Elevation of Boiling Point — Revision Notes

⚡ 30-Second Revision

Definition: — Increase in boiling point of a solvent upon adding a non-volatile solute.
Formula: — $\Delta T_b = i \cdot K_b \cdot m$
$\Delta T_b$: — Elevation of boiling point ($T_b^{\text{solution}} - T_b^{\text{solvent}}$)
$i$: — Van't Hoff factor (number of particles/ions per formula unit; $i=1$ for non-electrolytes)
$K_b$: — Ebullioscopic constant (solvent-specific, e.g., $0.52,\text{K kg mol}^{-1}$ for water)
$m$: — Molality (moles of solute / kg of solvent)
Cause: — Lowering of vapor pressure by non-volatile solute.

2-Minute Revision

Elevation of boiling point ($\Delta T_b$) is a key colligative property. It describes the increase in the boiling temperature of a solvent when a non-volatile solute is dissolved in it. The fundamental reason is that the solute particles reduce the vapor pressure of the solvent.

Since boiling occurs when the vapor pressure equals the external atmospheric pressure, a higher temperature is needed for the solution to reach this point. The mathematical relationship is $\Delta T_b = i \cdot K_b \cdot m$.

Here, $i$ is the van't Hoff factor, accounting for the number of particles formed (e.g., $i=1$ for glucose, $i=2$ for $\text{NaCl}$). $K_b$ is the ebullioscopic constant, unique to each solvent (e.g., $0.

52, ext{K kg mol}^{-1}$for water). Molality ($m$) is the concentration in moles of solute per kilogram of solvent, preferred for its temperature independence. Remember to convert solvent mass to kilograms and correctly determine 'i' for electrolytes.

This property is vital for determining the molar mass of unknown non-volatile solutes.

5-Minute Revision

Elevation of boiling point is a colligative property, meaning it depends on the *number* of solute particles, not their chemical identity. When a non-volatile solute is added to a pure solvent, it lowers the solvent's vapor pressure.

Since boiling occurs when the vapor pressure equals the external atmospheric pressure, the solution must be heated to a higher temperature to achieve this, resulting in an elevated boiling point. The elevation, $\Delta T_b$, is the difference between the solution's boiling point ($T_b$) and the pure solvent's boiling point ($T_b^0$).

The quantitative relationship is given by $\Delta T_b = i \cdot K_b \cdot m$.

$i$ (van't Hoff factor): — This accounts for dissociation/association. For non-electrolytes (e.g., glucose, urea), $i=1$. For electrolytes (e.g., $\text{NaCl}$, $\text{CaCl}_2$), $i$ is the number of ions formed (e.g., $\text{NaCl} \rightarrow 2$ ions, $i=2$; $\text{CaCl}_2 \rightarrow 3$ ions, $i=3$).
$K_b$ (Ebullioscopic constant): — A constant specific to the solvent, representing the $\Delta T_b$ for a $1,m$ solution. For water, $K_b = 0.52,\text{K kg mol}^{-1}$.
$m$ (Molality): — Moles of solute per kilogram of solvent. Always convert solvent mass to kilograms.

Example: Calculate the boiling point of a solution containing $6,\text{g}$ of urea (molar mass $60,\text{g/mol}$) in $200,\text{g}$ of water. ($K_b$ for water = $0.52,\text{K kg mol}^{-1}$, $T_b^0$ for water = $100^circ\text{C}$).

1
Moles of urea: — $6,\text{g} / 60,\text{g/mol} = 0.1,\text{mol}$.
2
Mass of water in kg: — $200,\text{g} = 0.2,\text{kg}$.
3
Molality ($m$): — $0.1,\text{mol} / 0.2,\text{kg} = 0.5,\text{mol/kg}$.
4
Van't Hoff factor ($i$): — Urea is a non-electrolyte, so $i=1$.
5
$\Delta T_b$: — $i \cdot K_b \cdot m = 1 \cdot 0.52,\text{K kg mol}^{-1} \cdot 0.5,\text{mol/kg} = 0.26,\text{K}$.
6
Boiling point of solution ($T_b$): — $T_b^0 + \Delta T_b = 100^circ\text{C} + 0.26^circ\text{C} = 100.26^circ\text{C}$.

Remember to pay attention to units and the correct application of 'i'.

Prelims Revision Notes

Definition: — Elevation of boiling point ($\Delta T_b$) is the increase in the boiling temperature of a solvent when a non-volatile solute is added.
Colligative Property: — It depends only on the number of solute particles, not their chemical nature.
Underlying Cause: — Addition of a non-volatile solute lowers the vapor pressure of the solvent. Since boiling occurs when vapor pressure equals external atmospheric pressure, a higher temperature is required for the solution to boil.
Formula: — $\Delta T_b = i \cdot K_b \cdot m$

- **$\Delta T_b$:** Elevation in boiling point ($T_b^{\text{solution}} - T_b^{\text{solvent}}$). Units: K or $^circ\text{C}$. - **$i$ (Van't Hoff Factor):** Accounts for dissociation/association. - Non-electrolytes (e.

g., glucose, urea): $i=1$. - Electrolytes (e.g., $\text{NaCl}$, $\text{CaCl}_2$): $i = \text{number of ions formed}$. For $\text{NaCl}$, $i=2$. For $\text{CaCl}_2$, $i=3$. For $\text{Al}_2(\text{SO}_4)_3$, $i=5$.

- **$K_b$ (Ebullioscopic Constant):** Molal elevation constant, specific to the solvent. - Units: $\text{K kg mol}^{-1}$ or $^circ\text{C kg mol}^{-1}$. - For water: $K_b = 0.52,\text{K kg mol}^{-1}$.

- **$m$ (Molality):** Concentration term, moles of solute per kilogram of solvent. - Formula: $m = \frac{\text{moles of solute}}{\text{mass of solvent (in kg)}}$. - Moles of solute = $\frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}}$.

- Always convert mass of solvent from grams to kilograms ($1,\text{kg} = 1000,\text{g}$). Molality is temperature-independent.

Applications: — Primarily used for determining the molar mass of unknown non-volatile solutes.
Key Points for NEET:

- Be careful with unit conversions (g to kg). - Correctly identify and apply the van't Hoff factor for electrolytes. - Understand the inverse relationship between $\Delta T_b$ and molar mass (for a fixed amount of solute and solvent). - Remember that $K_b$ is a property of the *solvent*. - Higher $i \cdot m$ product means higher $\Delta T_b$ and thus higher boiling point.

Vyyuha Quick Recall

Boil Elevates Keeping Molality In Mind.

Boil Elevates: $\Delta T_b$ (Boiling point Elevation)
Keeping: $K_b$ (Ebullioscopic Constant)
Molality: $m$ (Molality)
In: $i$ (Van't Hoff Factor)
Mind: $\Delta T_b = i \cdot K_b \cdot m$