Raoult's Law — Revision Notes

⚡ 30-Second Revision

Raoult's Law (Non-volatile solute): — $P_s = P^0 \chi_{\text{solvent}}$ or $\frac{P^0 - P_s}{P^0} = \chi_{\text{solute}}$
Raoult's Law (Volatile components A & B): — $P_A = P_A^0 \chi_A$, $P_B = P_B^0 \chi_B$
Total Vapor Pressure: — $P_{\text{total}} = P_A + P_B = P_A^0 \chi_A + P_B^0 \chi_B$
Ideal Solution: — Obeys Raoult's Law, $\Delta H_{\text{mix}} = 0$, $\Delta V_{\text{mix}} = 0$, A-A, B-B, A-B forces similar.
Positive Deviation: — $P_{\text{obs}} > P_{\text{ideal}}$, A-B forces < A-A, B-B forces, $\Delta H_{\text{mix}} > 0$, $\Delta V_{\text{mix}} > 0$. Examples: Ethanol + water, Acetone + $CS_2$.
Negative Deviation: — $P_{\text{obs}} < P_{\text{ideal}}$, A-B forces > A-A, B-B forces, $\Delta H_{\text{mix}} < 0$, $\Delta V_{\text{mix}} < 0$. Examples: Acetone + chloroform, Nitric acid + water.

2-Minute Revision

Raoult's Law is key to understanding solution vapor pressure. For a non-volatile solute, it states that the solution's vapor pressure ($P_s$) is the pure solvent's vapor pressure ($P^0$) multiplied by the solvent's mole fraction ($\chi_{\text{solvent}}$).

This means adding a non-volatile solute always lowers the vapor pressure. The relative lowering of vapor pressure, $(P^0 - P_s)/P^0$, equals the solute's mole fraction ($\chi_{\text{solute}}$), making it a colligative property useful for molar mass determination.

For solutions of two volatile components (A and B), each component's partial vapor pressure ($P_A$, $P_B$) is its pure vapor pressure ($P_A^0$, $P_B^0$) times its mole fraction ($\chi_A$, $\chi_B$). The total vapor pressure is the sum of these partial pressures.

Ideal solutions perfectly follow this, having similar intermolecular forces and no heat or volume change on mixing. Real solutions deviate: positive deviation (higher vapor pressure) occurs when A-B forces are weaker, leading to endothermic mixing and volume expansion.

Negative deviation (lower vapor pressure) occurs when A-B forces are stronger, leading to exothermic mixing and volume contraction. Remember these deviations and their molecular basis for conceptual questions.

5-Minute Revision

Let's quickly review Raoult's Law, a fundamental principle for solutions. It governs how vapor pressure changes when components are mixed.

Scenario 1: Non-volatile solute in a volatile solvent.

When you add a substance that doesn't evaporate easily (like sugar) to a liquid that does (like water), the vapor pressure of the solution decreases. Raoult's Law quantifies this: the vapor pressure of the solution ($P_s$) is directly proportional to the mole fraction of the solvent ($\chi_{\text{solvent}}$) and the vapor pressure of the pure solvent ($P^0$).

So, $P_s = P^0 \chi_{\text{solvent}}$. An important consequence is that the *relative lowering* of vapor pressure, which is $(P^0 - P_s)/P^0$, is equal to the mole fraction of the solute ($\chi_{\text{solute}}$).

This is a colligative property, meaning it depends only on the number of solute particles, not their identity. This is often used to find the molar mass of an unknown non-volatile solute.

Example: Pure water at $30^{\circ}\text{C}$ has a vapor pressure of $31.8\,\text{mmHg}$. If you dissolve $1\,\text{mol}$ of urea in $9\,\text{mol}$ of water, the mole fraction of water is $9/(9+1) = 0.9$. The solution's vapor pressure would be $31.8 \times 0.9 = 28.62\,\text{mmHg}$.

Scenario 2: Two or more volatile components (Ideal Solutions).

If both components (say, A and B) can evaporate, then both contribute to the total vapor pressure. Raoult's Law states that the partial vapor pressure of each component ($P_A$ or $P_B$) is its pure vapor pressure ($P_A^0$ or $P_B^0$) multiplied by its mole fraction in the liquid solution ($\chi_A$ or $\chi_B$).

So, $P_A = P_A^0 \chi_A$ and $P_B = P_B^0 \chi_B$. The total vapor pressure ($P_{\text{total}}$) is simply the sum of these partial pressures: $P_{\text{total}} = P_A + P_B$. Solutions that perfectly follow this are called ideal solutions.

They have similar intermolecular forces between A-A, B-B, and A-B molecules, resulting in no heat change ($\Delta H_{\text{mix}} = 0$) and no volume change ($\Delta V_{\text{mix}} = 0$) upon mixing. Benzene and toluene are classic examples.

Deviations from Raoult's Law (Non-Ideal Solutions):

Most real solutions are non-ideal and deviate from Raoult's Law. These deviations tell us about the intermolecular forces:

Positive Deviation: — The observed vapor pressure is *higher* than predicted. This happens when A-B intermolecular forces are *weaker* than the average of A-A and B-B forces. Molecules escape more easily. This leads to $\Delta H_{\text{mix}} > 0$ (endothermic) and $\Delta V_{\text{mix}} > 0$ (volume expansion). Example: Ethanol and water.
Negative Deviation: — The observed vapor pressure is *lower* than predicted. This happens when A-B intermolecular forces are *stronger* than the average of A-A and B-B forces. Molecules are held more tightly. This leads to $\Delta H_{\text{mix}} < 0$ (exothermic) and $\Delta V_{\text{mix}} < 0$ (volume contraction). Example: Acetone and chloroform.

For NEET, remember the formulas, the conditions for ideal solutions, and the characteristics (vapor pressure, $\Delta H_{\text{mix}}$, $\Delta V_{\text{mix}}$, intermolecular forces) for both positive and negative deviations. Practice numerical problems and conceptual questions linking these aspects.

Prelims Revision Notes

Raoult's Law: Key Points for NEET

1. Definition and Scope:

For Non-volatile Solute: — The vapor pressure of a solution ($P_s$) containing a non-volatile solute is directly proportional to the mole fraction of the solvent ($\chi_{\text{solvent}}$) and the vapor pressure of the pure solvent ($P^0$).

* Formula: $P_s = P^0 \chi_{\text{solvent}}$ * Relative Lowering of Vapor Pressure (RLVP): $\frac{P^0 - P_s}{P^0} = \chi_{\text{solute}}$ * RLVP is a colligative property, dependent only on the number of solute particles.

For Volatile Components (Ideal Solutions): — The partial vapor pressure of each component (A) in the solution ($P_A$) is directly proportional to its mole fraction in the solution ($\chi_A$) and its vapor pressure in the pure state ($P_A^0$).

* Formula: $P_A = P_A^0 \chi_A$ * Total Vapor Pressure: $P_{\text{total}} = P_A + P_B = P_A^0 \chi_A + P_B^0 \chi_B$ (from Dalton's Law of Partial Pressures).

2. Ideal Solutions:

Obey Raoult's Law over the entire range of concentrations.
Intermolecular forces: A-A, B-B, and A-B interactions are comparable.
Thermodynamic properties: $\Delta H_{\text{mix}} = 0$ (no heat change on mixing), $\Delta V_{\text{mix}} = 0$ (no volume change on mixing).
Examples: Benzene + Toluene, n-Hexane + n-Heptane.

3. Non-Ideal Solutions (Deviations from Raoult's Law):

Occur when A-B intermolecular forces are significantly different from A-A and B-B forces.
Positive Deviation:

* Observed vapor pressure is *higher* than predicted by Raoult's Law. * Intermolecular forces: A-B interactions are *weaker* than A-A and B-B interactions (molecules escape more easily). * Thermodynamic properties: $\Delta H_{\text{mix}} > 0$ (endothermic, heat absorbed), $\Delta V_{\text{mix}} > 0$ (volume increases). * Examples: Ethanol + Water, Acetone + Carbon Disulfide.

Negative Deviation:

* Observed vapor pressure is *lower* than predicted by Raoult's Law. * Intermolecular forces: A-B interactions are *stronger* than A-A and B-B interactions (molecules held more tightly). * Thermodynamic properties: $\Delta H_{\text{mix}} < 0$ (exothermic, heat released), $\Delta V_{\text{mix}} < 0$ (volume decreases). * Examples: Acetone + Chloroform (due to H-bonding), Nitric acid + Water.

4. Key Calculations:

Mole fraction: — $\chi_i = \frac{n_i}{\sum n_j}$
Molar mass determination: — Using RLVP, if $P^0, P_s$, and masses of solute/solvent are known.

5. Relation to Henry's Law:

Raoult's Law is a special case of Henry's Law for the solvent, where Henry's constant ($K_H$) equals the pure vapor pressure ($P^0$).
Henry's Law applies to the solubility of a gas in a liquid, while Raoult's Law applies to the vapor pressure of liquid components.

Vyyuha Quick Recall

Really All Out Under Liquid Tension:

Raoult's Law: $P_A = P_A^0 \chi_A$
All components contribute (if volatile)
Outside (vapor) pressure depends on mole fraction (liquid)
Under (liquid) forces dictate deviations
Lowering of VP for non-volatile solute
Total pressure is sum of partials

For Deviations: Positive Deviation: Push Down (weaker A-B forces, higher VP, $\Delta H, \Delta V$ positive) Negative Deviation: Nice Dip (stronger A-B forces, lower VP, $\Delta H, \Delta V$ negative)