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pH calculation lectures » calculation of pH of salt using simplified methods
As usual, the most general approach is unsuitable for calculations done by hand. For salts with one strong and one weak component the best way of pH calculation it to treat conjugate acid (or base) as the only source of H+ (or OH-) ions, and do the calculations in the same way as it was described in weak/acid base section.
For example if we have solution of salt of weak acid (with dissociation constant Ka) and strong base, reaction of hydrolysis is
and the equilibrium is described by conjugate base dissociation constant
13.1where
13.2Starting from these equations we can calculate pOH and pH of the solution using method and assumptions shown for weak acid an base. Exactly the same approach can be used for salt of strong acid and weak base - just using the Ka constant for acid conjugate with weak base. If the acid (or base) is polyprotic we can use one of the methods described in the polyprotic simplified section.
In the case of salt of weak acid and weak base situation is more complicated, but sometimes we can get pretty good results assuming similar degree of both hydrolysis processes (as seen above).
Let's say we have a solution of AB salt of weak acid and weak base of concentration C and dissociation constants Ka and Kb. Our first assumption is that the hydrolysis is not too strong, so that in the equilibrium [A-]=[B+]=C. If so, equations for Ka and Kb take forms
13.3
13.4We will solve them for [H+] and [OH-]:
13.5
13.6Multiplying:
13.7and rearranging:
13.8Please note that these Ka and Kb values are not related by KaKb=Kw, as they describe different substances.
Now it is time for the second assumption - that degree of both hydrolysis reactions is similar, so [HA]=[BOH]. We have seen similar assumption justified in 12.12 - symmetry does the trick. If so
13.9which gives us concentration of HA that can be used for [H+] calculation when inserted into 13.5
13.10or
13.11This approach - although simplification is based on intuition rather than deep analysis - gives surprisingly good results. It is also worth noting here that equation 13.11 is in fact not different from 12.9 as pKw-pKb=pKa.
For ammonium acetate (CH3COONH4) pKa=4.75 and pKb=4.75 too. This salt is so symmetrical, that results of pH calculation just must be perfect:
| C (M) | pH calculator | pH eq. 13.10 |
|---|---|---|
| 1 | 7.00 | 7.00 |
| 10-8 | 7.00 | 7.00 |
And what about aniline dichloroacetate? pKa=1.48 and pKb=9.4, so there is a large difference in the strength.
| C (M) | pH calculator | pH eq. 13.10 |
|---|---|---|
| 1 | 3.05 | 3.04 |
| 0.1 | 3.11 | 3.04 |
| 0.01 | 3.37 | 3.04 |
The more diluted the solution, the worse the results, but for concentrated solution predicted pH value is perfect.
General rule of thumb is that both equations - 12.9 and 13.10 - give good results only for concentrated solutions.
