**Core Concept**
Amino acids have distinct properties at different pH levels due to their ionizable groups. At isoelectric pH (pI), amino acids exhibit a unique characteristic that can be utilized in various biochemical assays. The isoelectric point is the pH at which the net charge on an amino acid is zero.

**Why the Correct Answer is Right**
The isoelectric pH is the point where the negative charge on the carboxyl group and the positive charge on the amino group balance each other out. This occurs when the pH equals the average of the pKa values of the ionizable groups. At the isoelectric pH, amino acids are least soluble in water and exhibit minimal movement in an electric field. This property is utilized in techniques such as isoelectric focusing, which separates amino acids based on their isoelectric points.

**Why Each Wrong Option is Incorrect**
**Option A:** Amino acids are most soluble in water at their isoelectric pH. **Incorrect** because amino acids are actually least soluble in water at their isoelectric pH due to the absence of net charge.

**Option B:** Amino acids are most basic at their isoelectric pH. **Incorrect** because amino acids are actually neutral at their isoelectric pH, as the positive and negative charges balance each other out.

**Option C:** Amino acids are least stable at their isoelectric pH. **Incorrect** because amino acids are generally most stable at their isoelectric pH, as the absence of net charge reduces the likelihood of electrostatic interactions that can lead to protein denaturation.

**Clinical Pearl / High-Yield Fact**
Isoelectric focusing is a technique that separates proteins based on their isoelectric points, which can be useful in identifying and purifying specific proteins in biochemistry and molecular biology applications.

**Correct Answer:** C.