SOLUTIONS

A Solution is a homogenous mixture of two or more components. It is defined by using the

terms solute and solvent.

Solvent: The component that is present in largest quantity is called solvent. It determines the physical
state of solution.

Solute: One or more components present in solution other than solvent is called solute.

Binary solutions: Solution consisting of two components only.

Types of Solutions
According to the phase of solvent, a binary solution can be classified in following types:

Types of Solutions Solute Solvent Examples

Gaseous solutions Gas Gas Mixture of O2 and N2

Liquid Gas Chloroform mixed with N2 Gas

Solid Gas Camphor in nitrogen gas

Liquid Solutions Gas Liquid Oxygen dissolved in water

Liquid Liquid Ethanol dissolved in water

solid Liquid Glucose dissolved in water

Solid Solutions Gas solid Solution of H2 and Pd

Liquid solid Amalgam of Hg with Na

Solid solid Alloy

Different Methods of Expressing Concentration of Solutions:-

The composition of solution is defined in terms of concentration. There are several ways to define
concentration of solution as follows:
Solubility : Solubility of a substance is the maximum amount that can be dissolved in given amount of
solvent at specific temperature. Factors affecting the solubility:
- Nature of solute
- Nature of solvent
- Temperature
- Pressure

Solubility of Solid in a Liquid

Nature of solute and solvent:
According to the nature of solute and solvent the solubility of solid in a liquid follow the principle “ Like
dissolves like”
If the nature of solute and solvent is same, the intermolecular force of interaction would be same. That
helps in solubility of solute in solvent.
Polar solute dissolves in polar solvent. For example: NaCl and sugar dissolves in water. Non-polar
solute dissolves in non-polar solvent. For example: Naphthalene and anthracene dissolves in benzene
not in water.

Saturated solution: If the concentration of solute in solution remain constant at given set of
temperature and pressure is called saturated solution. If we add more solute in it, it would precipitate
out.
Un-Saturated solution: If the concentration of solute in solution can increase at given set of
temperature and pressure is called un-saturated solution. If we add more solute in it, it would get
dissolve and increase the concentration of solution.

Effect of temperature:
The solubility of solute in solvent always follows the dynamic equilibrium.
Solute + Solvent → Solution.
It follows the Le Chateliers principle for the change in temperature at dynamic equilibrium.
If the solution is formed by giving heat means dissolution is endothermic. By increasing the
temperature, the reaction will proceed in forward direction and solubility of solute increases.
If the heat is released in formation of solute means dissolution is exothermic. By increasing the
temperature, the reaction will proceed in backward direction and solubility of solute decreases.
Effect of pressure: Pressure has no significant effect on solubility of solid in liquid.
Solubility of Gas in a Liquid
Nature of solute and solvent : Solubility of gas in liquid is also somewhat affected by nature of solute
and solvent. Oxygen dissolves only a small extent in water but HCl is highly soluble in water because of
polar nature of solute and solvent.
 Effect of pressure: Solubility of gas in liquid is highly affected by temperature and pressure. As the
pressure of the gas above the surface of the liquid increases, it increases the solubility of gas in liquid.
The quantitative relation of this equation is given by Henry’s Law.
Henry’s Law: It states that, “At constant temperature, the solubility of gas in a liquid is directly
proportional to the partial pressure of the gas present above the surface of the liquid or solution.”
If we consider mole fraction of gas in a solution to measure its solubility then it can be said that,
“Mole fraction of gas in a liquid is proportional to the partial pressure of gas above the liquid or
solution.”
Now the Henry’s Law can be stated as , “ The partial pressure of a gas in vapour phase (p) is
proportional to the mole fraction of gas(x) in solution.”
Expression for Henry’s Law:
Pαx
p= KH. x p slope=KH
KH is Henry’s Law constant

Important point regarding Henry’s Law:

 Different gases have different KH values at the same temperature. That is KH depends on the nature of
gas.
 Higher the value of KH at given pressure, lower is the solubility of gas in given liquid.
 KH value of particular gas increases with increasing temperature. It indicates that solubility of gas
decreases with increasing temperature.

Effect of temperature: Dissolution of gas in a liquid is an exothermic process. As dissolution process

involves dynamic equilibrium, it follows Le Chaterlier’s principle. Hence the solubility of gas in liquid,
decreases with increase in temperature.
Vapour Pressure: The pressure exerted by the gas in equilibrium with a solid or liquid in a closed
container at a given temperature is called the vapour pressure.

Vapour Pressure of a Liquid Solution

Liquid solution are formed when solvent is in liquid phase. Solute may be solid, liquid or gas. On the
basis of solute, the liquid solution is classified in 3 types as:

(i) Solid in liquid

(ii) Liquid in liquid
(iii) Gas in liquid

Vapour Pressure of a Liquid-Liquid Solution

Let us take a binary solution made up of two volatile liquids 1 and 2. As the liquid start evaporating; a
stage will come when the vapour pressure of liquid will be in equilibrium with the corresponding liquid.
As we know that vapour pressure of liquid is proportional to its mole fraction. The quantitative
relationship between the vapour pressure and mole fraction in binary solution is given by Raoult’s Law.

Raoult’s Law:
It states that for the solutions of volatile liquid, the partial vapour pressure of each component of the
solution is directly proportional to its mole fraction present in solution.

For component 1,

p1 ∝ x1
p1 = p1° x1...(1)
p1 = Vapour pressure of component 1 in solution.
p1° = Vapour pressure of pure liquid component 1 at the same temperature
x1 = Mole fraction of component 1 in solution.

Similarly for component 2 :

P2 = p2° x2 ...(2)

According to Dalton’s Law of partial pressure, The total pressure (ptotal ) over the solution phase in the
container will be the sum of partial pressure of the components in solution. If the solution is made up
of two volatile liquids then total pressure above the solution is:
ptotal = p1 + p2 ...(3)

ptotal = Total pressure over the solution phase

p1 = Vapour pressure of component 1 in solution
p2 = Vapour pressure of component 1 in solution
Substituting the values of p1 and p2 in eq...(3) we get:

ptotal = p1° x1 + p2° x2 ...(4)

As, total mole fraction of components in any solution is 1. Therefore,

x1 + x2 = 1
x1 =(1 - x2)...(5)

Putting the value of x1 in eq (4) we get:

ptotal = p1°(1- x2) + p2° x2

ptotal = p1° - p1° x2 + p2° x2

ptotal = p1° +( p2°- p1°) x2 ...(6)

The equation ...(6) is known as the mathematical expression for Raoult’s Law for the solution made up
of two volatile liquids.

From this equation ...(6) we can conclude the following points :

• ptotal can be related to mole fraction of any of the one component.

• ptotal varies linearly with x2
• ptotal increases or decreases with increase of x1
 This can be represented on graph as follows assuming p1° < p2°:

Conclusion from graph:

 Plot of p1° vs x1 is linear

 Plot of p2° vs x2 is linear
 Maximum value of ptotal = p2°
 Minimum value of ptotal = p1°
Composition of vapour phase at equilibrium is determined by using Dalton’s Law. Let y 1 and y2 be the
mole fraction of liquid 1 and 2 in solution then partial vapour pressure of each component is written
as:
p1 = y1 ptotal... (7)
Equation ...(7) gives you the value of partial vapour pressure of each component in vapour phase.

y1= p1 / Ptotal = p10 x1 / Ptotal….(8)

Vapour Pressure of a Solid-Liquid Solution

When a non-volatile solid is added to the solvent to form a solution, then the vapour pressure of
solution is found lower than vapour pressure of the pure solvent at same temperature. The decrease in
the vapour pressure of the solution is solely depends on the quantity of non-volatile solute present in
solution.
The vapour pressure of such solution is given by using general equation of Raoult’s Law.
Assume that water is component 1 and non-volatile component is component 2, then vapour pressure
of the solution will be equal to the vapour pressure of solvent in solution. Vapour pressure of
solvent p1 is proportional to its mole fraction in solution and given as :
p1 ∝ x1
p1 = p1° x1...(1)
p1 = Vapour pressure of component 1 in solution.
p1° = Vapour pressure of pure liquid component 1at the same temperature
x1 = Mole fraction of component 1 in solution.

Ideal and Non Ideal Solutions

Liquid-liquid solutions can be classified as ideal and non-ideal on the basis of certain properties.
 Ideal Solution
 Obeys the Raoult’s Law over the entire range of concentration.
 ΔHmixing = 0
 ΔVmixing = 0
Example :
 n-hexane and n-heptane,
 bromoethane and chloroethane
 Ethyl chloride and ethyl bromide
 Chlorobenzene and bromo benzene
 Benzene and toluene
It can be summarised as : If a Solution formed by mixing the two components A and B, in which
intermolecular force of attraction between A and B (A‒B) is nearly equal to intermolecular force of
attraction between pure components (A‒A and B‒B) then no heat would be evolved or absorbed in
forming the solution. Also volume of the solution will be equal to the total volume of the individual
component taken to form the solution.

Non-Ideal Solution
 Does not obey the Roult’s Law over the entire range of concentration.
 ΔHmixing ≠ 0
 ΔVmixing ≠ 0
 Example: Solution of chloroform and acetone
It can be summarised as: If a Solution formed by mixing the two components A and B , in which
intermolecular force of attraction between A and B (A‒B) is not equal to intermolecular force of
attraction between pure components (A‒A and B‒B). This new interaction (A‒B) is either less than or
more than the interaction of the pure components (A‒A and B‒B). This leads to the positive or
negative deviations from Raoult’s Law.

Positive Deviation from Raoult’s Law

 The vapour pressure of solution formed by mixing two components is higher than predicted from
Raoult’s Law.
 The new intermolecular interactions formed by mixing the component A and B (A‒B) are weaker than
the intermolecular interactions of pure component (A‒A and A‒B).
Examples :
 ethanol and acetone
 carbon disulphide and acetone.
 Ethanol and cyclohexane
 Benzene and acetone
 Benzene and carbon tetrachloride
 Carbon tetrachloride and chloroform.
 Graph representing the positive deviation:

Negative Deviation from Raoult’s Law

 The vapour pressure of solution formed by mixing two components is lower than predicted from
Roult’s Law
 The new intermolecular interactions formed by mixing the component A and B (A-B) are stronger than
the intermolecular interactions of pure component (A-A and A-B)
Example:
 phenol and aniline,
 chloroform and acetone.
 Acetic acid and pyridine
 Chloroform and benzene
 Water and nitric acid
 Diethyl ether and chloroform

Graph representing the negative deviation:

Azeotropes :These are mixture of two liquids having same composition in liquid as well as vapour
phase and boil at the constant temperature. This liquid mixture cannot be separated into pure
component even on fractional distillation.

Types of Azeotropes
Minimum boiling azeotrope: The solution which show large positive deviation from Raoult’s Law.
Example: solution of 95% ethanol in water.
Maximum boiling azeotropes: The solution which show large negative deviation from Raoult’s Law.
Example: solution of 68% nitric acid and 32% water by mass.
Colligative properties: The properties of solution which depends on only the number of solute
particles but not on the nature of solute are called colligative properties.
Types of colligative properties: There are four colligative properties namely,
1. Relative lowering of vapour pressure
2. Elevation of boiling point
3. Depression of freezing point
4. Osmotic pressure
Relative lowering of vapour pressure:
The difference in the vapour pressure of pure solvent and solution represents lowering in
vapour pressure .
Relative lowering of vapour pressure: Dividing lowering in vapour pressure by vapour pressure of pure

solvent is called relative lowering of vapour pressure

Relative lowering of vapour pressure is directly proportional to mole fraction of solute. Hence it is a
colligative property.

Elevation of boiling point: (EBULLIOSCOPY)

Boiling Point:- The boiling point is the temperature at which the vapour pressure of a liquid equals to
the external atmospheric pressure surrounding the liquid.
When a non-volatile solute is added to a volatile solvent its vapour pressure of the solution is lowered
, it is apparent that the boiling point of the solution will be higher than that of pure solvent. In other
words the boiling point of the solvent is elevated by the addition of non-volatile solute to it.
The difference in boiling points of solution Tb and pure solvent Tb0 is called elevation in boiling point.
ΔTb = Tb - Tb0
For a dilute solution elevation of boiling point is directly proportional to molal concentration of the
solute in solution. Hence it is a colligative property.
ΔTb = Kb x molality
where Kb is the molal elevation constant or ebulllioscopic constant.
Defination of Kb – It is elevation of boiling point when one mole of solute is dissolved in
Determination of molecular mass of the solute:-
Molecular Mass of solute= Kb x mass of solute x 1000
ΔTb x mass of solvent

Graphical Representation of Elevation of Boiling Point:-

Depression of freezing point: (CRYOSCOPY)

Freezing Point:- The freezing point is the temperature at which a liquid changes to a solid.
The freezing point of a substance is not necessarily the same as its melting point.

When a non-volatile solute is added to a volatile solvent vapour pressure of the solution decreases.The
lowering of vapour pressure of solution causes a lowering of freezing point compared to that of pure
solvent.
The difference in freezing point of the pure solvent and solution is called the depression in
freezing point.
For a dilute solution depression in freezing point is a colligative property because it is directly
proportional to molal concentration of solute.
ΔTf = Kf x molality
where Kf is the molal depression constant or cryoscopic constant.
Defination of Kf – It is the depression of freezing point when one mole of solute is dissolved in 1000g
of the solvent.
Determination of molecular mass of the solute:-
Molecular Mass of solute= Kf x mass of solute x 1000
ΔTf x mass of solvent
Graphical Representation of Depression of Freezing Point :-

Osmosis:
The phenomenon of flow of solvent molecules through a semi permeable membrane from pure
solvent to solution is called osmosis.
Osmotic pressure: The excess pressure that must be applied to solution to prevent the passage of
solvent into solution through a semi permeable membrane is called osmotic pressure.

Osmotic pressure is a colligative property as it depends on the number of solute particles and not on
their identity.
For a dilute solution, osmotic pressure ( ) is directly proportional to the molarity (C) of the solution
i.e. = CRT

Determination of molecular mass of the solute:-

Osmotic pressure can also be used to determine the molar mass of solute using the

equation
Isotonic solution: Two solutions having same osmotic pressure at a given temperature are called
isotonic solution.
Hypertonic solution: If a solution has more osmotic pressure than other solution it is called hypertonic
solution.
Hypotonic solution: If a solution has less osmotic pressure than other solution it is called hypotonic
solution.
Endo-osmosis: Endosmosis is the movement of water across a semipermeable membrane into a region
of higher solute concentration.
Exo-osmosis: Exosmosis is the outward movement of water from a cell through a semipermeable
membrane.
Reverse osmosis: The process of movement of solvent through a semipermeable membrane from the
solution to the pure solvent by applying excess pressure on the solution side is called reverse osmosis.
Condition :- When Pext > π
Application of Reverse Osmosis

DESALINATION OF SEA WATER

Colligative properties help in calculation of molar mass of solutes.
Abnormal molar mass: Molar mass that is either lower or higher than expected or normal molar mass
is called as abnormal molar mass.
The abnormality in the molecular mass of the solute particles occurs due to either of the following:
Association of solute particles or Dissociation of solute particles in a particular solvent.
Association of Solute Particles
It is possible that some solute molecules start to associate inside the solution. This suggests, that there
are a decreased number of solute particles in the solution. As colligative properties depend on the
number of solute particles in the solution, so there will be a decrease in the colligative property along
with the solute particles. The colligative properties are inversely proportional to the molecular mass
of solute; thus, we get a higher molar mass of the solute. For Example, ethanoic acid or acetic acid
(CH3COOH) associate in solution to form a dimer due to hydrogen bonding.
Dissociation of Solute Particles
It is very likely that some solute molecules, generally electrolytes dissociate into two or more
ions/particles when they are dissolved in a solution. This causes an increase in solute particles in the
solution, hence there is an increase in colligative properties of solutions. As colligative properties and
molecular mass of solute vary inversely, hence the molar mass of the solute is decreased.

Van’t Hoff factor:

Van’t Hoff factor (i) accounts for the extent of dissociation or association.

Value of i is less than unity in case solute undergo association and the value of i is greater than unity
in case solute undergo dissociation.
Inclusion of van’t Hoff factor modifies the equations for colligative properties as:
Calculating Degree of Association and Dissociation:-
Degree of dissociation (α): It is defined as the fraction of total molecules which dissociate into simpler
molecules or ions.

m= number of particles in solution

Degree of association (α): It is defined as the fraction of the total number of molecules which associate
or combine together resulting in the formation of a bigger molecules.

m = number of particles associating in solution.

Which WORKING FORMULA to use in the numerical how will you all identify???

1. In the question if molarity word is present then use the formula,

2. In the question if molality word is present then use the formula,

3. In the question if mole fraction word is present then use the formula,

4.Henry’s Law

5.In the numerical if a non-volatile solute is present in a volatile solvent and then about
vapour pressure is spoken then use the formula,
6. In the numerical if two volatile liquids are mixed or two miscible liquids form ideal
solution and then about vapour pressure is spoken then use the formula,

7. In the numerical if boiling point is spoken about then use the formula,

8. In the numerical if freezing point is spoken about then use the formula,

9. In the numerical if osmotic pressure is spoken about then use the formula,

one of the values of R = 0.0821 L atm K-1 mol-1

10.How will you find out the Kb and Kf value if it is not given in the question:-

11.In which all numerical you will use van’t Hoff factor with the formula,

 When an ionic solute is dissolved in water

 When acid is dissolved in water
 Acetic acid/ benzoic acid dissolved in benzene
 When words like percentage association or dissociation is used in the question
 When the words dimer , trimer , completely dissociated or associated is used in the question