Need Help With Isoelectronic Point pI Equation

[Pruddy]

Homework Statement

Why must the PI be an average of two PKa's

Homework Equations

pI = (Pka1 + pKa2)/2

The Attempt at a Solution

the pI is the point when the net charge of a compound is zero.

I don't really know why it must be the average of two pKa's. Please I need help!

 

[Lamebert]

I assume you're mentioning this in the context of biochemistry. What is the pKa of a substance? It's the pH at which half of the molecules are dissociated. If you have a negatively charged ion and a positively charged ion, then at some given pH (that is, the pI) the NET charge is equal to zero. That is, the anion and cation experience equal dissociation rates: the zwitterion or uncharged form may exist in situ, but the (# positive charges) - (# negative charges) = 0. At this pI, there is an equal likelyhood that the anion will exist as there is the cation, and as such, the net charge is zero.