Acid–Base Equilibria: Activity-Based Definition of pH

The negative logarithm of hydrogen ion concentration applies only to ideal solutions. In real solutions, pH must account for hydrogen ion activity, which reflects the effective concentration of hydrogen ions. Activity incorporates both concentration and an activity coefficient, providing a more accurate representation of how hydrogen ions behave in solution.

Adding salt like potassium chloride increases ionic strength, which decreases activity coefficients and increases hydrogen ion activity. This causes a slight pH decrease. However, the hydrogen ion concentration increases significantly, demonstrating that activity and concentration respond differently to ionic strength changes.

Activity coefficients decrease as ionic strength increases. In pure water with extremely low ionic strength, activity coefficients approach one, making activity nearly equal to concentration. As ionic strength rises through electrolyte addition, activity coefficients drop further, reducing the activity coefficient's value and affecting the solution's effective hydrogen ion concentration.

pH is defined as the negative logarithm of hydrogen ion activity. This can be expressed as the negative logarithm of the product of hydrogen ion concentration and its activity coefficient. This formulation accounts for non-ideal behavior and provides accurate pH measurements in real solutions where activity differs from concentration.

Pure water has extremely low ionic strength because few ions are present to interact with hydrogen ions. When ionic strength is very low, activity coefficients approach one, meaning hydrogen ion activity nearly equals its concentration. This approximation breaks down when electrolytes are added, increasing ionic strength and decreasing activity coefficients.

Ideal solutions assume activity equals concentration, so pH depends solely on hydrogen ion concentration. Non-ideal solutions require considering hydrogen ion activity, which accounts for ion interactions through the activity coefficient. Real solutions behave non-ideally, especially at higher ionic strengths, making activity-based pH definitions more accurate.

Potassium chloride increases ionic strength, which decreases activity coefficients and increases hydrogen ion activity. Although hydrogen ion concentration rises significantly, the activity increase is slight because the activity coefficient decrease partially offsets the concentration increase. This demonstrates that pH depends on activity, not concentration alone.