Final answer:
A solution with a pH of 13 has 10^8, or 100,000,000, times fewer H+ ions than a solution with a pH of 5, due to the logarithmic nature of the pH scale.
Step-by-step explanation:
The question is asking to compare the concentration of H+ ions in two solutions with different pH levels. Using the fact that the pH scale is logarithmic, we know that each pH unit represents a tenfold change in hydrogen ion concentration. Since a solution with a pH of 13 has a lower concentration of H+ ions than a neutral solution (pH 7), it is considered basic. Conversely, a solution with a pH of 5 is acidic and has a higher concentration of H+ ions than a neutral solution.
To find out how many times fewer H+ ions a solution with a pH of 13 has compared to a solution with a pH of 5, we subtract the higher pH from the lower pH: 13 - 5 = 8. This tells us that there is an eightfold difference in logarithmic units between the two solutions. Therefore, for every single logarithmic step, there is a tenfold difference, and for eight steps, we calculate 108. In conclusion, a solution with a pH of 13 has 108, or 100,000,000, times fewer H+ ions than a solution with a pH of 5.