Lecture on Ideal and Non-Ideal Solutions and Colligative Properties
Quick Review on Colligative Properties
Colligative Properties
- Properties of ideal solutions that depend only on the number of solute particles and not on their nature.
- Four main colligative properties:
- Relative lowering of vapor pressure
- Elevation of boiling point
- Depression of freezing point
- Osmotic pressure
Relative Lowering of Vapor Pressure
- Lowering of Vapor Pressure: When a non-volatile solute is added to a volatile liquid, its vapor pressure decreases.
- Relative lowering of vapor pressure: Ratio of the lowering of vapor pressure to the original vapor pressure.
- Formula:
- For dilute solutions:
$$ \frac{P^0_A - P_s}{P^0_A} = \chi_B $$
- For all cases (dilute and concentrated):
$$ \frac{P^0_A - P_s}{P_s} = \frac{n_B}{n_A} $$
- To calculate molarity (m):
$$ \frac{P^0_A - P_s}{P_s} = m \cdot M_1 \cdot 1000 $$
Elevation of Boiling Point
- Elevation in Boiling Point: When a non-volatile solute is added, the boiling point of the solution increases.
- Formula:
$$ \Delta T_b = K_b \cdot m $$
- $\Delta T_b =$ elevation in boiling point
- $K_b =$ ebullioscopic constant or molal elevation constant
Depression of Freezing Point
- Depression in Freezing Point: The freezing point of the solution decreases.
- Formula:
$$ \Delta T_f = K_f \cdot m $$
- $\Delta T_f =$ depression in freezing point
- $K_f =$ cryoscopic constant or molal depression constant
Osmotic Pressure
- Osmosis: Net movement of solvent molecules through a semi-permeable membrane from a region of lower concentration to a higher concentration.
- Osmotic Pressure (π): Minimum pressure applied to a solution to prevent the influx of solvent.
- Formula:
$$ \pi = C \cdot R \cdot T $$
$$ C = \frac{n}{V} $$
Ideal and Non-Ideal Solutions
Ideal Solutions
- Definition: Solutions that obey Raoult's law for all compositions.
- Properties:
- Observed vapor pressure = Theoretical vapor pressure (calculated using Raoult's law)
- All interactions (A-A, B-B, A-B) are identical.
- $$ \Delta H_{mixing} = 0 $$, $$ \Delta V_{mixing} = 0 $$
- Entropy increases during mixing ($\Delta S_{mixing} > 0$)
- Gibbs free energy change during mixing ($\Delta G_{mixing} < 0$)
- Examples: Benzene - toluene, n-Hexane - n-Heptane, etc.
Non-Ideal Solutions
- Definition: Solutions that show deviation from Raoult's law.
- Positive Deviation: $ P_{observed} > P_{theoretical} $
- Interactions: $ A-B < A-A $ or $ B-B $
- $$ \Delta H_{mixing} > 0 $$, $$ \Delta V_{mixing} > 0 $$
- Negative Deviation: $ P_{observed} < P_{theoretical} $
- Interactions: $ A-B > A-A $ or $ B-B $
- $$ \Delta H_{mixing} < 0 $$, $$ \Delta V_{mixing} < 0 $$
- Examples: Positive Deviation - Ethanol - Acetone, Negative Deviation - Chloroform - Acetone
Van't Hoff Factor (i)
Need for Van't Hoff Factor
- Calculation discrepancy for solutions with solutes that dissociate or associate.
- Observed value of colligative property (ΔT_b, ΔT_f, Π): based on actual particles in solution.
- Calculated value of colligative property: based on formulas assuming no dissociation/association.
- Definition:
$$ i = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}} $$
$$ i = \frac{M_{calculated}}{M_{observed}} $$
- Non-electrolytes: $ i = 1 $
- Electrolytes dissociating: $ i > 1 $
- Electrolytes associating: $ i < 1 $
Formulas Involving Van't Hoff Factor
- Relative lowering of vapor pressure:
$$ \frac{P^0_A - P_s}{P^0_A} = \chi_B \cdot i $$
- Elevation in boiling point:
$$ \Delta T_b = K_b \cdot m \cdot i $$
- Depression in freezing point:
$$ \Delta T_f = K_f \cdot m \cdot i $$
- Osmotic pressure:
$$ \pi = i \cdot C \cdot R \cdot T $$
Dissociation/Association Adjustment
- Dissociation: $ A_n \rightarrow nA $
$$ i = 1 + (n - 1)\alpha $$
- Association: $ nA \rightarrow A_n $
$$ i = 1 + \frac{1 - \alpha}{n} $$
Summary
In solutions, the behavior regarding colligative properties can vary significantly depending on whether the solute is non-electrolyte or electrolyte (dissociates or associates). Understanding colligative properties and their impact on vapor pressure, boiling point, freezing point, and osmotic pressure is crucial in predicting solution behavior. The Van't Hoff factor is a pivotal concept to correct the theoretical formulas to match practical observations, especially in solutions where dissociation or association occurs.