Acids and Bases - Titration Curves

Strong Acid Titration Curve

Titration is a technique used in analytical chemistry to determine the concentration of an unknown acid or base. Titration involves the slow addition of one solution where the concentration is known to a known volume of another solution where the concentration is unknown until the reaction reaches a desired level. For acid/base titrations, a color change from a pH indicator is reached or a direct reading using a pH meter. This information can be used to calculate the concentration of the unknown solution.

If the pH of an acid solution is plotted against the amount of base added during a titration, the shape of the graph is called a titration curve. All acid titration curves follow the same basic shapes.

At the beginning, the solution has a low pH and climbs as the strong base is added. As the solution nears the point where all of the H⁺ are neutralized, the pH rises sharply and then levels out again as the solution becomes more basic as more OH^- ions are added.

The first curve shows a strong acid being titrated by a strong base. There is the initial slow rise in pH until the reaction nears the point where just enough base is added to neutralize all the initial acid. This point is called the equivalence point. For a strong acid/base reaction, this occurs at pH = 7. As the solution passes the equivalence point, the pH slows its increase where the solution approaches the pH of the titration solution.

Weak Acids and Strong Bases - Titration Curves

A weak acid only partially dissociates from its salt. The pH will rise normally at first, but as it reaches a zone where the solution seems to be buffered, the slope levels out. After this zone, the pH rises sharply through its equivalence point and levels out again like the strong acid/strong base reaction.

There are two main points to notice about this curve.

The first is the half-equivalence point. This point occurs halfway through a buffered region where the pH barely changes for a lot of base added. The half-equivalence point is when just enough base is added for half of the acid to be converted to the conjugate base. When this happens, the concentration of H⁺ ions equals the K_a value of the acid. Take this one step further, pH = pK_a.

The second point is the higher equivalence point. Once the acid has been neutralized, notice the point is above pH=7. When a weak acid is neutralized, the solution that remains is basic because of the acid's conjugate base remains in solution.

Polyprotic Acids and Strong Bases - Titration Curves

The third graph results from acids that have more than one H⁺ ion to give up. These acids are called polyprotic acids. For example, sulfuric acid (H₂SO₄)is a diprotic acid. It has two H⁺ ions it can give up.

The first ion will break off in water by the dissociation

H₂SO₄ → H⁺ + HSO₄^-

The second H⁺ comes from the dissociation of HSO₄^- by

HSO₄^- → H⁺ + SO₄^2-

This is essentially titrating two acids at once. The curve shows the same trend as a weak acid titration where the pH does not change for a while, spikes up and levels off again. The difference occurs when the second acid reaction is taking place. The same curve happens again where a slow change in pH is followed by a spike and leveling off.

Each 'hump' has it's own half-equivalence point. The first hump's point occurs when just enough base is added to the solution to convert half the H⁺ ions from the first dissociation to its conjugate base, or it's K_a value.

The second hump's half-equivalence point occurs at the point where half the secondary acid is converted to the secondary conjugate base or that acid's K_a value.

On many tables of K_a for acids, these will be listed as K₁ and K₂. Other tables will list only the K_a for each acid in the dissociation.

This graph illustrates a diprotic acid. For an acid with more hydrogen ions to donate [e.g., citric acid (H₃C₆H₅O₇) with 3 hydrogen ions] the graph will have a third hump with a half-equivalence point at pH = pK₃.