Preface: Buffer solution (acid-base buffer). I am provided with a weak base, which I will designate B. pKa for B's conjugate acid--which I will designate BH--is 8.1, and its mole weight (sic) is 121.1. I'm assuming the latter is the molar mass, though I don't know how that helps me solve this problem.
Problem: 0.1 M (moles/L) of B was dissolved in 1.0 L water, then titrated to pH 8.1 and 7.5. I am to assume no change in volume (sounds like an odd assumption to me, how do you titrate something without [significantly] altering the volume? I always assumed titration is only done by adding a liquid to another liquid, is this not correct?).
I am to find the the concentration of BH at pHs 8.1 and 7.5.
This question looked really easy to me at the first glance, but after a few hours I realized I had no idea on how to go about this.
I've tried calculating the equilibrium concentrations and going from there. This just ends up in x != x in my calculations (where x is the concentration of some substance), which obviously doesn't hold.
I've used the acid dissociation-, base dissociation- and Henderson–Hasselbalch equations, but nothing seems to do the trick. I might not be the brightest person to have grazed the surface of the planet, but I'm confident that I've got a firm grasp on elementary arithmetics.
The answer is provided, and should be 0.05 M at pH = 8.1.
I would highly appreciate somebody showing or explaining the thought process to me.
I tagged this as homework due to the nature of this question, but it isn't. I don't know anybody who knows much chemistry in "real life", so I figured I'd pin my hopes on a friendly soul answering this question. Thanks in advance.