# pH Calculations

### Contents

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#### The pH of Non-Buffered Solutions

The pH of a weak base solution is calculated in the same manner as that of a weak acid solution, using Kb instead of a Ka.

To calculate the pH of a mixture of acids in aqueous solution, first decide which acid has the lowest pKa. Calculate the pH as if the strongest acid were the only one in solution. We can ignore the contributions to the pH of the weaker acids because they will be minor in comparison to that of the strongest acid in the group. The exact solution to such a problem requires more complex mathematics and will not be covered in this SparkNote.

#### Hydrolysis Reactions

A salt of a strong acid and a strong base (such as NaCl from HCl and NaOH) produces a neutral solution when dissolved in water. However, when a salt of a weak acid and a strong base (e.g. NaAc from acetic acid and NaOH), a strong acid and a weak base (e.g. NH4Cl from ammonia and HCl), or a weak acid and a weak base (NH4Ac) is dissolved in water, the solution does not have a neutral pH. These phenomena are explained by the reaction of the salts of weak acids and weak bases with water in hydrolysis reactions. As shown in , these hydrolysis reactions produce the parent weak acids and weak bases of the salts:

Figure %: Hydrolysis reactions

As you can see in the figure above, the salt of a weak acid, such as acetate ion, acts as a base in water, and the salt of a weak base, such as ammonium ion, acts as a weak acid. From our previous discussion on the reactions of acids and bases with water in Disassociations, you should know that the Kb of acetate ion can be calculated from the Ka of acetic acid, and that the Ka of ammonium ion can be calculated from the Kb of ammonia, as shown in .

Another type of hydrolysis reaction comes from the reaction of metal ions with high charges. Such ions act as Lewis acids to water molecules, as shown in . A metal ion can bond to water by accepting an lone pair from the oxygen of a water molecule, and this increases the acidity of water molecule. Like other acids, we can calculate the Ka and calculate the pH of a solution containing such ions.

Figure %: Why metal ions decrease the pH of aqueous solutions

To calculate the pH of a solution containing the salt of a weak acid or a weak base, treat the problem exactly as you did when calculating the pH of weak acid and base solutions above in Calculating pH's, Heading . Mixtures of salts of weak acids and weak bases present a challenging mathematical problem that we will not cover in our treatment of acid-base chemistry.