# What is degree of dissociation for polyprotic acids?

My textbook says that degree of dissociation= [HA]dissociated/[HA]initial * 100%. However, it also says that citric acid has a greater degree of dissociation than acetic acid because citric is triprotic whereas acetic is monoprotic.

This reasoning doesn't fit with the top definition because, more protons donated doesn't necessarily mean more acid molecules dissociated (triprotic acid vs monoprotic acid for example; for every acid molecule dissociated, triprotic acid donates more protons).

So my question is, how does one define degree of dissociation for polyprotic acids?

• I think you missed the word greater in the second line after "citric acid has a ..." Apr 5 '15 at 18:17

Saying that the degree of dissociation $$(\alpha)$$ of citric acid is greater because its triprotic is not correct. The degree of dissociation should be calculated for each dissociation separately. The degree of dissociation of citric acid's first dissociation $$\ce{C6H8O7 <=> C6H7O7- + H+}$$ is greater than that of acetic acid, because its $$\mathrm{p}K_\mathrm{a}$$ is smaller (3.13 vs 4.76)$$^1$$, meaning it's a stronger acid.
The second value of $$\alpha$$ for citric acid, however, will be very to close to acetic acid's, because the second dissociation has approximately the same $$\mathrm{p}K_\mathrm{a}$$ (4.76)$$^1$$. The third $$\alpha$$ will be smaller, since the $$\mathrm{p}K_\mathrm{a}$$ of the third dissociation is greater (6.40)$$^1$$.
Note that $$\alpha$$ is represented on the $$y$$-axis in a 0-1 scale. For each of the four states of the molecule, there is a different $$\alpha$$, and different values of $$\alpha$$ happen simultaneously.
$$^1$$ $$\mathrm{p}K_\mathrm{a}$$ values taken from Wikipedia.