# Confusing definition of mol when considering second order rate equations

I am confused by "$$\text{mol}$$".

I denote the unit of a physical quantity with square brackets (e.g. $$[V]=l$$), and the value of a physical quantitiy using curly brackets (e.g. $$\left\{ V\right\}$$ = 0.01).

A simple second order rate equation for number concentrations $$n=N/V$$ is given by, $$\dot{n} = k^*_{on}n^2,\;\;[1]$$ where the $$[k^*_{on}]=l/s$$.

The same second order rate equation but for molar concentration $$c=\frac{N}{N_AV}$$, is given by $$\dot{c} = k_{on}c^2,\;\;[2]$$ where $$[k_{on}]=\frac{l}{\text{mol}~s}$$.

When transforming equation $$[1]$$ into equation $$[2]$$, we get the relation

$$k_{on} = \left\{k_{on}\right\}\frac{l}{\text{mol}~s} = k^*_{on}N_A = \left\{k^*_{on}\right\}\left\{N_A\right\}\frac{l}{\frac{1}{\left[N_A\right]}s}$$

Hence $$\frac{1}{\left[N_A\right]} = \text{mol}$$?

But this would be in contraction to the definition I find on wikipedia where it is written that:

In short, for particles 1 mol = $$6.02214076×10^{23}$$.

Hence, $$1~\text{mol} = \left\{N_A\right\}$$.

I think the sentence cited above in the wikipedia article is very confusing. But the wiki article about the Avogadro constant helped me resolve my confusion, which defines $$mol$$ via the Avogadro constant:

$$N_A = \left\{N_A\right\}[N_A] = 6.022\times10^{23} \text{mol}^{-1}.$$

Hence

$$k_{on} = k^*_{on}N_A = \left\{k^*_{on}\right\}\left\{N_A\right\}\frac{l}{\frac{1}{[N_A]}s}=\left\{k^*_{on}\right\}\left\{N_A\right\}\frac{l}{mol~s}$$

This definition is also given on the hompege of the National Institute of Standards and Technology (NIST), see here.

• The Wikipedia article was edited by someone who wants to change the definition of mole, and has written an article about it. The version of the Wikipedia article you saw did not have a neutral point of view because it did not reflect the current official definition of the unit.
– Karsten
Commented Nov 25, 2020 at 14:28
• I think this definition is right. It got estrablished new since 19. May 2019. See here: physics.nist.gov/cgi-bin/cuu/Value?na Commented Nov 26, 2020 at 16:21
• Yes, I edited the Wikipedia article to reflect the current official definition.
– Karsten
Commented Nov 26, 2020 at 18:26
• Nice! Good job @KarstenTheis Commented Nov 27, 2020 at 20:23