Chemistry
Methods to Determine the Dissociation Constant of a Weak Acid
Quick fact
The pH at the half-equivalence point of a titration is numerically equal to the pKa of the weak acid—this is a direct consequence of the Henderson-Hasselbalch equation.
Why this is interesting
Every time you squeeze a lemon into your tea, you're witnessing a weak acid in action—but how do chemists actually measure the 'strength' of such acids? The answer lies in a constant that can be unlocked through several clever experimental tricks.
Read the full explanation
Understanding Methods to Determine the Dissociation Constant of a Weak Acid
A weak acid only partially dissociates in water, establishing an equilibrium: HA ⇌ H⁺ + A⁻. The dissociation constant, Ka, is the ratio of the concentrations of products to reactants at equilibrium. To determine Ka, you need to measure these concentrations. The most common method is pH titration: you add a strong base incrementally and record the pH after each addition. The resulting titration curve shows a characteristic S-shape. At the half-equivalence point, where exactly half of the acid has been neutralized, the concentrations of HA and A⁻ are equal, and the Henderson-Hasselbalch equation simplifies to pH = pKa. Thus, the pH at this point directly gives pKa, and Ka = 10⁻ᵖᵏᵃ. Another method uses spectrophotometry if the acid or its conjugate base absorbs light at different wavelengths. By measuring the absorbance at varying pH, you can determine the ratio of species and calculate Ka. Conductometry measures the electrical conductivity, which changes as the acid dissociates, allowing Ka to be extracted from the relationship between concentration and conductivity.
A deeper explanation
The principle behind all methods is to probe the equilibrium position under controlled conditions. In titration, the addition of base shifts the equilibrium, but at the half-equivalence point, the buffer capacity is maximum and the ratio [A⁻]/[HA] = 1, which gives the most accurate pH measurement. The pH meter measures the activity of H⁺, and using the known total acid concentration, you can solve for Ka. Spectrophotometry exploits the Beer-Lambert law: if the acid and conjugate base absorb differently, the absorbance at a given wavelength is a weighted average of the two forms. By measuring absorbance at several pH values, you can construct a plot of absorbance vs. pH, and the inflection point corresponds to pKa. Conductometry relies on the fact that the conductivity of a solution is proportional to the concentration of ions. As the weak acid dissociates, ions are formed, and by measuring conductivity at various concentrations, you can apply Ostwald's dilution law to calculate Ka. Modern methods may also use nuclear magnetic resonance (NMR) to track chemical shifts of pH-sensitive nuclei. The choice of method depends on the acid's properties, available instrumentation, and required accuracy.