J.R. S. answered 10/12/18
Ph.D. University Professor with 10+ years Tutoring Experience
Look up the pKa for the amino and carboxyl and pyrole nitrogen group of histidine. The values I found are
pKa1 = 1.82 for the carboxyl
pKa2 = 9.17 for the amino N
pKa3 = 6.00 for the pyrole N
Thus, histidine can exist in 4 forms depending on pH. Going from acidic pH to basic pH, you will have pyrole N with + charge, amino N with a + charge and carboxyl will have no charge
Increasing pH, you have pyrole N with + charge, amino N with a + charge, and carboxyl with - charge.
Increasing pH further, you have pyrole N with 0 charge, and amino N with + and carboxyl with -
Finally, at higher pH, you have pyrole N with 0 charge, amino N with 0 charge and carboxyl with -
The pI is the pH at which the amino acid has no net charge. In this case it will end up being the average of the pKa2 and pK3 or 1/2 (pK2 + pK3) = 1/2 (9.17 + 6.00) = 7.59 = pI