Question

PH is given by the formula pH = -log [H+]

where (H+) is the concentration of
hydrogen in moles per liter. If the pH of
Bill's swimming pool is 7.8 and the pH of
Maura's swimming pool is 7.2, whose
pool has a greater concentration of
hydrogen? How many times greater is it?

Answer 1

• Maura's
• 4 times

Explanation:

The logarithm function is monotonic with a positive slope everywhere. So, the logs of numbers are in the same order as the numbers themselves. pH is the negative of the logarithm, so the pH values are in the reverse order of the numbers themselves.

Maura's pool has a lower pH, so will have a higher concentration of hydrogen ions.

The log of a ratio is the difference of the logs. Here, the difference of the logs is 7.8 -7.2 = 0.6, so the ratio of H+ concentrations in the two pools is ...

10^0.6 ≈ 4.0

Maura's pool has 4× the H+ concentration of Bill's pool.