Question

Define molal elevation constant or ebullioscopic constant.

Answer 1

Hint: The molal elevation constant or ebullioscopic constant is associated with the colligative property of elevation in boiling point when a non-volatile solute is added to the pure solvent.
Knowing about this colligative property, we can define the constant easily.

Complete Solution :
Let us study the colligative property of elevation in boiling point;
Elevation in boiling point-
The phenomenon of elevation in boiling point describes the rise in boiling point of a solution containing solute dissolved in solvent than the boiling point of pure solvent.
Addition of non-volatile solute to pure solvent is responsible for the rise in the boiling point of the resulting solution with respect to the primary pure solvent. The elevation in boiling point can be stated as,
\[\Delta {{T}_{b}}={{K}_{b}}\times m\times i\]
where,
$\Delta {{T}_{b}}$ = change in boiling point
${{K}_{b}}$ = molal elevation constant or ebullioscopic constant
m = molality of the solution
i = Van’t Hoff factor (usually equal to unity when molecules do not dissociate)

Hence,
Molal elevation constant or ebullioscopic constant can be defined as follows;
It is defined as the elevation in boiling point when the molality of the solution is unity i.e. when one mole of the non-volatile solute is dissolved in one Kg of pure solvent. It can be stated as:
\[{{K}_{b}}=\dfrac{\Delta {{T}_{b}}}{m}\]
and the unit is degree/molality i.e. K/m.
It is a characteristic constant whose value is independent of nature of solute but is dependent upon the nature of solvent.

Note: Molal elevation constant from enthalpy of vaporisation diagram can be stated as,
\[{{K}_{b}}=\dfrac{R{{T}_{b}}^{2}}{1000{{l}_{v}}}\]
where,
${{T}_{b}}$ = boiling point of liquid
${{l}_{v}}$ = latent heat of vaporisation per gram of solvent = $\dfrac{{{\Delta }_{vap}}H}{M}$
${{\Delta }_{vap}}H$ = latent heat of vaporisation per mole of solvent
M = molecular mass of the solvent.