Polyprotic acids and bases dissociation constants

First, and the simplest approach to defining equilibriums constants for polyprotic acid is to treat every step of dissociation separately:

Then we have three stepwise dissociation constants:

There are also overall dissociation constants defined, of which first is identical to the stepwise one, while the second and the third take forms:

It is not very difficult to find out relations:

or

For polyprotic acids with greater number of protons analogous constants are used.

Same holds for polyprotic bases.

In case of polyprotic substances the idea of conjugate acids and bases becomes a little bit confusing, as the same substance can play both roles:

and the numeration of dissociation steps is reversed, so that first acid dissociation step described by K_a1:

creates conjugate base for the last dissociation step:

described by K_b3. So for the substance with three protons relations analogous to 2.5 take forms: