Question

Can the \(\mathrm{pH}\) of a solution be negative? Explain.

Short answer

Yes, the pH of a solution can be negative, particularly in highly acidic solutions with hydrogen ion concentrations greater than 1 M or under extreme conditions. This happens because the pH is inversely proportional to the hydrogen ion concentration, and the pH scale is not limited to the range from 0 to 14.

Step-by-step solution

Recall the definition of pH

The pH of a solution is a measure of its acidity or alkalinity. Mathematically, pH is defined as the negative base 10 logarithm of the hydrogen ion concentration ([H+]) in moles per liter. It can be expressed as: pH = -log10([H+])

Calculate the pH in cases where [H+] is greater than 1 M

By definition, pH is inversely proportional to the hydrogen ion concentration. When the concentration of hydrogen ions in a solution is greater than 1 M (mol/L), the pH of that solution will be less than zero. For example, if a solution has a hydrogen ion concentration of 10 M: pH = -log10(10) pH = -1 So in this case, the pH of the solution is negative.

Understand the practical implications of a negative pH

Negative pH values are possible in highly acidic solutions. The pH scale is not limited to the range from 0 to 14, but under normal conditions (e.g., under atmospheric pressure and at room temperature), pH values typically range from 0 to 14. Nonetheless, it is essential to understand that extreme conditions, such as high pressures or temperatures, may cause highly acidic or highly alkaline solutions, resulting in negative pH values or values over 14. In conclusion, the pH of a solution can indeed be negative, especially in highly acidic solutions with hydrogen ion concentrations greater than 1 M or under extreme conditions.