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If 1 mole of X is approximately $6.02 \cdot 10^{23}$ X, why is it a unit?

How does it have the characteristics of a unit? Is it just a different way of writing the Avogadro's constant? Does amount actually have a unit or is it unitless?

Martin Vesely
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Natrium
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A mole is unit with SI dimension of "amount of substance," not unlike a dozen. It is not needed, in the sense that it would be possible to do physics and chemistry without it, but it would be horribly inconvenient to be forced to talk about the actual numbers of particles involved in a thermodynamically large system all the time. It exists for simplicity and convenience - similar to how the grocery store does not generally talk about the price of a single egg.

My original answer to this question referred to the mole as dimensionless, which conflicts with the SI convention. My feelings on this subject are well-summarized by this answer by SE user Vera K. While I generally do not treat "amount of substance" as a physical dimension in its own right, this is a convention, and not the dominant one in physics and chemistry.

J. Murray
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    No, it's not a dimensionless unit, it has the dimension of amount of substance, see the SI brochure, section 2.3.3. – Massimo Ortolano Apr 24 '20 at 19:42
  • But as far as I understand, the SI defines it as a dimension for simplicity's sake. How can amount of substance be a dimension if it is just a number of particles of that substance? – Natrium Apr 25 '20 at 08:44
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    @Natrium Dimensions are equivalent classes of quantities within a system of quantities, chosen by convention. So, in the system of quantities currently in use the amount of substance is a quantity defined as the ratio of the counting entities of interest divided by the Avogadro's constant (not number, because it's unit is not 1), and to this quantity a specific dimension is associated. So, the first sentence of this answer is really wrong. You can certainly conceive a system of quantities where the amount of substance is dimensionless, but it's not the one currently in use. – Massimo Ortolano Apr 25 '20 at 13:32
  • @MassimoOrtolano While that presumes that SI is the only game in town, your point is well-taken. I have never really abided by the SI convention in this respect, insofar as I generally would consider "amount of energy per mole" to simply be an amount of energy, but since SI is the dominant convention it is inappropriate to break from it without referencing it. I will edit my answer. – J. Murray Apr 25 '20 at 14:36
  • @J.Murray Many physicists try to live with their own system of units and, after all, the SI is just a recommended system of units, but there is an inherent risk in this: the SI is the only system that can actually provide consistent values for quantities, and trying to leave with a different system of units can put you at risk of proposing measurements (e.g. to verify theories) that cannot be performed in any consistent way. – Massimo Ortolano Apr 25 '20 at 15:17
  • For instance, in my professional life I had to convince several professional physicists that the speed of light cannot be measured any longer, and that that what they called speed of light measurement was actually a length measurement. – Massimo Ortolano Apr 25 '20 at 15:17