Answer
$(c)$ is the one that better represents this solution.
Work Step by Step
1. Considering a pure solution:
$[OH^-] = [B^+] = x$
2. Use the Kb formula:
$Kb = \frac{[OH^-][B^+]}{[Base]} = \frac{x^2}{[Base]}$
3. If the solution is diluted to half, the $OH^-$ will change, the base will half its concentration, but the Kb will still stay the same:
$Kb = \frac{y^2}{[Base]*0.5}$
4. Using algebra to solve:
$Kb = \frac{x^2}{[Base]} = \frac{y^2}{[Base]0.5}$
- We can eliminate the [Base]
$x^2 = \frac{y^2}{0.5}$
$0.5 * x^2 = y^2$
- We can use square roots to solve:
$\sqrt {0.5 * x^2} = \sqrt {y^2}$
$0.7 * x \approx y$
- So the second solution will have 0.7 times the concentration of the first one.
- The image of the first solution has 25 protons, so the second should have 25 * 0.7 = 17.5.
(c) has 17 protons, so it is the closest one.
