State the Henderson–Hasselbalch equation and explain when it is used.

• A. pH = pKa + log([A-]/[HA]); used for buffer solutions.
• B. pH = pKa - log([A-]/[HA]); used for buffer.
• C. pH = pKw + log([OH-]/[H+]); used for buffers.
• D. pH = log([HA]/[A-]);

Answer: (A)

The Henderson–Hasselbalch equation shows how the pH of a buffer depends on the ratio of its conjugate base to its weak acid. It is pH = pKa + log([A-]/[HA]), and it’s used to estimate or adjust the pH of buffer solutions that contain a weak acid HA and its conjugate base A- in appreciable amounts. This comes from the acid dissociation constant expression Ka = [H+][A-]/[HA]; taking logs and solving for pH gives pH = pKa + log([A-]/[HA]).

In a buffer, changing the ratio of A- to HA shifts the pH: more A- raises pH (toward the pKa), more HA lowers it. When the ratio is 1, pH equals pKa. Temperature matters because pKa itself changes with temperature, so the buffer’s pH responds to both the ratio and the pKa at that temperature.

Why the other forms aren’t correct in this context: pH = pKa - log([A-]/[HA]) would invert the effect of the ratio, pH = pKw + log([OH-]/[H+]) describes water’s autoprotolysis but isn’t the buffer equation, and pH = log([HA]/[A-]) misses the pKa term and gives a reciprocal relationship that does not equal the buffer pH.