Well, it sounds like you're in quite a pH pickle! But don't worry, I'll try to help you out with a dose of humor.
First, let's focus on the problem at hand. You mentioned that you're getting a positive value for the base dissociation constant (Kb), and it seems too big. Now, I'm not saying that your calculations are "positively" wrong, but let's double-check them.
To find Kb, we can use the relationship between Ka (acid dissociation constant) and Kb. Since pyrrolidine is a weak base, we can assume that Ka = Kw/Kb, where Kw is the ion product constant for water (1.0 x 10^(-14) at 25°C).
In this case, if the pH of the pyrrolidine solution is 10.82, we can deduce that the pOH is 14 - 10.82 = 3.18. Now, let's convert this pOH value back to OH- concentration.
Using the equation pOH = -log[OH-], we find that [OH-] is equal to 10^(-pOH). Plugging in the values, we get [OH-] ≈ 7.06 x 10^(-4) M.
Since the base (pyrrolidine) reacts with water to form OH- ions, we can consider this reaction: C5H9N + H2O ⇌ C5H9NH+ + OH-. From this reaction, we can see that the concentration of OH- is equal to the concentration of the base (pyrrolidine) that dissociates.
Now, let's calculate Kb. Since [OH-] = [pyrrolidine], Kb = [C5H9NH+] [OH-] / [C5H9N]. Remember that the concentration of C5H9NH+ is zero initially, so we can ignore that term.
Therefore, Kb = [OH-]^2 / [pyrrolidine]. Substituting the values we found earlier, we get Kb ≈ (7.06 x 10^(-4))^2 / (1.00 x 10^(-3)).
Now, plug it into a calculator, and see if you get a more reasonable value for Kb. If not, let me know, and we'll try to figure out what's going on together. Just remember, even if the numbers seem to make no sense, don't let them drive you crazy. Keep a smile on your face, and you'll conquer any chemistry challenge!