The balanced reaction equation is:
KOH + HCl H2O + KCl.
As one can see, 1 mol of potassium hydroxide reacts with 1 mol of hydrochloric acid:
The number of the moles of HCl reacted is the product of the concentration and the volume of the HCl solution:
Therefore, the number of the moles of KOH reacted is:
The concentration of the 45 cm3 solution that contains 1.25·10-3 mol of KOH is:
The mass of KOH in the solution is:
The mass of KOH in 45 mL is proportional to the mass of KOH in 250 mL:
The percentage purity of KOH is:
The percentage impurity of KOH is:
As KOH is a strong electrolyte, the number of the moles of hydroxide anions is equal to the number of the moles of KOH:
i. The concentration of the pure KOH is 0.028 moles/dm3
ii. The percentage purity of KOH is 9.7%
iii. The percentage impurity of KOH is 90.3 %
iv. The number of moles of hydroxyl ions present in the pure KOH that reacted is 1.25·10-3 mol.
P.S. I suppose that there is a mistake in the concentration of HCl used. If it was 0.5 M and not 0.05 M, the purity of KOH would be 97%, the percentage impurity would be 3%, the concentration of the pure KOH would be 0.28 moles/dm3 and the number of moles of hydroxyl ions present in the pure KOH that reacted would be 1.25·10-2 mol.