Step 1: Boiling point elevation is a colligative property, and the working formula is \( \Delta T_b = K_b\,m \). The constant \( K_b \) in this line is the quantity to be defined.
Step 2: Set the molality equal to one in the formula. Then \( \Delta T_b \) becomes numerically equal to \( K_b \). So \( K_b \) is simply the boiling point elevation shown by a solution that contains exactly one mole of solute in one kilogram of solvent.
Step 3: Because it is tied to a fixed one molal concentration, \( K_b \) depends only on the nature of the solvent and not on the solute. Each solvent has its own value (for example \( 0.52\ K\,kg\,mol^{-1} \) for water).
Step 4: Rearranging the formula, \( K_b = \Delta T_b/m \), so its units are kelvin times kilogram divided by mole, written \( K\,kg\,mol^{-1} \).