Question

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

Short answer

Yes, the \(\mathrm{pH}\) of a solution can be negative. This occurs when the concentration of hydrogen ions (\(H_3O^+\)) in the solution is greater than 1, which indicates a highly acidic solution. Although the typical \(\mathrm{pH}\) scale ranges from 0 to 14, it can extend beyond this range based on the acidity or basicity of a solution.

Step-by-step solution

Definition of pH

The \(\mathrm{pH}\) of a solution is defined as the negative logarithm of the hydronium ion concentration (\([H_3O^+]\)), which is the concentration of hydrogen ions (H+). Mathematically, it is expressed as: $$ \mathrm{pH} = -\log_{10} [H_3O^+] $$

Range of \(\mathrm{pH}\)

Normally, the \(\mathrm{pH}\) scale ranges from 0 to 14, where a \(\mathrm{pH}\) of 7 is neutral, a \(\mathrm{pH}\) less than 7 is acidic, and a \(\mathrm{pH}\) greater than 7 is basic. In principle, the \(\mathrm{pH}\) scale can extend beyond this range based on the concentration of hydrogen ions in the solution.

Negative \(\mathrm{pH}\)

Since the \(\mathrm{pH}\) is a logarithmic scale, it is possible to have negative \(\mathrm{pH}\) values. Remember that the formula for \(\mathrm{pH}\) is: $$ \mathrm{pH} = -\log_{10} [H_3O^+] $$ To have a negative \(\mathrm{pH}\), \(-\log_{10} [H_3O^+]\) needs to be negative, meaning that the \(\log_{10} [H_3O^+]\) needs to be positive. This will happen when the concentration of hydrogen ions in the solution is more than 1: $$ [H_3O^+] > 1 $$ Solutions like this are strongly acidic, and can indeed have negative \(\mathrm{pH}\) values.

Conclusion

The \(\mathrm{pH}\) of a solution can be negative. This happens when the concentration of hydrogen ions (\(H_3O^+\)) in the solution is greater than 1, indicating a highly acidic solution. Although the conventional \(\mathrm{pH}\) scale ranges from 0 to 14, it can extend beyond this range depending on the acidity or basicity of a solution.