+ y). Polyprotic acids Polyprotic acids are acids that can lose more than one proton. The constant for dissociation of the first proton may be denoted as Ka1, and the constants for dissociation of successive protons as Ka2, etc. Citric acid is an example of a polyprotic acid H3A, as it can lose three protons. {| class="wikitable" style="width: 230px; |+ Stepwise dissociation constants |- ! |Equilibrium!!Citric acid |- | H3A H2A− + H+||pKa1 = 3.13 |- | H2A− HA2− + H+|| pKa2 = 4.76 |- | HA2− A3− + H+|| pKa3 = 6.40 |} When the difference between successive pKa values is less than about 3, there is overlap between the pH range of existence of the species in equilibrium. The smaller the difference, the more the overlap. In the case of citric acid, the overlap is extensive and solutions of citric acid are buffered over the whole range of pH 2.5 to 7.5. Calculation of the pH with a polyprotic acid requires a speciation calculation to be performed. In the case of citric acid, this entails the solution of the two equations of mass balance: CA is the analytical concentration of the acid, CH is the analytical concentration of added hydrogen ions, βq are the cumulative association constants. Kw is the constant for self-ionization of water. There are two non-linear simultaneous equations in two unknown quantities [A3−] and [H+]. Many computer programs are available to do this calculation. The speciation diagram for citric acid was produced with the program HySS. N.B. The numbering of cumulative, overall constants is the reverse of the numbering of the stepwise, dissociation constants. {| class="wikitable" |+ Relationship between cumulative association constant (β) values and stepwise dissociation constant (K) values for a tribasic acid. ! Equilibrium!! Relationship |- | A3− + H+ AH2+||Log β1= pka3 |- | A3− + 2H+ AH2+||Log β2 =pka2 + pka3 |- | A3− + 3H+ AH3||Log β3 = pka1 + pka2 + pka3 |} Cumulative association constants are used in general-purpose computer programs such as the one used to obtain the speciation diagram above. See also Henderson–Hasselbalch equation Buffering agent Good's buffers Common-ion effect Metal ion buffer Mineral redox buffer References External links Acid–base chemistry Acid–base physiology Equilibrium chemistry