Colligative Properties

Do you know what are colligative properties? The term "colligative" originates from the Latin word "colligatus," translating to "bound together." Within the context of defining a solution, the meaning of colligative properties elucidate the interconnection between the solution's properties and the concentration of the solute within it. These properties demonstrate how the behavior of the solution is intricately linked to the quantity of dissolved solute particles, showcasing the bound relationship between them.

1.0Introduction

Colligative properties meaning involves "When a non-volatile solute is introduced into a volatile solvent, the vapor pressure of the resulting solution decreases. This reduction in vapor pressure connects to several properties of solutions, which also include as colligative properties examples :

(1) The relative decrease in the solvent's vapor pressure 

(2) The lowering of the solvent's freezing point

(3) The elevation of the solvent's boiling point, and 

(4) The osmotic pressure of the solution. 

These properties are dependent on the number of solute particles, regardless of their specific nature, concerning the total number of particles within the solution. Such properties fall under the category of colligative properties. We will discuss each colligative properties types, Which will be mainly based on colligative properties of water, where water will work as the main solvent.

Thus, we can say Colligative properties definition involves solution traits influenced by the quantity, not the type, of solute particles present. They include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

2.0Types of Colligative properties

In this section we will study different types of colligative properties and examples of colligative properties-

1. Lowering of vapor pressure -

• The lowering of vapor pressure occurs due to the introduction of a non-volatile solute into a solvent. 
• In a pure solvent, the entire surface is occupied by solvent molecules. However, with the addition of a non-volatile solute, the surface becomes shared between solute and solvent molecules, reducing the fraction of the surface covered by solvent molecules. As vapor pressure primarily arises from solvent molecules, the presence of the solute diminishes the available surface area for solvent molecules, resulting in a lower vapor pressure for the solution compared to that of the pure solvent at the same temperature.
• Relative lowering depends upon relative number of solute particles. Therefore, it is called as a colligative property.
• If at a certain temperature, P° is the vapour pressure of pure solvent and P_s is the vapour pressure of solution, then, 

2. Depression in Freezing Point

• The freezing point of a liquid is that temperature at which the liquid and its solid state exist in equilibrium with each other.
• Freezing point depression is a phenomenon observed when the freezing point of a solvent decreases upon the addition of a solute. This occurs because the presence of the solute disrupts the solvent's ability to form a solid crystal lattice, thereby lowering its freezing point.

In practical terms, this effect is commonly seen when salt is added to water to melt ice on roads during winter. The salt lowers the freezing point of the water, preventing it from solidifying at 0°C (32°F).

The depression in the freezing point can be calculated using the formula:

                                      $\Delta T_f=i\cdot K_f\cdot m$

Where:

• ΔT_f is the change in freezing point.
• i  is the van't Hoff factor, which represents the number of particles into which the solute dissociates in the solvent.
• K_f is the cryoscopic constant, specific to each solvent.
• m is the molality of the solution (moles of solute per kilogram of solvent).

3. Elevation of the boiling point

The elevation of the boiling point refers to an increase in the temperature at which a liquid boils, usually due to the addition of solutes (such as salt or sugar) to the liquid. This phenomenon occurs because the presence of solutes disrupts the normal boiling process by reducing the vapor pressure of the solvent.

If T⁰_b is the boiling point of pure solvent and T_b is the boiling point of the solution then, 

T_b > T⁰_b and the elevation in boiling point ΔT_b = T_b – T⁰_b

•   The elevation in boiling point (ΔT_b) is directly proportional to lowering of vapour pressure of the solution i.e.

ΔT_b ∝ (P^o – P_s) from graph and  ΔT_b ∝ ΔP∝ n_B/n_A

ΔT_b ∝ n_B/n_A =  w_B M_A /  m_BW_A         (for a solvent P⁰ & M_A = constant)

ΔT_b  ∝  w_B /  m_BW_A     or   ΔT_b =  Kw_B /  m_BW_A 

where K = elevation constant

if w_B /  m_B  = 1 mole and W_A = 1 g

then ΔT_b = K (Elevation constant or molecular elevation constant)

If w_B /  m_B = 1 and W_A = 1000 gram; Then ΔT_b = K_b (molal elevation constant)

$\frac{K}{1000}$ = K_b (molal elevation constant or Ebullioscopic constant)

$\Delta {\mathrm{T}}_{\mathrm{b}}=\frac{{\mathrm{K}}_{\mathrm{b}}\times {\mathrm{w}}_{\mathrm{B}}\times 1000}{{\mathrm{m}}_{\mathrm{B}}\times {\mathrm{W}}_{\mathrm{A}}}$

$\Delta {\mathrm{T}}_{\mathrm{b}}=\frac{{\mathrm{w}}_{\mathrm{B}}}{{\mathrm{m}}_{\mathrm{B}}}\times \frac{1000}{{\mathrm{W}}_{\mathrm{A}}}\times {\mathrm{K}}_{\mathrm{b}}$

ΔT_b = molality × K_b

ΔT_b ∝ molality 

Hence elevation in boiling point (ΔT_b) is a colligative property.

•  K_b depends only on nature of solvent which can be explained by thermodynamic relation.

Where, T_b⁰ = Boiling point of solvent.

M_w = Molar mass of solvent.

ΔH_vap = Enthalpy of vaporization per mole of solvent

L_v = Latent heat of vaporization per gram of solvent

T_b = Boiling point of solution

T⁰_b = Boiling point of solvent

The vapour pressure curve for solution lies below the curve for pure  water.

The diagram shows that ΔT_b denotes.

The elevation in boiling point of a Solvent in solution.

4. Osmosis and Osmotic Pressure

Osmosis: Osmosis is defined as the spontaneous net flow of solvent molecules through a semipermeable membrane from a solvent to a solution or from a dilute solution to a concentrated solution.

Osmotic Pressure (p or π)

• The external pressure which must be applied on the solution in order to stop the flow of solvent into the solution through the semipermeable membrane is equal to osmotic pressure. OR
• Hydrostatic pressure develops in a vertical column when solution and solvent are separated by SPM.

Osmotic pressure   = hydrostatic pressure 

where, h = increase in level in the tube of unit cross section

d = density of solution 

g = acceleration due to gravity

3.0Van't Hoff law for Dilute Solution

Van't Hoff's law for dilute solutions describes the relationship between the osmotic pressure of a solution and the concentration of solute particles in that solution. 

According to its Gas equation, PV = nRT is also followed by a dilute solution when pressure of gas is replaced by osmotic pressure of solution.

$\pi =\left(\frac{n}{v}\right)\mathrm{R},\pi =\mathrm{CRT}$

Where,

π = osmotic pressure of solution (atm)                                   

V = volume of solution (L)

n = moles of solute

R = (S) Universal gas constant / Solution constant = 0.0821 L atm mol^–1K^–1; 0.083 L bar mol^–1K^–1

Note- At constant temperature π is a colligative property.