2.9:
Ladder Diagrams: Acid–Base Equilibria
Ladder diagrams are graphical representations useful for evaluating the chemistry of a given system during analysis.
A Ladder diagram used for assessing the reactivity of acids and bases consists of a vertical line of pH scale and a short horizontal line that correlates to the pH equal to the pKa value, separating the solution into two regions.
Consider the reaction between the HF and F−. At equilibrium, the HF and F− concentrations are equal, and the pH value equals its pKa of 3.17.
The ladder diagram shows a higher concentration of HF at pH values below its pKa, whereas the concentration of F− dominates above this.
Similarly, the HF and NH3 system ladder diagram shows another horizontal line at the pH equal to pKa, NH3 of 9.24. HF and NH4+ species dominate at the pH values below the HF pKa value of 3.17.
However, if the pH values are between 3.17 and 9.24, the NH4+ and F− species dominate, and above 9.24, F− and NH3 species predominate.
2.9:
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 pKa values in the system. At equilibrium, the pH value of the system corresponds to one of the pKa values, which divide the system into more acidic and more basic regions. At pH values higher or lower than any given pKa 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 pKa 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.