For phenylalanine amino acid if at pH = 1.83, concentration of zwitter ion and its conjugate acid are same i.e.

While at pH 5.48, concentration of conjugate base and conjugate acid of zwitter ion are same i.e.

At what pH, concentration of zwitter ion and its conjugate base will be same? i.e

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Solution

As at pH = 1.83, concentration of zwitter ion and its conjugate acid are same i.e. $p K_{a 1} = 1.83$ and at pH 5.48, concentration of conjugate base and conjugate acid of zwitter ion are same i.e. isoelectric point pl = 5.48
So, $\frac{P K a_{1} + P K a_{2}}{2} = 5.48 \Rightarrow \frac{1.83 + p K a_{2}}{2} = 5.48 \Rightarrow p K a_{2} = 9.13$
So, concentration of zwitter ion and its conjugate base will be same in pH =9.13

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