I've been a little stuck on a textbook problem concept that I just can't seem to wrap my head around. The question is as follows:
"How many moles of H3O+ or OH− must you add to a 5.6L of strong acid solution to adjust its pH from 4.52 to 5.25? Assume a negligible volume change."
I decided to approach this problem by first converting the provided pH values into pOH, then found [OH−] for both. I then converted [OH−] to nOH− by multiplying by 5.6L. I subtracted the two values (final-initial) to yield ≈8.10*10-9 mol.
This solution was incorrect. The textbook says that the solution is 1.4*10-4 mol, which does make sense looking at the way they solved it, keeping pHs, finding Δ[H3O+] and using the autoionization equation of water to justify Δ[H3O+]=[OH−] needed. But I don't know why my solution doesn't make sense. Wouldn't [H3O+] and [OH−] change proportionally to one another, given that Kw=[H3O+][OH−]? So wouldn't a change in the mols of OH- in the solution as per the change in pOH reflect the moles of OH- added? I would greatly appreciate knowing where I went wrong...