Need Help With Isoelectronic Point pI Equation

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The isoelectric point (pI) is defined as the pH at which a compound has a net charge of zero, occurring when the positive and negative charges are balanced. It is calculated as the average of two pKa values because these represent the dissociation points of the acidic and basic forms of the molecule. At the pI, the rates of dissociation for the anion and cation are equal, leading to the formation of a zwitterion or neutral state. Understanding the relationship between pI and pKa is crucial in biochemistry for predicting the behavior of amino acids and proteins in different pH environments. Thus, the pI reflects the balance of charged species in solution.
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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!
 
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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.
 
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