Finding the pH of a buffer question

Question

What is the pH of a buffer made from 0.350 mol of HBrO (Ka = 2.5 × 10⁻⁹) and 0.160 mol of KBrO in 2.0 L of solution?

Answer 1

Henderson Hasselbalch equation:

pH = pKa + log [conj.base]/[acid]

pKa = -log Ka = -log 2.5x10^-9 = 8.60

[conj.base] = [ BrO^-] = 0.160 mol / 2.0 L = 0.080 M

[acid] = [HBrO] = 0.350 mol / 2.0 L = 0.175 M

pH = 8.60 + log (0.080 / 0.175) = 8.60 + log 0.457

pH = 8.60 + (-0.34)

pH = 8.26

NOTE: You could have done this problem without dividing by 2.0 L and just have used 0.160 mol / 0.350 mol. You can do this because the volume didn't change, but it's a good habit/practice to convert to M concentrations in case you run into a problem where the volume does change.