as stepping away from SI... I am not saying that your sentences are wrong, but this doesn't answer why SI is wrong :( $\endgroup$
    – Džuris
    Mar 23, 2017 at 21:11
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    $\begingroup$ +1 To put this answer simply, SI doesn't intend to minimize the number of base units in use. $\endgroup$ Mar 23, 2017 at 21:15
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    $\begingroup$ @EricDuminil In physics, when temperature appears in a formula it is essentially always multiplied by Boltzmann’s constant $k_B$, which has the effect of converting it to an energy. So you might as well just directly work with the energy equivalent that you get after multiplying by $k_B$. $\endgroup$
    – tparker
    Oct 28, 2021 at 12:26
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    $\begingroup$ @EricDuminil You won't find any, except for some trivial exceptions like where you have a ratio of two temperatures so the $k_B$'s cancel out. Fundamentally, temperature is best thought of as having the units of energy, and the existence of Boltzmann's constant is basically a historical accident because it took scientists a while to realize that. Most theorists just set $k_B = 1$. There isn't really any reason to leave it in; unlike with $c$ or $\hbar$, there aren't even any qualitatively interesting limits where $k_B$ goes to 0 to to $\infty$. $\endgroup$
    – tparker
    Oct 29, 2021 at 13:02
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    $\begingroup$ @EricDuminil Well, yes, I certainly agree that it makes more sense to express temperatures in terms of energy than vice versa. But as a practical matter, Joules are generally too large of a unit to usefully measure temperature, because one Joule corresponds to 10^22 Kelvin, which is hotter than pretty much anything in the universe. $\endgroup$
    – tparker
    Oct 29, 2021 at 15:20
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How often do we get to use candela, another base SI unit? However, people dealing with intensity of lamps needed it, so it was added:

"Prior to 1948, various standards for luminous intensity were in use in a number of countries. These were typically based on the brightness of the flame from a "standard candle" of defined composition, or the brightness of an incandescent filament of specific design... Germany, Austria and Scandinavia used the Hefnerkerze, a unit based on the output of a Hefner lamp.It became clear that a better-defined unit was needed".

For other stories concerning adoption and reclassification of SI units see Are units of angle really dimensionless?

With mole the reference point is chemistry, and some analogs of mole were used long before it was adopted by SI. In 1865 Loschmidt first estimated the number of molecules in a cubic centimetre of a gas under normal conditions as 1.83 × 1018, and in 1889 determined the gram-molecular volume of gases under normal conditions, after Horstmann introduced the concept of gram-molecular weight in 1881. The term "mole" was introduced in 1900 by Ostwald, a leading chemist at the time, in his textbook. He originally defined it as "the molecular weight of a substance in mass grams", but later clarified "that amount of any gas that occupies a volume of 22414 mL in normal conditions is called one mole". SI only adopted the mole in 1971.

Johansson is perhaps the most vocal recent critic of the mole, and he also advocates exchanging it for unit one, see his Metrological thinking needs the notions of parametric quantities, units and dimensions:

"The claim of this paper is that metrology would profit from distinguishing between true and parametric quantities, units and dimensions. In particular, these distinctions have repercussions on how to look at the unit one, the mole and the corresponding quantities and dimensions... The third part takes for granted that both the mole and the unit one are parametric units, and it argues that, for pedagogical reasons, the mole should be exchanged for the unit one, and the parametric quantity amount of substance be renamed as ‘elementary entities’.

But his reasons are more principled:

"The introduction of the base unit mole in the SI brochure differs in structure from the introductions of all the other six base units of the SI system; it contains two paragraphs, the others only one (corresponding to the first paragraph below). The brochure says:

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is “mol”.

2.When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles or specified groups of such particles. [2, p 115]

This means that, strictly speaking, the base quantity at hand is not just amount of substance, but amount (of substance) of elementary entities of a certain kind. This means that, strictly speaking, the base quantity at hand is not just amount of substance, but amount (of substance) of elementary entities of a certain kind; briefly, amount(-of substance)-of-$E_p$, where the subscript $p$ functions as a parameter whose “values” are atoms, molecules, ions, electrons, etc. Therefore, the quantity amount of substance had better be called a parametric quantity. The main reason behind the requirement of paragraph 2 is, I take it, that it makes no physical–chemical sense to compare amounts of different kinds of elementary entities.

...to compare an amount of atoms with an amount of molecules would be like comparing a number of houses with a number of blocks. When the elementary entities spoken of in the definition become specified, then the mole unit becomes specified. That is, the term ‘mole’ has in practice, ever since its introduction in the SI (1971), been used as if it means not just mole but mole-of-$E_p$. The mole is not a base unit on a par with the six property base units; it cannot be used in significant physical–chemical comparisons until the subscript parameter $p$ in mole-of-$E_p$ has been given a certain “value”."

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  • $\begingroup$ I don't know about the rest of the paper, but that last sentence is terrible; it makes perfect sense to compare a mole of oxygen and a mole of hydrogen - you need two of the latter and one of the former to burn hydrogen to make water, and that's precisely the use case the mole was developed to fill. There's other (obvious) reasons why you need to specify the type of entity - namely, 18g of water has one mole of water but two moles of hydrogen, and if you don't specify which one you mean it's ambiguous. That's some pretty strong flaws in that paper just from one sentence. $\endgroup$ Mar 23, 2017 at 21:44
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    $\begingroup$ Reading more into the SI brochure, I think it's important to highlight that in the definition of the mole, it is meant to describe the amount of substance in the system, not just any dimensionless quantity. The substance must be specified as consisted of elementary entities, so a mole of coil turns is nonsense, but a mole of cars or ants might make sense. $\endgroup$
    – Elliot Yu
    Mar 23, 2017 at 21:49
  • $\begingroup$ @EmilioPisanty I am afraid, it may be partly my fault for mangling the quote. It may or may not not matter for your objection, but I inserted a fuller version. $\endgroup$
    – Conifold
    Mar 24, 2017 at 23:47
  • $\begingroup$ I guess that does make it slightly less bad - now it's only just platitudes, I think. $\endgroup$ Mar 25, 2017 at 9:56

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