Elevation in Boiling Point | Colligative Properties Class 12

Elevation in Boiling Point

Ebullioscopy | Colligative Properties | Solutions Class 12

1. What is Boiling Point Elevation?

The boiling point of a liquid is the temperature at which its vapor pressure becomes equal to the atmospheric pressure.

                    Concept: When a non-volatile solute is added to a solvent, the vapor pressure decreases. Therefore, the solution must be heated to a higher temperature to make its vapor pressure equal to 1 atm. This increase is called Elevation in Boiling Point.
                

2. Mathematical Expression

If $T_b^\circ$ is the boiling point of pure solvent and $T_b$ is the boiling point of the solution:

$$ \Delta T_b = T_b - T_b^\circ $$

Experimentally, for dilute solutions, the elevation ($\Delta T_b$) is directly proportional to the molal concentration ($m$) of the solute.

$$ \Delta T_b = K_b \times m $$

Where:

$m$ = Molality (moles of solute / kg of solvent)
$K_b$ = Molal Elevation Constant or Ebullioscopic Constant.

Unit of $K_b$: $K \cdot kg \cdot mol^{-1}$ or $^\circ C/m$.

3. Calculation of Molar Mass ($M_2$)

Substituting molality $m = \frac{w_2 \times 1000}{M_2 \times w_1}$:

$$ M_2 = \frac{1000 \times K_b \times w_2}{w_1 \times \Delta T_b} $$

Where $w_2$ is mass of solute and $w_1$ is mass of solvent (in g).

4. Thermodynamic Relation for $K_b$

$K_b$ depends only on the nature of the solvent.

$$ K_b = \frac{R \cdot M_1 \cdot (T_b^\circ)^2}{1000 \cdot \Delta_{vap}H} $$

Where:

$R$ = Gas Constant ($8.314 J \cdot K^{-1} \cdot mol^{-1}$)
$M_1$ = Molar mass of solvent (g/mol)
$\Delta_{vap}H$ = Enthalpy of vaporization

5. For Electrolytes (Van't Hoff Factor)

If the solute undergoes association or dissociation (e.g., $NaCl$, $MgCl_2$), we must include the Van't Hoff factor ($i$).

$$ \Delta T_b = i \times K_b \times m $$

Example: For $NaCl$, $i=2$ (ideal). The elevation is double that of Glucose ($i=1$).

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