We calculate the Molarity by the following formula -
Molarity = Number of Moles of solute/Volume of solution (in litre)
A solution is made up of little components of solute dissolve in the solvent.
Number of Moles = Given Mass/Molecular Mass
The Relationship between 2 solutions with same number of Moles is given as
C1V1 = C2V2
Where C and V are concentration and volume of solution respectively.
In this question we are given - Molecular Mass of KOH = 56g/mole Volume = 500ml
Given Mass = 84g
Number of moles = 84g / 56g / mole = 1.5 mole
Volume = 500 / 1000 = 0.5 litre
(We divide by 1000 to convert it into litres since 1litre = 1000ml).
Molarity = 1.5 mole / 0.5 litre = 3 mole / litre or 3M