Henderson equation : The pH of an acid buffer can be calculated from the dissociation constant, Ka, of the weak acid and the concentrations of the acid and the salt used.
The dissociation expression of the weak acid, HA, may be represented As
HA < -- -- -- > H+ + A-
Ka = [H+][A-] / [HA]
[H+] = [HA] Ka / [A-] ……………… 1
The weak acid is only slightly dissociated and its dissociation is further depressed by the addition of the salt (Na+ A- ) which provides A- ions (Common ion effect). As a result the equilibrium concentration of the unionised acid is nearly equal to the initial concentration of the acid. The equilibrium concentration [A- ] is presumed to be equal to the initial concentration of the salt added since it is completely dissociated. Thus we can write the equation (1) as
[H+] = Ka ([acid] / [salt] ) ….. ..2
where [acid] is the initial concentration of the added acid and [salt] that of the salt used.
Taking negative logs of both sides of the equation (2), we have
-log[H+] = -logKa - log ([acid]/[salt])
-log[H+] = pH and -logKa = pKa
pH = pKa + log ([salt]/[acid])
This relationship is called the Henderson-Hasselbalch equation or simply Henderson equation.
In a similar way, the Henderson-Hasselbalch equation for a basic buffer can be derived. This can be stated as :
pOH = pKb + log ([salt]/[acid])
Significance of the Henderson-Hasselbalch equation. With its help
1. The pH of a buffer solution can be calculated from the initial concentrations of the weak acid and the salt provided Ka is given.
However, the Henderson-Hasselbalch equation for a basic buffer will give pOH and its pH can be calculated as (14 - pOH).
2. The dissociation constant of a weak acid (or weak base) can be determined by measuring the pH of a buffer solution containing equimolar concentrations of the acid (or base) and the salt.
Since, [salt] = [acid], log ([salt]/[acid]) = log 1 =0
pKa = pH
The measured pH, therefore, gives the value of pKa of the weak acid.
Likewise we can find the pKb of a weak base by determining the pOH of equimolar basic buffer.
3. A buffer solution of desired pH can be prepared by adjusting the concentrations of the salt and the acid added for the buffer.
It is noteworthy that buffer solutions are most effective when the concentrations of the weak acid (or weak base) and the salt are about equal. This means that pH is close to the value of pKa of the acid (or pKb of the base).