I will follow Voet and Voet's treatment in the third edition of Bichemistry (p. 361). EH
2+ EH
E
-. The acid dissociation constant for the first dissociation is K
E1, and the acid dissociation constant for the second dissociation is K
E2. V
max and K
m are the pH-independent parameters of the monoprotonated (active) form of the enzyme, EH. The apparent values (which depend on pH) are V'
max= V
max/f2 and K'
m = K
m(f1/f2) Therefore V'
max/K'
m = (V
max/K
m)(1/f1). f1 =[H
+]/K
E1 + 1 + K
E2/[H
+]
It should be possible to calculate V'
max/K'
m from the pH and the two pK
a values you were given.