A 25.0-mL sample of 0.125 M pyridine is titrated with 0.100 MHCl. Calculate the pH at 0 mL of added acid.

Question

abb0t · Answer

So you have: $\sf \color{red}{Pyr + H^+ \rightleftharpoons  Pyr-H  + Cl^-}$
Since it says, find the pH at 0 mL added, that is basically telling you the pH BEFORE you perform the titration. Which is relatively simple. 

pH = -log[$\sf H^+$]

vincent-lyon.fr · Answer

You need to know the pKb of pyridine.

abb0t · Answer

I don't think you need the pK$\sf _b$ prior to addition of the acid? 
but definitely before reaching equivalence point at which point you will have a buffer and you can use henderson-hasselbach equation to find pH.

vincent-lyon.fr · Answer

Isn't there a typo in the question?
Shouldn't it be "Calculate the pH at 10 mL of added acid." ? (maybe 20 mL?)

With this 0 mL, the wording is so strange.

abb0t · Answer

Oh, nevermind, I think i was thinking of the acid, but @Vincent-Lyon.Fr is correct. This is a weak base, so you need your K$\sf _b$ since it undergoes incomplete dissociation.