KEY2CHEM

Acid-Base Titration Curves

Acid-base titration curves allow for the quantitation of acid-base reactions. In particular, useful information such as quantity of base required to fully react with the acid, the $$pK_a$$ of a weak acid, and the $$pK_b$$ of a weak base, can be determined. In the titration of a weak acid with a strong base (where the strong base is the titrant), the equivalence point is the point where moles acid initially present equals moles strong base added. Halfway to the equivalence point is the midpoint, where half the acid has been converted to its conjugate base. At this point, $$pH = pK_a$$.

Example 1.

In the titration curve below, which statement is true? A. A strong polyprotic acid is being titrated with a strong base.

B. A weak monoprotic acid is being titrated with a strong base.

C. A weak base is being titrated with a strong acid.

Solution

B. A weak monoprotic acid is being titrated with a strong base.

The pH starts out low, indicating that the starting solution is an acid. Near the equivalence point, the pH changes rapidly, indicated by the sharp, nearly vertical rise in pH over a very small volume range. Because the $$pH > 7$$ at the equivalence point (when all of the acid has been converted to its conjugate base), the titration is that of a weak acid being titrated with a strong base. For a strong acid being titrated with a strong base, the $$pH = 7$$ at the equivalence point. Since there is only one equivalence point, the acid is a monoprotic acid (one ionizable proton).

Example 2.

The titration curve below shows a weak acid being titrated with a strong base. What is the $$pK_a$$ of the weak acid? A. 4

B. 7

C. 10

Solution

A. 4

At the midpoint (half-way to the equivalence point), the $$pH = pKa$$, since half of the acid has been converted to conjugate base.

Example 3.

Which statement about the titration of a weak base with a strong acid is true?

A. At the equivalence point, $$pH = 7$$.

B. At the equivalence point, $$pH > 7$$.

C. At the equivalence point, $$pH < 7$$.

Solution

C. At the equivalence point, $$pH < 7$$.

At the equivalence point, all of the weak base $$\require{mhchem}\ce{B}$$ will be converted into its conjugate acid $$\require{mhchem}\ce{BH+}$$, which acts as a weak acid. The solution of this weak acid $$\require{mhchem}\ce{BH+}$$ will have $$pH< 7$$.