Final answer:
The concentration of hydrogen ions increases 1000 times when the pH of a solution is changed from 5 to 2, not 5 times as initially stated, due to the logarithmic nature of the pH scale.
Step-by-step explanation:
The question pertains to the change in hydrogen ion concentration when an acid with a pH of 5 is further acidified to a pH of 2. The change in pH represents a change in the concentration of hydrogen ions (H+).
By definition, pH is the negative logarithm of the hydrogen ion concentration: pH = -log[H+]. Going from a pH of 5 to a pH of 2, means that the hydrogen ion concentration increases by a factor of 10 for each unit decrease in pH. Consequently, changing the pH from 5 to 2 (a change of 3 pH units) corresponds to an increase in hydrogen ion concentration by a factor of 103, or 1000 times.
This is much more than the initially stated '5 times' increase. Understanding the logarithmic nature of the pH scale is critical here, as it shows that each unit change on the pH scale represents a tenfold change in hydrogen ion concentration.