Problem 15 - Chemistry An Atoms First Approach

Question

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

Step-by-Step Solution

Answer

Yes, the pH of a solution can be negative if the molar concentration of hydrogen ions \([H^+]\) is greater than 1, which can occur in extremely acidic solutions. This is because the pH is calculated as \[pH = -\log_{10} [H^+]\], and logarithm values become negative when their argument is greater than 1.

Step 1: Understanding pH

pH is a measure of the acidity of a solution, which represents the concentration of hydrogen ions (H+) in the solution. It is defined as the negative logarithm (base 10) of the molar concentration of hydrogen ions. Mathematically, it can be expressed as: \[ pH = -\log_{10} [H^+] \] where [H^+] is the molar concentration of hydrogen ions in the solution.

Step 2: Calculating pH

To calculate the pH of a solution, we need to find the concentration of hydrogen ions. We can then plug it into the formula mentioned above. For example, consider a solution with [H^+] = 0.01 M (mol/L). The pH of the solution can be calculated as follows: \[ pH = -\log_{10} (0.01) = 2\] In this case, the pH of the solution is 2.

Step 3: Can pH be negative?

The pH of a solution can be negative if the molar concentration of hydrogen ions [H^+] is greater than 1. This can occur in very acidic solutions. Mathematically speaking, logarithm values become negative when their argument (input) is greater than 1. For example, if the [H^+] > 1: \[ pH = -\log_{10}([H^+]) < 0\] In this case, the pH of the solution will indeed be negative.

Step 4: Conclusion

Yes, the pH of a solution can be negative. This occurs when the molar concentration of hydrogen ions [H^+] in the solution is greater than 1. This is often seen in extremely acidic solutions.