## Explanation of Colligative Properties Chemistry Notes

Relative Lowering in Vapour pressure :

According to Raoult’s law, “the relative lowering in vapour pressure of solution for a non-roletile solute is equal to mole fraction of solute.” Because solution in very dilute. So ng « na So, the value of ng is relatively negligible than na
Hence, Molar mass of non-volatile solute can be determined form above equation if other all quantities are known.

Elevation in Boiling Point :

→ Boiling Point : Boiling point of a liquid is that temperature at which the vapour pressure of liqud becomes equal to atmospheric pressure. The vapour pressure of pure solvent is more than solution and vapour pressure increases with increase in temperature. → So, solution will be heated more for making vapour pressure of solution equal to atmospheric pressure. Since the vapour pressure of solution is less so, it will be heated more than solvent. It is the reason that the boiling point of solution is higher than solvent.

→ If boiling point of solvent is T°b and boiling point of solution is Tb then, Tb > T°b Here, the difference of Tb and T i.e., (Tb – T°b)is called elevation of boiling point (∆Tb).

The elevation in boiling point can be explained by plotting a graph between vapour pressure and temperature. → The vapour pressure of solvent increases with temperature as shown by curve AB in figure (2.6). The vapour pressure of solution at a temperatue is lesser than vapur pressure of solvent. So, curve CD of vapour pressure of solution is shown below curve AB. It is clear from graph that the temperetures at which the vapour pressure of solvent and solution becomes equal to atmospheric pressure, are T°b and Tb respectively and
Tb> T°b

In figure 2.6 it is also clear that
∆Tb α ∆p (∆ p lowering in vapour pressure)
The lowering of vapour pressure is directly proportional to mole fraction of a solute.
So, ∆ P ∝ xB (xB = mole fraction of solute)
∆Tb ∝ xB
∆Tb = kxB ………..(viii) On putting the value of xB in eq. (viii)
∆Tb = k MA . m
∆Tb = Kb m …………..(ix)
(New constant Kb = k . MA)
New constant Kb is called ebullioscopic constant or molal elevation constant.
Elevation Constant(kb)
If molality of solution in equation (ix) (m) = 1
Then, ∆Tb = Kb
So, ebullioscopic constant of a solvent is equal to its elevation in boiling point when I mole solute is dissolved in 1000 g solvent. Its unit is Kkg mol-1.
Relation Between Elevation in Boiling Point and Molecular mass of Non-Volatile solute
We know that Where
MB = Molar mass of solute
Kb = Molal elevation constant
(Ebullioscopic constant)
WB = Mass of solute
∆Tb = Elevation in boiling point
WA = Mass of solvent in g
According to van’t Hoff, Kb can be related to latent heat of vaporisation solvent as follows: Where, MA = Molecular mass of solvent
R = Gas constant
Tb = Boiling point of solvent
vapH = Latent heat of vaporisation

Depression in Freezing Point :

→ Freezing Point: Freezing point of a substance is the temperature at which the solid and the liquid forms of the substance are in equlibrium ie, solid and liquid forms of substance have the same vapour pressure. Freezing point decreases on adding a non-volatile substance in a solvent.

→ Since the vapour pressure of solution is lower therefore its vapour pressure will be equal to vapour pressure of solid solvent at low temperature and freezing point of solution will lower then freezing point of pure solvent. This difference in freezing points is called depression in freezing point. (∆Tf)

if the freezing point of pure solvents is ∆Tf and freezing point of solution is Tf then → The vapour pressure of liquid solvent decreases with decrease in temperature on cooling) as shown by curve AB in figure 2.7. At point B, solvent freezes in the form of solid. After this, vapour pressure decreases immediately with curve BC because the vapour pressure of solid is very low. At point B, liquid solvent and solid solvent are in equilibrium. The vapour pressure of both is equal. → Hence, point B represents freezing point (T0f) of solution. So, ∆Tf = T0f – Tf represent, depression in freezing point as shown in figure 2.7. It is also clear from 2.7 that, ∆Tf α ∆p (∆p = Lowering of vapour pressure) The lowering of vapour pressure is directly proportional to mole fraction of solute. So,
∆p ∝ xb(xb = Mole fraction of solute)
∆Tf ∝ xb
∆Tf = kxb ………… (xii) = Kf.m (∵ Kf, k.MA) …(xiii)
Kf is called molal depression constant or cryoscopic constant.
If m = 1
∆Tf = Kf

Molal Depression Constant (Kf)

→ Molal depression constant of a solvent is equal to its depression in freezing point while one mole solute is dissolved in 1000 g solvent. Its unit is K kg mol-1.

→ Relation Between Depression in Freezing Point and Molecular mass of Non-Volatile Solute Diffusion :

• The process in which molecules move from region of higher concentration to region of lower concentration, is called diffusion.
• Example When concentrated potassium permanganate is added in filled container of water, then violet colour spreads every where after some time.

Osmosis :

→ “The net spontaneous flow of the solvent molecules from the solvent to the solution or from a less concentrated solution to a more concentrated solution through a semipermeable membrane is called osmosis.”

→ We take inverted thistle funnel to explain the process of osmosis. Semi-permeable membrane tied on mouth of this funnel. This is represented in figure 2.8. Semi-permeable membrane allows only particles of solvent.

→ The molecules of solute can not pass through membrane. Funnel, filled with concentrated solution of copper sulphate (CuSO4), is placed in a beaker containing water. → After some time it is observed that the level of solution increases in this funnel. This is due to flow of molecules of solvent towards solution through semi-permeable membrane. This process is called osmosis. Osmosis is greek word which means Osmos = to push”. First of all, it was seen by Abe Nollet in 1748.

Semi-permeable Membrane :

→ A membrane which allows the solvent molecules to pass through but not the solute particles is known as semipermeable membrane. For example bladder of pig, parchment paper or synthetic like cellophane etc. These membranes are like continuous sheet or film. These have microscopic pores or network of pores.

→ Due to this reason, only solvent molecules can pass through them but not of solute. Semi permeable membrane can also be synthesized from chemicals. For example, when the aqueous solution of potassium ferrocyanide and copper sulphate is mixed in porous container then the precipitate of copper ferrocyanide with gelatin is filled in pores of porous container and this acts as semi-permeable membrane.
2CuSO4 + K4 [Fe(CN)6] → Cu2 [Fe(CN)6] + 2 K2 SO4
Besides this, many types of polymeric membranes like cellulose acetate and cellophane are also available. Osmosis and Diffusion :

→ As we have studied that the spontaneous flow of molecules of solvent from pure solvent to solution through semi-permeable membrane or dilute solution to concentrated solution is called osmosis. Whereas particles (molecules or ions) of various substances occur freely with each other in process of diffusion. We can differentiate osmosis and diffusion as follows:

 Osmosis Diffusion This process takes place through semi-permeable membrane. This process does not require semi-permeable membrane. In this process, the movement of molecules of solvent takes place in one direction only. In this proces, molecules of both solute and solvent can move. But their direction is reverse. In this process, the molecules of solvent move from region of lowerconcentration to region of higher concentration. In this proces. molecules (solute and solvent) move from region of higher concentration to region of lower cencentration. Osmosis can be prevented by using extra pressure in the region of higher concen tration or can he reversed. This can not be prevented. This process takes place only in liquids procees takes place in both liquids and goses. Osmotic Pressure :

→ The external pressure applied on solution which is required to prevent the flow of molecules of solvent through semi-permeable membrane and to establish equilibrium insurface, is called osmatic pressure.

OR

→ Osmotic pressure is that pressure which becomes equal to vapour pressure of solution on decreasing vapour presure of pure solvent or that excess pressure which is applied on solution side so that the vapour pressure of solution becomes equal to vapour pressure of solvent. We can explain osmotic pressure by experiment with apparatus showing in figure 2.9.

→ A glass container divides in two parts with the help of semi-permeable membrane for experiment. A narrow tube of glass is attached in one part by which solvent is filled while a broad tube is attached in second part in which frictionless piston for presention of water is attached. Solution is taken in this part.

→ When process starts, the molecules of solvent will try to move in solution through semi-permeable membrane due to which piston will move upwards. While the level of water will decrease in narrow tube. → If some external pressure is applied above piston then this pressure prevents flow of solvent. It can be seen clearly in narrow tube which will fixed the level of solvent in this position.

Important Points :

• Osmosis always takes place from dilute solution to concentrated solution.
• The hydrostatic pressure developed due to osmosis is called osmotic pressure.
• The pressure required to prevent osmosis is called osmotic pressure
• A solution has only vapour pressure. In this, osmotic pressure will develop only when it comes in contact with
• solvent of low concentration and osmosis takes place through semi-permeable membrane.

Measurement of Osmotic Pressure :

There are following methods for the determination of osmotic pressure :

• Pfeffer’s method
• Berkley-Hartley method
• de Vries plasmolytic method
• Morse-Frazer method
• Townsend’s reverse osmosis method Reverse Osmosis :

If more pressure is used than osmotic pressure on solution then the flow of solvent takes place from solution to pure solvent through semi-permeable membrane. This proces is called reverse osmosis. This process is used in the purification of sea water and hard water etc.

isotonic Solution :

Those two solutions which do not allow flow of solvent after separating from semi-permeable membrane i.e., their osmotic pressures are same, are called isotonic solutions. Their molar concentrations are also same.

Hypertonic Solution :

The solution among two solutions having different osmotic pressure, whose osmatic pressure is higher, is called hypertonic solution, relative to other solution.

Hypotonic Solution :

The solution among two solutions having different osmotic pressure, whose osmotic pressure is low, is called hypotonic solution, relative to other solution.

Laws of Osmotic Pressure :

The behaviour of molecules of solute in dilute solutions is like that of behaviour of gas molecules. van’t Hoff has also applied gas laws on solutions which are as follows:

Boyle-van’t Hoff Law :

The osmotic pressure of a solution at constant temperature is inversely propertional to its volume.
i.e., π ∝ $$\frac{n}{\mathrm{~V}}$$
π ∝ C (at constant temperture)
Where n = Number of moles
π = Osmotic pressure
V = Volume
Here C = n/V Charle’s – van’t Hoff Law :

• The volume of solution at constant osmotic pressure is directly proportional to its absolute temperature.
• V ∝ T (at constant osmotic pressure)
• $$\frac{\mathrm{V}}{\mathrm{T}}$$ = Constant (Here T = tempereture in Kelvin)

van’t Hoff Pressure – Temperature Law :

• The osmotic pressure of dilute solution at constant volume is directly proportional to its absolute temperature.
• π ∝ T(where V is constant)
• $$\frac{\pi}{\mathrm{T}}$$ Constant

Avogadro van’t Hoff Law The number of molecules of solute is equal in same volume of solutions at constant osmotic temperature and osmotic pressure.
∴ Osmotic pressure of two solutions
π1 = π2
Volume V1 = V2 then temperature T1 = T2
then n1 = n2

General Equation for Osmotic Pressure :

On combining above laws
π ∝ C(Boyle – Van’t Hoff law)
π ∝ T (van’t Hoff pressure – temperature law)
π ∝ CT (R = Gas constant)
π = CRT
Here C = Concentration
R = (Gas constant 0.0821 L atm K-1 mol-1) The above equation is called van’t Hoff equation for dilute solutions. Osmotic Pressure and Molecular Weight of Solute :

Osmotic pressure is directly proportional to molarity at given temperature. i.e..
π = CRT (van’t Hoff equation) Where

• π = Osmotic pressure
• C = Molarity
• R = Gas constant
• T = Temperature
• MB = Molar mass of solute
• WB = Mass of solute