Titration Curves
Learning Goals
● Describe the chemical processes and relative abundance of the acidic and basic species as a strong acid is added to a basic solution.
● Use a titration curve to correlate the relative abundance of acidic and basic species with the pH of the solution under study.
● Determine the original concentration of a solute in solution based on titration curve data.
● Explain how the first derivative of the titration curve can be used to determine the equivalence points of a polyprotic acid.
● Use a titration curve to determine the pKa1 and pKa2 values for a polyprotic acid.
Acids, Bases, and the pH Scale
The Brønsted–Lowry theory defines acids and bases as substances that exchange protons. Since a proton is simply a hydrogen atom without a neutron or electron, its shorthand symbol is H+. In aqueous solution, an acid loses (donates) a proton while a base gains (accepts) a proton.
In donating its proton, the acid increases the concentration of protons in water. Conversely, bases remove protons from water. When a proton is removed from water, the resulting ion is hydroxide (OH-). Therefore, bases increase the concentration of hydroxide in water.
The concentration of protons in water can vary by many orders of magnitude. Thus, the range in proton concentration across different solutions is immense. To make this range more manageable (smaller), we have established the pH scale.
pH = -log[H+]
In this equation, the symbol “p” means to “take the base-10 logarithm of a number and then multiply the result by -1.” If we are working with the concentration of hydroxide, the equation becomes:
pOH = -log[OH-]
Different acids and bases vary greatly in their respective abilities. An acid or base that exchanges a proton 100% of the time is termed “strong”. When this rate is less than 100%, the species is considered “weak”. We can represent strong and weak acids and bases in chemical equations:
The major difference between these chemical equations is whether the reaction proceeds in reverse. When a strong acid or base interacts with a proton, it does not reverse its action. The chemical reaction only proceeds forward and a single arrow is used. When the acid or base is weak, the products can reverse their action and reform into the reactants. Equilibrium is established when the forward and reverse reactions happen at the same rate. This explains why the equilibrium arrows are used (⇌). Because weak acids and bases exist in equilibrium with their products, we can write equilibrium constant expressions (K):
Ka and Kb are known as the acid dissociation constant and base dissociation constant respectively. Ka and Kb receive the same mathematical treatment as [H+] and [OH-]:
pKa = -log[Ka] pKb = -log[Kb]
pKa values are of major importance in organic chemistry, biochemistry, and pharmacology. For example, the pKa value of medications often governs their effectiveness.
Titration Curves
Bases and acids react with each other. We can represent this process as a chemical equation:
Let’s say that we have the base in a beaker with the acid above it in a syringe. Let’s look at what happens to the amounts of reactants and products as we add increasing amounts of the acid to the base.
