Colligative Properties — Revision Notes

⚡ 30-Second Revision

RLVP — $\frac{P^0 - P_s}{P^0} = i X_B$
EBP — $\Delta T_b = i K_b m$
DFP — $\Delta T_f = i K_f m$
OP — $\Pi = i CRT$
Van't Hoff Factor ($i$) — Ratio of observed to theoretical particles.

- Non-electrolyte: $i=1$ - Electrolyte (dissociation): $i \ge 1$ - Association: $i \le 1$

$K_b$ — Ebullioscopic constant (K kg mol$^{-1}$)
$K_f$ — Cryoscopic constant (K kg mol$^{-1}$)
Units — $T$ in Kelvin for $\Pi$, $m$ in mol/kg for $\Delta T_b, \Delta T_f$, $C$ in mol/L for $\Pi$.

2-Minute Revision

Colligative properties are solution properties that depend on the *number* of solute particles, not their chemical identity. They are observed in dilute solutions with non-volatile solutes. The four main properties are: Relative Lowering of Vapor Pressure (RLVP), Elevation in Boiling Point (EBP), Depression in Freezing Point (DFP), and Osmotic Pressure (OP).

RLVP is the fractional decrease in vapor pressure, equal to the mole fraction of the solute ($iX_B$). EBP ($\Delta T_b = i K_b m$) and DFP ($\Delta T_f = i K_f m$) are directly proportional to the molality ($m$) of the solution, with $K_b$ and $K_f$ being solvent-specific constants. Osmotic Pressure ($\Pi = iCRT$) is proportional to the molarity ($C$) and absolute temperature ($T$).

For electrolytes or associating solutes, the van't Hoff factor ($i$) must be included. For dissociation, $i > 1$; for association, $i < 1$; for non-electrolytes, $i=1$. These properties are crucial for determining molecular masses of unknown solutes and have applications in various fields, including biology and industry. Remember to convert temperature to Kelvin for osmotic pressure calculations and use molality for boiling/freezing point changes.

5-Minute Revision

Colligative properties are fundamental to understanding solution behavior. They are defined as properties that depend solely on the *number* of solute particles in a given quantity of solvent, irrespective of their chemical nature. This applies to dilute solutions containing non-volatile solutes. The four key properties are:

1
Relative Lowering of Vapor Pressure (RLVP) — When a non-volatile solute is added, the solvent's vapor pressure decreases. Raoult's Law states $\frac{P^0 - P_s}{P^0} = i X_B$, where $P^0$ is pure solvent vapor pressure, $P_s$ is solution vapor pressure, $X_B$ is solute mole fraction, and $i$ is the van't Hoff factor.
2
Elevation in Boiling Point (EBP) — The solution boils at a higher temperature than the pure solvent. The elevation is $\Delta T_b = i K_b m$, where $K_b$ is the ebullioscopic constant (solvent-specific) and $m$ is molality.
3
Depression in Freezing Point (DFP) — The solution freezes at a lower temperature than the pure solvent. The depression is $\Delta T_f = i K_f m$, where $K_f$ is the cryoscopic constant (solvent-specific) and $m$ is molality.
4
Osmotic Pressure (OP) — The pressure required to stop the net flow of solvent across a semi-permeable membrane. The van't Hoff equation is $\Pi = iCRT$, where $C$ is molarity, $R$ is the gas constant, and $T$ is absolute temperature.

**Van't Hoff Factor ($i$)**: This factor accounts for the actual number of particles in solution. For non-electrolytes (e.g., glucose, urea), $i=1$. For electrolytes, $i > 1$ due to dissociation (e.g., NaCl $i \approx 2$, CaCl$_2$ $i \approx 3$). For association (e.g., ethanoic acid in benzene), $i < 1$. If the degree of dissociation ($\alpha$) is given, $i = 1 + (n-1)\alpha$, where $n$ is the number of ions produced. For association, $i = 1 + (\frac{1}{n}-1)\alpha$.

Key Points for NEET: Always use the van't Hoff factor. Use molality for $\Delta T_b$ and $\Delta T_f$ (temperature-independent) and molarity for $\Pi$ (measured at specific temperature). Convert all temperatures to Kelvin for osmotic pressure calculations.

These properties are extensively used to determine the molecular mass of unknown solutes. For example, if 18 g of glucose (M.M. = 180 g/mol) is dissolved in 1 kg of water, $m = 0.1\text{ mol/kg}$. If $K_f = 1.

86\text{ K kg mol}^{-1}$, then$\Delta T_f = 1 \times 1.86 \times 0.1 = 0.186\text{ K}$. The solution freezes at$-0.186^\circ\text{C}$.

Prelims Revision Notes

1
Definition — Colligative properties depend *only* on the *number* of solute particles, not their nature. Solute must be non-volatile; solution must be dilute.
2
Four Properties & Formulas (with van't Hoff factor $i$)

* Relative Lowering of Vapor Pressure (RLVP): $\frac{P^0 - P_s}{P^0} = i X_B$ * $P^0$: Vapor pressure of pure solvent. * $P_s$: Vapor pressure of solution. * $X_B$: Mole fraction of solute. * Elevation in Boiling Point (EBP): $\Delta T_b = i K_b m$ * $\Delta T_b = T_b^{\text{solution}} - T_b^{\text{pure solvent}}$ * $K_b$: Ebullioscopic constant (solvent-specific, K kg mol$^{-1}$).

* $m$: Molality (moles of solute / kg of solvent). * Depression in Freezing Point (DFP): $\Delta T_f = i K_f m$ * $\Delta T_f = T_f^{\text{pure solvent}} - T_f^{\text{solution}}$ * $K_f$: Cryoscopic constant (solvent-specific, K kg mol$^{-1}$).

* $m$: Molality. * Osmotic Pressure (OP): $\Pi = i CRT$ * $\Pi$: Osmotic pressure (atm or Pa). * $C$: Molarity (moles of solute / L of solution). * $R$: Gas constant ($0.0821\text{ L atm mol}^{-1}\text{ K}^{-1}$ or $8.

314\text{ J mol}^{-1}\text{ K}^{-1}$). *$T$: Absolute temperature (Kelvin).

1
Van't Hoff Factor ($i$) — Accounts for dissociation/association.

* Non-electrolytes (glucose, urea): $i=1$. * Electrolytes (NaCl, CaCl$_2$): $i > 1$. For complete dissociation, $i = \text{number of ions}$. * Association (ethanoic acid in benzene): $i < 1$. * Degree of dissociation ($\alpha$): $i = 1 + (n-1)\alpha$. * Degree of association ($\alpha$): $i = 1 + (\frac{1}{n}-1)\alpha$.

1
Molecular Mass Determination — All colligative properties can be used to find the molecular mass of an unknown non-volatile solute. Osmotic pressure is best for macromolecules.
2
Important Conversions — Temperature to Kelvin for $\Pi$ calculations. Mass of solvent to kg for molality. Volume of solution to L for molarity.
3
Comparison of Solutions — To compare colligative properties, compare the product $i \times m$ (or $i \times C$). Higher $i \times m$ means greater $\Delta T_b$, greater $\Delta T_f$ (thus lower freezing point), and greater $\Pi$.

Vyyuha Quick Recall

To remember the four colligative properties and their dependence: Really Easy Determination Of Molecular Mass.

RLVP (Relative Lowering of Vapor Pressure) $\rightarrow$ Mole fraction ($X_B$)
EBP (Elevation in Boiling Point) $\rightarrow$ Molality ($m$)
DFP (Depression in Freezing Point) $\rightarrow$ Molality ($m$)
OP (Osmotic Pressure) $\rightarrow$ Molarity ($C$)

And don't forget the 'i' factor for electrolytes: 'I' for Ions!