Question

Differentiate between molar and molal elevation constants. Give two different formulae involving these two constants for the determination of molecular mass of solute.

Hint:

Always remember: $K_b$ → kg of solvent; $K_b'$ → litre of solvent.

Answer 1

Step 1: Definitions.
\begin{itemize} \item
Molar elevation constant (K$_b'$): It is the elevation of boiling point produced when one mole of solute is dissolved in 1 litre of solvent. \item
Molal elevation constant (K$_b$): It is the elevation of boiling point produced when one mole of solute is dissolved in 1000 g (1 kg) of solvent. \end{itemize} Step 2: Formula with molal elevation constant.
\[ \Delta T_b = K_b \times m \] where, \(m = \frac{1000 \times w}{M \times W}\)
Thus, \[ M = \frac{1000 \times K_b \times w}{\Delta T_b \times W} \] Here, \(w\) = mass of solute, \(W\) = mass of solvent in g, \(M\) = molar mass of solute. Step 3: Formula with molar elevation constant.
\[ \Delta T_b = K_b' \times C \] where, \(C = \frac{w}{M \times V}\) (molar concentration)
Thus, \[ M = \frac{K_b' \times w}{\Delta T_b \times V} \] Here, \(V\) = volume of solvent in litres. Conclusion:
Molar elevation constant is defined with respect to litre of solvent, while molal elevation constant is defined with respect to kg of solvent. Both can be used to calculate molar mass of solute.