The amino acid histidine has a side chain for which the pKa is 6.0. How would I show what fraction of the histidine side chain will carry a positive charge at pH 5.4?

So, if the Pka is higher than the pH, the group is protonated.

 

The histidine has an immidozole ring side chain, so there's 2 nitrogen groups. the 1 n group is slightly more acidic because its bound to a hydrogen, the other 3N group has a lone pair, and is more basic.

 

I think both of these groups can get protonated, but at pH of 5.4, I'm not sure if they would both be protonated, or just the more basic 3N group. My guess is that its just the 3N group that has a positive charge... but don't quote me on that.

by any chance, could you use the henderson-hasselbalch equation to solve for this?

the details might be too minute for the HH equation to deal with, but I'm not sure about that.