The Henderson-Hasselbalch equation would be applicable here if they had given you the pKas for ammonium and formic acid. But they don't. However, even if they did, it would be a waste of time to use any equations here and do any number crunching.
Let me answer this question here,
But I feel like when you mix two solutions together, they will react towards equilibrium (Keq) and the concentrations will change. So should I do a initial-change-final table?
first. There are plenty of times you will have to set up an ICE table, but this is not one of them. When we mix, for example, the two solutions in A, the number of moles of NH4+ in the resulting solution will be the same as the number of moles of NH4+ in 15mL of .10M NH4+(aq), and the number of moles of NH3 in the resulting solution will be the same as the number of moles of NH3 in 10mL of .10M NH3(aq). Why? Because for every NH4+ that's converted into NH3, the proton that is lost converts an NH3 into an NH4+. This holds for any time you mix a conjugate acid with its conjugate base.
The question asks which solution has the greatest pH; in other words, we are looking for the least acidic or most basic solution. Solution B is more basic than solution A, because we have more conjugate base and less conjugate acid; in other words solution A has more acidic protons than solution B, because NH3 has no acidic protons whereas NH4+ has one. By the same reasoning, solution D is more basic than solution C. (Sodium formate will completely dissociate into Na+ and HCO2-.) We've narrowed our choices to B and D.
The proportions of conjugate base to conjugate acid are the same in B and D, so now the question boils down to this: which is more basic, ammonia (NH3) or formate (HCO2-)? Answer: ammonia. Therefore, solution B is more basic than solution D.
How do we know ammonia is more basic than formate? Ammonia is a strong base that you should have memorized as such, and formate is the conjugate base of a strong acid (formic acid, which should also be memorized as a strong acid). The conjugate base of a strong acid is a weak base. [
Having trouble memorizing your strong acids and bases? Exercise your orgo! NH3 is both a strong base and a good nucleophile in a lot of organic reactions. The conjugate base of formic acid (i.e., formate) is resonance stabilized.]
To be honest, we do use an understanding of the H-H equation here, because we're evaluating solutions' relative pH based on their concentration of conjugate base ([A-]), concentration of conjugate acid ([HA]), and relative acidity/basicity (pKa), but to plug numbers in was not the intent of whoever wrote this question.
