Calculating the volume of 0.05mol/dm3 KOH is required to neutralise 25.0cm3 of 0.0150mol/dm3 HNO3

HNO3+KOH—> KNO3+H2O

You first need to construct a balanced chemical equation to describe the reaction:

KOH + HNO3 > KNO3 + H2O

Work out the no. moles of HNO3 being neutralized:

Moles = Volume x Concentration = (25/1000) x 0.0150 = 0.000375 moles

From the balanced equation the molar ratio of KOH to HNO3 is 1:1 so you also need 0.000375 moles of KOH to neutralise the nitric acid

Now you can work out the volume of KOH required:

Volume = Moles/Concentration = (0.000375)/0.05 = 0.0075 dm^3 = 7.5 cm^3

the old alchemists made significant contributions to science even though there starting premises were off a bit. their conclusions after failure would steer them into better directions for investigation. science is no more than close observation and the initial mistakes result in rethinking and retrying experiments.