Acidity of hydrochloric acid in acetic acid

A question asked to find the $\mathrm pK_\mathrm a$ of $\ce{HCl}$ in acetic acid. The equation of $\ce{HCl}$ disassociating in water is: $$\ce{HCl + CH3COOH \leftrightharpoons CH3COOH2+ + Cl-}$$ I predicted that the $\mathrm pK_\mathrm a$ should be higher as acetic acid is a weaker base than water so it would be less willing to accept a proton from a $\ce{HCl}$.

However when I finally calculated the $\mathrm pK_\mathrm a$, I got 8.56. This was much higher than I expected. Also doesn't this imply that $\ce{Cl-}$ is stronger as a base than $\ce{HCl}$ is as an acid in acetic acid, which doesn't sound right.

So I am asking if this value totally wrong or is it actually quite reasonable?

So basically I am asking, is this value totally wrong or is it actually quite reasonable?

It's quite reasonable. Compare to page 32 of this reference.

This was much higher than I expected. Also doesn't this imply that
Cl− is stronger as a base than HCl is as an acid in acetic acid, which doesn't sound right.

To answer whether Cl- is a stronger base than HCl is an acid, you need to know the self-dissociation constant of acetic acid, the equivalent of Kw for water. It is about $10^{-10}$. So whereas the middle of the pH scale is thought of as 7, the middle for acetic acid would be 5. So, yes, Cl- is a stronger base than HCl is an acid in acetic acid.

• thanks for you answer and for the reference. Also, what I meant to ask is 'is $\ce{Cl-}$ a stronger base than $\ce{HCl}$ as an acid' if you get what I mean. I will edit my question. Sorry for my badly worded question. Jan 26 '16 at 23:56
• @Nanoputian To answer whether Cl- is a stronger base than HCL is an acid, you need to know the self-dissociation constant of acetic acid, the equivalent of Kw for water. It is about 10^(-10). So whereas the middle of the pH scale is thought of as 7, the middle for acetic acid would be 5. So, yes, Cl- is a stronger base than HCl is an acid in acetic acid. Jan 27 '16 at 12:18

Glacial acetic acid is a powerful solvent, but not as polar as water. Whereas HCl has a pKa of -6.3 in water, its pKa in acetic acid will be less acidic (greater numerically).

It helps to think of the three hydrohalic acids as covalent molecules (especially HCl, since that is what we are discussing). They are ionic only when hydrogen bonding provides a lower energy state for solvated ions, especially H+, but also the anion. Cl- is poorly solvated by acetic acid compared to Br- and I-, and the protonation of acetic acid is not especially energetic.

Acetic acid is called a differentiating solvent for the hydrohalic acids: HI is strongest, HBr less so and HCl is least strong.