The chemical reaction involved in this titration process would be:
NaOH(aq) + KHC8H4O4(aq) = KNaC8H4O4(aq) + H2O(l)
To determine the concentration of the NaOH solution, we, first, need to calculate the moles of NaOH that is used up in the reaction given the amount of KHP solution that is used. We do as follows:
Moles NaOH = 0.500 M KHP ( .025 L solution ) ( 1 mol NaOH / 1 mol KHP ) = 0.0125 mol NaOH reacted
Volume of NaOH solution used = 53.5 mL - 25.0 = 28.5 mL
Molarity is the number of moles of a solute per liter of solution. We calculate as follows:
Molarity of NaOH = 0.0125 mol / .0285 mL = 0.44 M