Ka is measured as the amount of acid HA that dissociates at equilibrium in water at a given temperature. Ka is a constant, it's a physical property of an acid. Ka for a particular acid HA can only change in response to different temperatures, where difference amounts will dissociate -- which is then dependent on the dissociation reaction of HA being endothermic/exothermic.
H2O + HA <---equilibrium--> A- + H3O+
Ka = [H3O+][A-]/[HA]
It's the same thing as writing
Ka = [H+][A-]/[HA], we just didn't show H2O in equilibrium reaction for the Ka expression.
Ka doesn't change... If you change any concentrations, the reaction will shift to return to equilibrium. If you add more HA, more H+ and A- form. If you have less HA, then less H+ and A- will form. Ka is just the ratio... and that ratio is constant. No matter how much or how little HA you add.
so pKa is just -log(Ka) which obviously doesn't have anything to do with amount of acid present. It's just taking the -log(some constant number). And the constant number is just the ratio that dissociates for a particular HA.
If you add HA to this same exact solution at equilibrium, then more H+ will form and more A- will form. So, [H+] and [A-] are dependent on [HA]. You're able to get the [H+] technically from the Ka equation.. since Ka is constant. So if a Ka were equal to some constant number C...
C = [H+][A-]/[HA]
(C*[HA])/[A-] = [H+]
So [H+] is affected by acid concentration, but Ka is constant and is affected by the strength of the acid and just how much is physically dissociates. It's just a physical property.
Hope this is convincing enough, I know it's not really a thorough proof using equations. I'm not really sure how to go about explaining it strictly using equations... figure'd I'd take a shot at answering it though. It's all about taking into account that Ka is a physical property for a given acid, and it's a constant that is only affected by temperature. Much like Keq or Ksp are constants / physical properties.
