Final answer:
The pH would remain the same since the pH of a buffer depends on the ratio of the concentrations of the conjugate base to the conjugate acid, which does not change when both are doubled.
Step-by-step explanation:
If the concentrations of both the acid and its conjugate base are doubled in a solution, the pH would remain the same. This is because the pH of a buffer solution depends on the ratio of the concentrations of the conjugate acid to its conjugate base. Doubling both concentrations does not change this ratio; therefore, the pH stays constant. As explained by the Henderson-Hasselbalch equation, pH changes only when there is a change in the ratio of the conjugate base ([A-]) to conjugate acid ([HA]). This property is fundamental to the behavior of buffer solutions and is critical to maintaining pH stability in many biochemical and industrial processes.