What is the dimension of Avogadro's constant?

Question

What is the dimension of Avogadro's constant ($N_mathrm{A}$).
On Wikipedia it says it is dimensionless, but in Nigel Wheatley's article (pdf) On the dimensionality of the Avogadro constant and the definition of the mole it says it is $mathsf{N}^{-1}$.
begin{align}
text{Number of particles} &= N_mathrm{A}times text{Amount of substance}\
[text{Amount of substance}] &= mathsf{N}\
[text{Number of particles}] &= mathsf{1}
end{align}
If $[N_mathrm{A}] = mathsf{N}^{-1}$ then the above equation follows, otherwise it doesn't. Is this the right value?

Gwyn · Answer

The dimension/unit of the Avogadro constant $N_mathrm{A}$ is actually $1/mathsf{N}$ or $pu{mol-1}$. It is shown that way in your first reference as well, i.e.
$$ N_mathrm{A} = pu{6.02214076E23 mol-1}. $$
What is "dimensionless" is the Avogadro number or the number of atoms / molecules in a single $pu{mol}$ of that substance, sometimes written as $N$ or $N_0$.
The numerical value is the same, but the concept is different. Basically the relationship between the two is:
$N_0 = (pu{1 mol})times N_mathrm{A} = pu{6.02214076E23}$
See also the answer discussed in the comment by Ed V, where the new definition of the constant is explained: Effects of Changing Avogadro's Constant.

Publius · Answer

The dimensions of Avogadro's Constant is $1/mathsf{N}$. In SI units, this is $pu{1/mol}$.
Your unit analysis is correct. I have seen this type of question before, I believe the confusion is caused by people normally saying particles per mole, and "particles" is a "phantom" unit (similar to radian). But either way, the SI units are definitely $pu{1/mol}$.

What is the dimension of Avogadro's constant?

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