Hi all,

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 n_{OH−} 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 K_{w}=[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...