Final answer:
A solution with a pH of 11.7 is 1,000 times more basic than a solution with a pH of 8.7 because the pH scale is logarithmic, and each pH unit corresponds to a tenfold difference in hydronium ion concentration.
Step-by-step explanation:
To determine how many times more basic one solution is compared to another, you need to understand the pH scale, which is logarithmic. This means that for each unit of pH change, there is a tenfold change in hydronium ion concentration. The solution with a pH of 11.7 is three pH units higher than the solution with a pH of 8.7.
Since each pH unit represents a tenfold difference in basicity, you calculate the difference in basicity by raising 10 to the power of the difference in pH units, which is 10(11.7 - 8.7) or 103. Therefore, a solution with a pH of 11.7 is 1,000 times more basic than a solution with a pH of 8.7.