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how to find van't hoff factor

Definition of Colligative Properties

Colligative properties are the properties that help us to understand how a solutions' properties are linked to a solute's concentration in any solution. These properties are only dependent on the number of non-volatile solute particles and not on their type. Colligative properties are widely observed in dilute solutions.

We can also consider colligative properties as the properties observed by the dissolving of a non-volatile solute in an unstable solvent. Normally, the solvent properties are changed by the solute where its particles eliminate a portion of the solvent atoms in the fluid stage. This likewise brings about the decrease of the grouping of the solvent.

Colligative properties can be linked with multiple quantities which are useful in expressing the concentration of a solution, such as molarity, normality, and molality. The various types of colligative properties are:

  • Freezing point depression
  • Boiling point elevation
  • Osmotic pressure
  • Relative lowering of vapor pressure

The word 'colligative' is derived from the Latin word Colligatus. Colligatus translates to 'bound together.' In the situation of defining a solution, Colligative properties help us understand how the properties of the solution are associated with the concentration of solute in the solution.

Examples of Colligative Properties

We can notice the colligative properties of arrangements by going through the accompanying examples:

  • On the off chance that we add a spot of salt to a glass full of water, its freezing temperature is brought down impressively than its normal temperature. On the other hand, the boiling temperature is likewise increased and the arrangement will have a lower vapor pressure. There are also changes observed in its osmotic pressure.
  • In the same way, if we add alcohol to water, the solution's freezing point goes down below the normal temperature that is usually observed for either pure alcohol or water.

Learn more:- Dalton's Law of Partial Pressure

Different Types of Colligative Properties

Types of Colligative Properties

There are many types of colligative properties of a solution. Let us discuss them in detail:

Read Also: Class 11 Some Basic Concepts of Chemistry

Elevation in Boiling Point

The boiling point of water can be understood as the temperature at which the vapour pressure of water is the same as the atmospheric pressure. We also know that when a pure solvent is added to a non-volatile liquid, the solution's vapour pressure decreases. Hence to make vapour pressure and atmospheric pressure the same, we have to increase the temperature of the solution. This difference between the solution's boiling point and the boiling point of a pure solvent is known as the elevation in boiling point.

Elevation in Boiling Point

ΔTb =T 0 b-Tb

where, ΔTb: Elevation in the Boiling Point

T0 b: Boiling Point of a Pure Solvent

Tb: Boiling point of a Solution

Experimentally, it is observed that there's a correlation between the elevation in boiling point and the molality of the solute present in the solution represented by 'm'.

ΔTb ∝ m

ΔTb = kb m

where, kb: molal elevation constant

Hence, by substitution of the value of 'm'

ΔTb =1000 x kb x m2 /M2 x m1

where, m2: mass of solvent (g)

m1: mass of solvent (kg)

M2: Solute's molar mass

Lowering of Vapour Pressure

A volatile solvent's vapor pressure is lowered when a non-volatile solute is dissolved in it. Due to the presence of both solute and solvent particles on the surface of the solution, the surface area covered by the molecules of the solvent is reduced. Hence, the vapour pressure is decreased as it solely depends on the solvent.

Lowering of Vapour Pressure

 Now, Lowering of pressure = Po–Ps

And Relative lowering of vapor pressure = (Po - Ps)/Po

where, Po: Vapor pressure of the pure solvent

Ps: Vapor pressure of the solution

Raoult's law

In 1886, Raoult derived a relation between the mole fraction and relative lowering in vapour pressure.

P a = X A P o A

It's given as - (Po – Ps)/ Po = n/(n + N)

Where in n moles of solvent, n moles of solute are dissolved.

Depression in Freezing Point

The temperature at which a liquid's vapour pressure is equivalent to the vapour of the corresponding solid is known as the Freezing Point. In accordance with Raoult's law, the vapour pressure of a solvent decreases when a non-volatile solid is added to it and becomes equal to the vapor pressure of the solvent at a lower temperature. Hence, this difference between the freezing point of a pure solvent and the freezing point of its solution is known as the depression in the freezing point.

Depression in Freezing Point

ΔTf =T0f-Tf

ΔTf = -kf.M

where, ΔTf: Depression in the Freezing Point

Tof: Boiling Point of a Pure Solvent

Tf: Boiling point of a Solution

Like the boiling point, the freezing point also directly relates to the molality.

ΔTf =1000 x kf x m2 /(M2 x m1)

Where kf = molal depression constant

m2 = mass of solvent (g)

m1 = mass of solvent (kg)

M2 = Solute's molar mass

Osmotic Pressure

The solvent particles enter the solution when a semipermeable membrane is placed between a solvent and solution, increasing the volume of the solution. The semi-penetrable membrane permits just the solvent particles to go through it preventing the entry of larger atoms like solute. This phenomenon wherein the molecules of solvent flow spontaneously from a dilute to a concentrated solution or from a pure solvent to the solution is called Osmotic Pressure.

Osmotic pressure

Osmotic Pressure is a colligative property as it is not based on the nature of the solute but on the number of solute particles present. It has been proved experimentally that osmotic pressure (?) is directly proportional to the temperature (T) and molarity(C).

Hence, π  = CRT

where, R: Gas constant.

 π = (n 2 /V) RT

where there are n2 moles of solute and

V: Volume of the solution

=> n2= m2/M2

m2: weight of the solute

M2: Molar mass of solute

Thus, π = W2RT / M2V

Van't Hoff Factor of Colligative Properties

When the solute is dissolved in a solution, it undergoes either association or dissociation. Hence, the colligative properties change as the number of particles increases or decreases. Van't Hoff Factor can be used to express the extent of this association or dissociation.

i = Normal molar massAbnormal molar mass

i = Calculated Colligative PropertyObserved Colligative Property

Check out notes for the colligative properties of solutions.

Things to Remember of Colligative Properties

  • Colligative properties refer to those properties which are entirely dependent on the ratio of the number of solute particles to the total number of solvent particles.
  • The various types of colligative properties of different solutions are:
  1. Freezing point depression: ΔTf =1000 x kf x m2 /(M2 x m1)
  2. Boiling point elevation: ΔTb = kb m
  3. Osmotic pressure: π = (n 2 /V) RT
  4. Relative lowering of vapor pressure: (Po - Ps)/Po
  • Van't Hoff Factor, i = observed colligative property/calculated colligative property.
  • Read more about different types of solutions here.

Sample Questions of Colligative Properties

Ques. Estimate the osmotic pressure of a 5% solution of urea at 273K. (Mol.Mass=60)(R=0.0821LatmK –1 mole) (3 marks)

Ans. 5% solution of urea means that it contains 5g of urea per 100cm3 of the solution, i.e.,

W2 = 5g,

V=100cm3 = 0.1L

M2 = 60gmol–1,

R= 0.0821LatmK–1mol–1,

T= 273K

π = W2.RT/M2V

= 5g × 0.0821LatmK–1mol–1 × 273K / (60gmol–1×0.1L)

=18.68atm.

The osmotic pressure is 18.68atm.

Ques. A solution has 0.456g of camphor (mol. mass=152) in 31.4g of acetone (boiling point:56.30oC). Calculate its boiling point if the molecular elevation of acetone is 17.2o C per 100g. (5 marks)

Ans. m2=0.456g,

M2 =152 ,

m1=31.4g,

To=56.30oC,

kb=17.2oC/100gm

Hence, kb per 1000 gm of acetone: 1.72oC

ΔTb = kb m

=1000* kb* m2 / M2*m1

=1000 × 1.72 × 0.456/(152 x 31.4)

Therefore, the Boiling point of the solution (Tb)= Tbo +ΔTb

= 56.30+0.16

=56.46?C.

Ques. When 1g of non-electrolyte solute dissolves in a given 50g of benzene, it lowers its freezing point by 0.40K. The freezing depression constant of benzene is given as 5.12Kkgmol –1 . Calculate the molar mass of the solute. (2 marks)

Ans. Given w2 = 1g,

m1=50g,

ΔTf=0.40K,

kf= 5.12Kkgmol–1

Putting these values in the formula

ΔTf =1000 x kf x m2 /M2 x m1

M2=1000 x kf x m2/ m1 x ΔTf

M2= 1000 × 5.12 / (50 × 0.40)

=256gmol–1.

Ques. The molal elevation stable for liquid is 0.513 o C kg mol . While 0.2mole of sugar is dissolved in 250g of liquid, compute the temperature at which the solution boils under atmospheric pressure. (2 marks)

Ans. ΔTb = moles of sugar x 1000/weight of water in gm

ΔTb = 0.2 x 1000 / 250

ΔTb = 0.8

⇒ T0b-Tb = 0.8

For pure liquid, T0b =100oC

⇒ Tb= 0.8 + 100

=100.80oC

Ques. 300 cm3 of an aqueous solution contains 1.56g of a polymer. The osmotic pressure of such solution at 300 K is set up to be 2.57 ? 10 -3 bar. Find out the molar mass of the polymer. (3 marks)

Ans. Weight of polymer( W2) = 1.56g

According to the value of Osmotic pressure (π) = 2.57 ? 10-3 bar

Volume (V) = 300 cm3 = 0.3L

M2 = W2 RT / π V

Putting all values according to the formula

M2 = 1.56 x 0.083 x 300 / (0.3 x 2.57 x 10-3)

= 50381 g mol

how to find van't hoff factor

Source: https://collegedunia.com/exams/colligative-properties-definition-examples-types-vant-hoff-factor-chemistry-articleid-560

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