Chapter 2: Solutions

Chapter 2:

solutions

1.Introduction : A solution is a homogeneous mixture of two or more substances which are chemically non-reacting. We come across many types of solutions in our daily life. e.g., solid-liquid, liquid-liquid, gas-gas. In this chapter we will learn several properties of solutions and their applications.

Solution: A homogeneous mixture of two or more substances is known as solution

Solute: The substance present in smaller amount in a solution is called solute.

Solvent: The substance present in larger amount in a solution is called solvent.

Types of Solutions

The concentration of a solution can be expressed by different concentration terms which are described as follows.

Expressing concentration of solutions 

Concentration Terms :

% Concentration

Mass percentage. :It is the amount of solute in grams dissolved per 100 g of solution. e.g., 10% solution of sodium chloride means 10 g of solid sodium chloride present in 100 g of solution

% w/w =  × 100

Ex.     10% w/w urea solution = 10 g of urea is present in 100 g of solution.

= 10 g of urea is present in 90 g of water.

Mass by volume percentage (% w/v) : It is defined as mass of solute dissolved per 100 ml of solution. It is commonly used in medicine and pharmacy.

% wt/vol. (w/v)

% w/v = wt. of solute/100 mL of solution

 % w/v =

Ex. 

10%  (w/v) urea solution. = 10 g of urea is present in 100 mL of solution.

 But not 10 g of urea present in 90 ml of water  for dilute solution  :  volume solution = volume solvent.

Volume percentage (% v/v) : It is defined as volume of a solute dissolved per 100 ml of solution.

% v/v =  × 100

Strength of solution in g/L : Weight of solute (in gram) per litre (1000 mL) of solution.

Ex.  

10%  (w/v) sucrose solution, then specify its concentration in g/L

100 mL .......... 10 g

1000 mL ....... = 100 g/L

Molarity (M) : It is expressed as the number of moles of solute per litre of solution.

Molarity = No. of moles of solute per litre of solution.

Let     n =  No. of moles of solute ; N = No. of moles of solvent ;  V = volume of solution

no. of moles of solute = molarity x volume ( in L)

no. of m. moles of solute = molarity x volume ( in mL)

If V₁ mL of C₁ molarity solution is mixed with V₂ mL of C₂ molarity solution (same substance or solute)

C_f (V₁+V₂) = C₁V₁ + C₂V₂

 C_f =  =  where C_f = molarity of final solution

Molality (m) : It is defined as number of moles of solute per 1000 g or 1 kg of solvent.

Molality = No. of moles of solute per kg(1000 g) of solvent.

Let w gram of solute (Molar mass = Mg/mole) is dissolved in 'W' gram of solvent.

molality =   molality =

Molality not depends on temperature.

Normality : It is defined as number of gram equivalents of solute dissolved per litre of solution.

No. of equivalents per litre of solution =  = n-factor molarity

No. of equivalents = normality × volume (in L)

Equivalent mass =

No. of equivalent= =

'n' - factor

(i) For oxidizing/reducing agents : no. of e^– involved in oxidation/reduction half reaction per mole of oxidising agent /reducing agent.

e.g.  : 5e^– + 8H⁺ + MnO₄^– =Mn²⁺ + H₂O         n- factor  = 5

(ii) For acid/ base reactions : no. of H⁺ ions displaced/ OH^– ions displaced per mole of acid/ base.

e.g.  : NaOH    n - factor = 1        H₂SO₄      n - factor = 2

(iii) For salt :   n = Total charge on cations.

or                                                          

total charge on anions              

 e.g.  : Al₂(SO₄)₃                    n - factor = charge on the cation = 2 x 3 = 6

Mole-fraction (x) : It is the ratio of number of moles of a particular component to the total number of moles of all the components. e.g., mole-fraction of component A, x_A = , where n_A is the number of moles of component 'A' and n_B is the number of moles of component 'B'.

For binary mixture.

X_solute =  = ; X_Solvent  =  =

X_solute  + X_Solvent = 1

 Parts per million (ppm) : The number of parts of solute present in 1 million parts of solution are called its ppm. When a solute is present in small quantities (very minute amounts), it is easier to express the concentration in parts per million.

(a) ppm (w/w) =  × 10⁶

(b) ppm (w/v) =  × 10⁶

(c) ppm (moles/moles) =  × 10⁶

Table : 1

 Note : All volume related concentration terms are temperature dependent.

colligaive properties & constitutional properties

Constitutional Properties : Properties which are dependent on nature of particles are constitutional properties like electrical conductance.

Colligative properties  : The properties of the solution which are dependent only on the total no. of particles relative to solvent/solution or total concentration of particles in the solution and are not dependent on the nature of particle i.e. shape, size, neutral /charge etc. of the particles.

There are 4 colligative properties of solution

Osmotic pressure

Relative lowering in vapour pressure

Elevation in b.p. (T_b)

Depression in freezing pt. (T_f)

(i) Osmosis & Osmotic pressure :

Osmosis:  The spontaneous flow of solvent particles from solvent side to solution side or from solution of low concentration side to solution of high concentration side through a semipermeable membrane (SPM) is known as osmosis.

Ex.

Conclusion : After some time in (A) grape or egg will shrink and in (B) grape or egg will swell.

e.g. (i) A raw mango placed in concentrated salt solution loses water & shrivel into pickle.

(ii) People taking lot of salt, experience water retention in tissue cells. This results in puffiness or swelling called edema.

Biological Importance of Osmosis

The cell walls of plants and animals are semipermeable in nature and thus are responsible for the osmosis. When a cell comes in contact with water a tendency of flow of water into the cell is developed. The pressure developed inside the cell due to the inflow of water is called turgor.

If the cell comes in contact with a concentrated solution, cell would shrink, which is called plasmolysis. Cell walls are able to permit the flow of selected ions and molecules also along with water.

Various processes taking place due to osmosis are :

(a) Absorption of water from soil through the cell walls of roots.

(b) Movement of water from roots to the upper parts of plants & trees.

(c) Various types of locomotion in plants like stretching of leaves, opening of flowers, etc., are also based on osmosis.

(d) Germination is also caused due to osmosis as water moves into the seeds through cell walls. 

The phenomenon of osmosis : A solution inside the bulb is separated from pure solvent in the beaker by a semipermeable membrane, Net passage of solvent from the beaker through the memberane occurs, and the liquid in the tube rises untill equilibrium is reached. At equilibrium, the osmotic pressure exerted by the column liquid in the tube is sufficient to prevent further net passage of solvent.

Although the passage of solvent through the membrane takes place in both direction, passage from the pure solvent side to the solution side is more favoured and occurs faster. As a result, the amount of liquid on the pure solvent side decreases, the amount of liquid on the solution side increases, and the concentration of the solution decreases. 

Osmotic Pressure : The equilibrium hydrostatic pressure developed by solution column when it is seperated from solvent by semipermeable membrane is called O.P. of the solution.

  = gh     ;   = density of soln.

g = acceleration due to gravity   ; h = eq. height

1 atm  = 1.013 x 10⁵ N/m²

 

 

 

Definition  : The external pressure which must be applied on solution side to stop the process of osmosis is called osmotic pressure of the solution.

If two solutions of concentration C₁ and C₂ are kept separated by SPM, and C₁ > C₂ then particle movement take place from lower to higher concentration. So, extra pressure is applied on higher concentration side to stop osmosis. And P_ext. = (₁ – ₂)

Reverse Osmosis : If the pressure applied on the solution side is more than osmotic pressure of the solution then the solvent particles will move from solution to solvent side. This process is known as reverse osmosis.

Berkely : Hartely device/method uses the above pressure to measure osmotic pressure.

e.g. used in desalination of sea-water.

Vant – Hoff Formula (For calculation of osmotic pressure)

 

     concentration (molarity)

                T

             = CST

            S = ideal solution constant                    = atm. 

            = 8.314 J mol^–1 K^–1 (exp value)

            = R (ideal gas) constant

             = CRT =  RT (just like ideal gas equation)      

In ideal solution solute particles can be assumed to be moving randomly without any interactions.

 C = total concentration of all types of particles.

 = C₁ + C₂ + C₃ + s.................

=

Type of solutions :

(a) Isotonic solution : Two solutions having same osmotic pressure are consider as isotonic solution.

                        ₁ = ₂ (at same temperature)

(b) Hypotonic & Hypertonic solutions : If two solutions 1 and 2 are such that ₂ > ₁ , then 2 is called hypertonic solution and 1 is called hypotonic solution.

 

    

Conclusion :Pressure is applied on the hypertonic solution to stop the flow of solvent partices, this pressure become equal to (₂ – ₁) and if hypotonic solution is replaced by pure solvent then pressure becomes equal to ₂.

Solution containing volatile solute / solvents

Mixture of 2 volatile liquids

Raoult's law ( for volatile Liq. Mixture )

Statement of Raoult's law ( for volatile liq. mixture ): In solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction.

p_A µ x_A   =>   p_A = x_AP_Aº

p_A = Partial vapour pressure of component A

x_A = Mole fraction of component ‘A’ in solution.

P_Aº = Vapour pressure of pure component ‘A’ at given temperature

Derivation of total pressure over solution using Raoult’s law and Dalton’s law:

Let A, B be to two volatite liquids in a closed container as shown.

  p_A = x_AP_Aº

Similarly, for liquid B we have,

  p_B = x_BP_Bº

Total pressure over the solution P_T , according to Dalton's law is

P_T = p_A + p_B = x_AP_A⁰ + x_BP_B⁰

Determining composition of vapour phase:       

Let,

y_A = mole fraction of A in vapour phase above the solution and

y_B = mole fraction of B in vapour phase above the solution

Now, we have, p_A = y_A P_T     .....Dalton's law of partial pressure for a gaseous mixture     

 p_A = x_AP_A^{º         ...........}Raoult's law

  Thus,    p_A =  y_A P_T  = x_A P_Aº

  Also,    p_B =  y_BP_T  =  x_BP_Bº

x_A + x_B = 1 =  ; Thus

Graphical Representation of Raoult's Law:

p_A= x_AP_Aº   &   p_B  = x_B P_Bº

P_T = x_AP_Aº + x_B P_Bº

P_T =  ( P_Aº – P_Bº ) x_A + P_B⁰                                            

P_T =  ( P_Bº – P_Aº ) x_B + P_A⁰         

This represents equation of straight line. P_T v.s. x

Note:  If P_A^º > P_B^º , A is more volatile than B. B.P. of A < B.P. of B. 

Limitations of Raoult’s Law: Raoult's Law only works for ideal solutions. Very dilute solutions obey Raoult's Law to a reasonable approximation.

Ideal and Non-ideal Solution

Ideal Solutions : Those solutions which obey Raoult's law over the entire range of conc. are called ideal solutions. When the forces of attraction between A—A, B—B is similar to A—B, then A and B will form ideal solution.

  Properties of ideal solution :

(i) Raoult's law is obeyed         

(ii) DH_mix = 0, i.e., there should not be enthalpy change when components of ideal solutions are mixed.

(iii) DV_mix = 0, (1L + 1L = 2L) i.e., there should not be change in volume on mixing. e.g.; n-hexane and n-heptane; ethyl bromide and ethyl iodide; benzene and toluene; chlorobenzene and bromobenzene form ideal solutions.

(iii) DS_mix = +ve  

(iv) DG_mix = –ve

Non^_Ideal Solutions :

Those solutions which do not obey Raoult's over the entire range of concentration are called non-ideal solutions.

When the forces of attraction between A—A, B—B is different from A—B then 'A' and 'B' form non-ideal solutions. For these solutions :

(i) Raoult's law is not obeyed. 

(ii) DH_mix ¹ 0 ;  

(iii) DV_mix ¹ 0.

Types of Non-Ideal Solutions : Non-ideal solution can be two types.

•  Non ideal solutions showing positive deviation
• Non ideal solutions showing negative deviation          

Azeotropic Mixtures

Very large deviations from ideality lead to a special class of mixtures known as azeotropes, azeotropic mixtures, or constant-boiling mixtures.

Azeotropes : Liquid mixtures which distill over without changes in composition are called constant boiling mixtures or Azeotropes or Azeotropic mixtures.

A boiling liquid mixture at the azeotropic composition produces a vapour of exactly the same composition, and the liquid does not change its composition as it evaporates. Two types of azeotropes are known.

Minimum Boiling Azeotropes : Non-ideal solutions showing large positive deviation from Raoult's law form minimum boiling azeotropes which boil at temperature lower than boiling point of its components 'A' and 'B', e.g., water and benzene, chloroform and methanol.

Maximum Boiling Azeotropes : Non-ideal solutions showing large negative deviation from Raoult's law form maximum boiling azeotropes which boil at temperature higher than the boiling point of its components A and B respectively, e.g., a mixture of HCl and H₂O containing 20.2% HCl by weight boils at 108.5ºC higher than either pure HCI (– 85°C) or water (100°C).

Solubility of gases in liquids

Factors Affecting Solubility of Gas In Liquid :

(i) Nature of gas

(ii) Nature of liquid 

(iii) Temperature

(iv) Pressure

Henry's Law (effect of pressure on solubility of gases in liquids) :

Statement : The solubility of a gas in a liquid at a given temperature is directly proportional to its partial pressure at which it is dissolved.

 Let  x = Mole fraction of unreacted gas in solution at a given temperature as a measure of its solubility.

 p = Partial pressure of gas in equilibrium with the solution.

 By Henry's law:   x µ p     or   p µ x

That is;    p = K_Hx   or    x = ,    

where K_H = Henry's law constant.

Characteristics of Henry's Law constant (K_H).

(i) Unit same as those of pressure: torr or bar.         

(ii) Different gases have different value of K_H  for the same solvent.

(iii) The K_H value of a gas is different in different solvents and it increase with the increase in temperature.

(iv) Higher the value of K_H of a gas, lower will be its solubility. Since, x = .

Plot of p Vs x is a straight line passing through the origin with slope equal to K_H .

Plot of p Vs x for solution of HCl in cyclohexane.

Note : If a mixture of gases is brought in contact with solvent each constituent gas dissolves in proportion to its partial pressure. It means Henry's law applies to each gas independent of the pressure of other gas.

Effect of temperature : Solubility of gases in liquids decreases with rise in temperature.

Explanation : When dissolved, the gas molecules are present in liquid phase and the process of dissolution can be considered similar to condensation and heat is evolved in this process. We have learnt that dissolution process involves dynamic equilibrium and thus must follow Le Chatelier's principle. As dissolution of gases in liquids is an exothermic process, the solubility should decrease with increase of temperature.

Note : K_H values for both N₂ and O₂ increase with increase of temperature indicating that the solubility of gases increases with decrease of temperature. It is due to this reason that aquatic spcies are more comfortable in cold water rather than warm water.

Applications of Henry's law : It has several applications in biological and industrial phenomena.

(i) To increase the solubility of CO₂ in soft drinks and soda water the bottle is sealed under high pressure.

(ii) Scuba divers must cope with high concentrations of dissolved gases while breathing air at high pressure underwater. Increased pressure increases the solubility of atmosphere gases in blood. When the divers come towards surface, the pressure is gradually decreased. This releases the dissolved gases and leads to the formation of bubbles of nitrogen in the blood. This blocks capillaries and creates a medical condition known as bends, which are painful and dangerous to life. To avoid bends, as well as, the toxic effects of high concentrations of nitrogen in the blood, the tanks used by scuba divers are filled with air diluted with helium (11.7% helium, 56.2% nitrogen and 32.1% oxygen).

(iii) At high altitudes the partial pressure of oxygen is less than that at the ground level. This leads to low concentrations of oxygen in the blood and tissues of people living at high altitudes or climbers. Low blood oxygen causes climbers to become weak and unable to think clearly, symptoms of a condition known as anoxia.

Summary

Colligative properties & constitutional properties :

Constitutional Properties : Properties which are dependent on nature of particles are constitutional properties like electrical conductance.

Colligative properties  : The properties of the solution which are dependent only on the total no. of particles relative to solvent/solution or total concentration of particles in the solution and are not dependent on the nature of particle i.e. shape, size, neutral /charge etc. of the particles.

There are 4 colligative properties of solution :

Osmotic pressure
Relative lowering in vapour pressure

Elevation in b.p. (DT_b)

Depression in freezing pt. (DT_f)

(i) Osmosis & Osmotic pressure :

Osmosis:  The spontaneous flow of solvent particles from solvent side to solution side or from solution of low concentration side to solution of high concentration side through a semipermeable membrane (SPM) is known as osmosis.

Ex.

Conclusion : After some time in (A) grape or egg will shrink and in (B) grape or egg will swell.

e.g. (i) A raw mango placed in concentrated salt solution loses water & shrivel into pickle.

(ii) People taking lot of salt, experience water retention in tissue cells. This results in puffiness or swelling called edema.

Biological Importance of Osmosis

The cell walls of plants and animals are semipermeable in nature and thus are responsible for the osmosis. When a cell comes in contact with water a tendency of flow of water into the cell is developed. The pressure developed inside the cell due to the inflow of water is called turgor.

If the cell comes in contact with a concentrated solution, cell would shrink, which is called plasmolysis. Cell walls are able to permit the flow of selected ions and molecules also along with water.

Various processes taking place due to osmosis are :

(a) Absorption of water from soil through the cell walls of roots.

(b) Movement of water from roots to the upper parts of plants & trees.

(c) Various types of locomotion in plants like stretching of leaves, opening of flowers, etc., are also based on osmosis.

(d) Germination is also caused due to osmosis as water moves into the seeds through cell walls. 

The phenomenon of osmosis : A solution inside the bulb is separated from pure solvent in the beaker by a semipermeable membrane, Net passage of solvent from the beaker through the memberane occurs, and the liquid in the tube rises untill equilibrium is reached. At equilibrium, the osmotic pressure exerted by the column liquid in the tube is sufficient to prevent further net passage of solvent.

Although the passage of solvent through the membrane takes place in both direction, passage from the pure solvent side to the solution side is more favoured and occurs faster. As a result, the amount of liquid on the pure solvent side decreases, the amount of liquid on the solution side increases, and the concentration of the solution decreases. 

Osmotic Pressure : The equilibrium hydrostatic pressure developed by solution column when it is seperated from solvent by semipermeable membrane is called O.P. of the solution.

p = rgh ;

r = density of soln.

g = acceleration due to gravity;

h = eq. height

1 atm  = 1.013 x 10⁵ N/m²

 

Definition  : The external pressure which must be applied on solution side to stop the process of osmosis is called osmotic pressure of the solution.

If two solutions of concentration C₁ and C₂ are kept separated by SPM, and C₁ > C₂ then particle movement take place from lower to higher concentration. So, extra pressure is applied on higher concentration side to stop osmosis. And

P_ext. = (p₁ – p₂)

Reverse Osmosis : If the pressure applied on the solution side is more than osmotic pressure of the solution then the solvent particles will move from solution to solvent side. This process is known as reverse osmosis.

Berkely : Hartely device/method uses the above pressure to measure osmotic pressure.

e.g. used in desalination of sea-water.

Vant – Hoff Formula (For calculation of osmotic pressure)

p a concentration (molarity)

       a T

p = CST

S = ideal solution constant   p = atm. 

= 8.314 J mol^–1 K^–1 (exp value)

  = R (ideal gas) constant

p = CRT =  RT (just like ideal gas equation)      

In ideal solution solute particles can be assumed to be moving randomly without any interactions.

 C = total concentration of all types of particles.

= C₁ + C₂ + C₃ + s.................

=

Type of solutions :

(a) Isotonic solution : Two solutions having same osmotic pressure are consider as isotonic solution.

p₁ = p₂ (at same temperature)

  (b) Hypotonic & Hypertonic solutions : If two solutions 1 and 2 are such that p₂ > p₁ , then 2 is called hypertonic solution and 1 is called hypotonic solution.

Conclusion :Pressure is applied on the hypertonic solution to stop the flow of solvent partices, this pressure become equal to (p₂ – p₁) and if hypotonic solution is replaced by pure solvent then pressure becomes equal to p₂.

Note : Osmotic pressure of very dilute solutions is also quite significant. So, its measurement in lab is very easy.

Plasmolysis : When the cell is placed in solution having osmotic pressure greater than that of the cell sap, water passes out of the cell due to osmosis. Consequently, cell material shrinks gradually. The gradual shrinking of the cell material is called plasmolysis.

Abnormal Colligative Properties :  [Vant–Hoff  correction :]

For electrolytic solutes the number of particles would be different from the number of particles actually added, due to dissociation or association of solute.

The actual extent of dissociation/association can be expressed with a correction factor known as vant Haff factor (i).

Vant–Hoff  factor : i =

If solute gets associated or dissociated in solution then experimental / observed / actual value of colligative property will be different from theoretically predicted value so it is also known as abnormal colligative property.

This abnormality can be calculated in terms of Vant-Hoff factor.

i=== 

i > 1 dissociation

i < 1 association

i =

Modified formula \ p= iCRT

p= (i₁C₁ + i₂C₂ + i₃C₃.....) RT

Case - I    :  Electrolyte dissociates

Relation between i &  (degree of dissociation) :

Let the electrolyte be A_xB_y

e.g.  NaCl (100% ionised), i = 2. ;  BaCl₂ (100% ionised), i = 3. ; K₄[Fe(CN)₆] (75% ionised), i = 4.

Case - II  :  Electrolyte associates

Relation between degree of association  b & i.

if dimerise n = 2 ; trimerise n = 3 ; tetramerise n = 4.

e.g. CH₃COOH 100% dimerise in benzene, i = ;  C₆H₅COOH 100% dimerise in benzene, i =  

 (ii)  Relative lowering in vapour pressure ( RLVP) :            

Vapour Pressure :

The conversion of a liquid to a vapour takes place in a                     

visible way when the liquid boils, it takes place under all conditions.

say 5 gm liquid left at t_eq 

At eq. : the rate of evaporation = rate of condense                     

H₂ O (λ)    H₂ O (g)  

K_p = eq.                                                         

 finally                                                                       

The pressure exerted by vapours of the liquid when equilibrium is established between vapours & its liquid. is known as vapour pressure.

Vapour pressure is an equilibrium constant (K_P) of the  reaction.

                                       liquid vapours.

Since vapour pressure is an equilibrium constant so its value is dependent only on temperature for a particular liquid

It does not depends on the amount of liquid taken or surface area of the liquid or on volume or shape of the container. It is a characteristic constant for a given liquid.

Vapour Pressure of a solution

Vapour Pressure of a solutions of a non volatile solute ( solid solute ) is always found to be less than the vapour pressure of pure solvent .

Reason :   Some of the solute  molecules will occupy some surface area of the solutions so tendency of the solvent particles to go into the vapour phase is slightly decreased hence Pº > P_S, where Pº is vapour pressure of pure solvent and P_S is vapour pressure of the solution.

Lowering in VP  =  Pº – P_S    =  DP

and Relative lowering in  Vapour Pressure  =

Raoult's law (For non–volatile solutes): The vapour pressure of a solution of a non-volatile solute is equal to the vapour pressure of the pure solvent at that temperature multiplied by its mole fraction.

OR Relative Lowering in Vapour Pressure = mole fraction of the non volatile solute in solution

.

where n = number of moles of non-volatile solute and N = number of moles of solvent in the solution.

where w and W = mass of non-volatile solute and volatile solvent respectively

m and M = molar mass of non-volatile solute and volatile solvent respectively

If solute gets associated or dissociated ;     

(iii) Elevation in Boiling point  (DT_b)

Boiling point of a Liquid : The temprature at which vapour pressure of a liquid becomes equal to the external pressure present at the surface of the liquid is called b.p of liquid at that pressure.

Normal boiling point : The temperature at which boiling ocuurs when the external pressure is exactly 1 atm is called the normal boiling point of the liquid. (T_b)

Boiling pt of any solution :

Since V.P. of solution is smaller then v.p. of pure solvent at any temperature hence to make it equal to P_ext. we have to increase the temp. of solution by greater amount in comparision to pure solvent.

DH_{vapour of solvent}  =DH_{vapour solution}   

Graphical :

Using Raoult’s law :

  

T_b = K_b × molality

K_b is dependent on property of solvent and known as molal elevation constant of solvent  

 It is also known as ebullioscopic constant.

K_b = elevation in boiling point of 1 molal solution.

Units : = K kg mol^–1      

Using thermodynamics   :  K_b =

L_Vap – is latent heat of vapourization in cal/g or J/g

R = 2 cal mol^–1 K^–1 or 8.314 J mol^–1 K^–1.  ;  T_b = b.p. of liquid (in kelvin)

 K_b = K kg mol^–1

Also K_b = 

Here:DH_vap=molar enthalpy of vaporisation in cal/mole of J/mole  

M Þ mole wt. of solvent

 L_vap = 

If solute gets associated/dissociated   :DT_b = i × K_b × molality

(iv)  Depression in freezing pt (DT_f)

Freezing point : Temperature at which vapour pressure of solid becomes equal to v.p of liquid is called freezing point of liquid or melting point of solid.

DH_sub > DH_vap.

For - dil. solutions BE & CD can be assumed to be straight lines.

using similar triangles     

\ DT_f a P

\ DT_f = K_f . Molality

K_f = molal depression constant = cryoscopic  constant

K_f =  =

for water T_f = 273 K  &   L_Fusion = 80 cal / gm

  K_f  =  = 1.86 K kg mol^–1

At freezing point or below it  only solvent molecules will freeze not solute molecules (solid will be of pure solvent)