Step 1: Both quantities measure concentration, but they differ in what forms the denominator. Molality counts the solvent by mass, while molarity counts the solution by volume.
Step 2 (Molality): Take the moles of solute and divide by the mass of solvent expressed in kilograms. In symbols \( m = n_{solute}/W_{solvent(kg)} \), unit mol kg-1. As mass is fixed, this value is independent of temperature.
Step 3 (Molarity): Take the same moles of solute but divide by the total volume of the prepared solution in litres, \( M = n_{solute}/V_{solution(L)} \), unit mol L-1. Because the solution volume varies with temperature, molarity is temperature dependent.
Step 4: In short, molality is mole-per-kilogram-of-solvent and molarity is mole-per-litre-of-solution.