Ladder Diagrams: Acid–Base Equilibria

Understanding the chemistry between the reagents is necessary for performing any experiment. To this end, scientists have designed a tool called a ladder diagram, which is a graphical representation that helps illustrate the chemistry of a system.

A ladder diagram for acid-base equilibria consists of a vertical axis that represents pH and horizontal bars (steps on the ladder) that help position all the pK_a values in the system. At equilibrium, the pH value of the system corresponds to one of the pK_a values, which divide the system into more acidic and more basic regions. At pH values higher or lower than any given pK_a value, i.e. when the system is not at equilibrium, the dominant species will correspond to the one written in that region of the diagram.

For example, the ladder diagram of the HF and F^– acid-base equilibria system shows a horizontal line at pH 3.17, which is the pK_a value of HF. At pH values above 3.17, F^– predominates, whereas at pH values below 3.17, the HF concentration is higher.

The ladder diagram of this system can also be used to understand the effect of pH on the solubility of CaF₂. The solubility of CaF₂ can be increased by converting F^– into HF. In contrast, its solubility decreases if F^– dominantes. From the ladder diagram, it can be understood that pH values above 3.17 allow F^– to dominate, thereby decreasing the solubility of CaF₂.