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pH problem

shel
in Biochemistry and Molecular Biology

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I'm studying for my biochemistry final and encountered a pH problem that I don't know how to approach.

 

A compound is known to have a free amino group with a pKa of 8.8, and one other ionizable group with a pKa between 5 and 7. To 100 mL of a 0.2 M solution of this compound at pH 8.2 was added 40 mL of a solution of 0.2 M hydrochloric acid. The pH changed to 6.2 . Find the pKa of the second ionizable group.

 

The only way I know how to attack this is with Henderson Hasselbach but I haven't been able to solve it yet.

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OK, i know the answer is 5.6 but I sill don't know how to calculate it

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