To calculate the molarity of the base (KOH) in the solution, we need to consider the chemical reaction that takes place between HCl (acid) and KOH (base). The reaction can be represented as:

HCl + KOH → KCl + H₂O

From the balanced chemical equation, we can see that 1 mole of HCl reacts with 1 mole of KOH. Therefore, the number of moles of KOH present in the solution is equal to the number of moles of HCl that have reacted.

To calculate the number of moles of HCl that have reacted, we can use the formula:

Moles of HCl reacted = Molarity of HCl × Volume of HCl

Substituting the given values into the formula, we get:

Moles of HCl reacted = 1.5 M × 0.5 L = 0.75 moles

Since 1 mole of HCl reacts with 1 mole of KOH, the number of moles of KOH present in the solution is also 0.75 moles.

To calculate the molarity of the KOH in the solution, we can use the formula:

Molarity of KOH = Moles of KOH / Volume of solution

Substituting the known values into the formula, we get:

Molarity of KOH = 0.75 moles / 0.5 L = 1.5 M

Therefore, the molarity of the KOH (base) in the solution is 1.5 M.