Multiple pKa's of Vitamin C

Layman here. I was looking at vitamin C serums in skincare and wanted to know more about it. It has been awhile since taking chemistry in college so my understanding is rusty.


I want to better understand this diagram (Source: U of Iowa) that talks about the different forms vitamin C:


[![enter image description here](https://i.stack.imgur.com/qWYtb.jpg)](https://i.stack.imgur.com/qWYtb.jpg)


All I remember of $\mathrm{p}K\_\mathrm{a}$s was that high $\mathrm{p}K\_\mathrm{a}$s means the acid is very strong and dissociates all the way while lower $\mathrm{p}K\_\mathrm{a}$ means a weaker acid. So I'm a little lost on how to interpret this diagram in terms of the $\mathrm{p}K$ values, ie the $\ce{OH}$ group is deprotonated from $\ce{AsCH2}$ to $\ce{AsCH-}$ but I'm not sure how the $\mathrm{p}K$ value fits in all of this? Layman me wants to say at $\mathrm{pH}=4.1$ is when deprotonation happens, but I have a feeling that isn't right.




You actually have it backwards. A low $\mathrm{p}K\_\mathrm{a}$ is a strongly dissociating acid, and a high $\mathrm{p}K\_\mathrm{a}$ is a weakly dissociating acid. It would do you well to remember the origin of $\mathrm{p}K\_\mathrm{a}$ \eqref{pKa}, as well as the [Henderson–Hasselbalch equation](https://en.wikipedia.org/wiki/Henderson%E2%80%93Hasselbalch_equation) \eqref{HHeq}:


$$K\_\mathrm{a}=\ce{\frac{[A-][H3O+]}{[HA]}} \Rightarrow \mathrm{p}K\_\mathrm{a} = -\log(K\_\mathrm{a})= -\log \left( \ce{\frac{[A-][H3O+]}{[HA]}}\right)\tag1\label{pKa}$$


$${\mathrm {pH}}={\mathrm {p}}K\_{{\mathrm {a}}}+\log \_{{10}}\left({\frac {[{\mathrm {A}}^{-}]}{[{\mathrm {HA}}]}}\right)\tag2\label{HHeq}$$


From this we can surmise a physical meaning behind what the $\mathrm{p}K\_\mathrm{a}$ of an acid is—it is the $\mathrm{pH}$ of the solution when $\ce{[A-]=[HA]}$. This means that for $\mathrm{pH}>\mathrm{p}K\_\mathrm{a}$, $\ce{[A-]>[HA]}$. Since ascorbic acid is a diprotic acid, it has two $\mathrm{p}K\_\mathrm{a}$ values, one for each deprotonation.


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