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CBSE NOTES CLASS 12 CHEMISTRY CHAPTER 2

SOLUTIONS

Solution

Binary solution

Solute and solvent

Classification of solutions

Classification of solutions based on physical state of solute and solvent.

Classification of solutions based on the amount of solute dissolved in a solvent

Unsaturated solution

Saturated solution

Supersaturated solution

Solubility

Concentration of solutions

Methods of expressing concentration of solutions

Percentage by mass (w/w %):

Volume percentage (V/V %)

Mass by volume (w/V %)

Parts per million (ppm)

Mole fraction (χ)

Molarity (M)

Molality (m)

Normality (N)

Equivalent weight or gram equivalent

Relationship between molarity and normality

Formality (F)

Mass fraction

Laws of dilution

Solubility of a solid in a liquid

Effect of temperature on solubility of solids in liquids

Effect of pressure on solubility of solids in liquids

Solubility of a gas in a liquid

Effect of pressure on solubility of gases in liquids

Henry’s law

Applications of Henry’s law

Effect of temperature on solubility of gases in liquids

Vapour pressure of liquid-liquid solutions

Raoult’s law

Raoult’s law for solutions of solids in liquids

Dalton’s law of partial pressures

Konowaloff rule

Raoult’s law and Henry’s law

Ideal solutions

Non-ideal solutions

Non-ideal solutions showing positive deviation

Non-ideal solution showing negative deviation

Azeotropic mixture

Minimum boiling azeotropes

Maximum boiling azeotropes

Colligative properties

Some of the important colligative properties of solutions

Relative lowering of vapour pressure

Calculating molar mass of solute using relative lowering of partial pressure

Elevation in boiling point (ΔTb)

Calculation of molecular mass of solute using elevation in boiling point

Depression in freezing point (ΔTf)

Calculating Molar Mass of Solute using depression in freezing point

Antifreeze solution

Osmosis

Exosmosis

Endosmosis

Osmotic pressure (π)

Hypertonic solution

Hypotonic solution

Isotonic solution

Reverse osmosis

Abnormal molecular masses

van’t Hoff factor (i)

Degree of dissociation (α) and van’t Hoff factor (i)

Degree of association (α) and van’t Hoff factor (i)

CBSE NOTES CLASS 12 CHEMISTRY CHAPTER 2

SOLUTIONS

Solution

Solution is a homogeneous mixture of two or more substances in same or different physical phases.

The substances forming the solution are called components of the solution.

A solution of two components is called binary solution.

Solute and solvent

In a binary solution, solvent is the component which is present in large quantity while the other component is known as solute.

Classification of solutions

(A) Following types of solutions are seen on the basis of physical state of solute and solvent.

Type of Solution

Solute

Solvent

Example

Gaseous solution

Gas

Gas

Mixture of oxygen and nitrogen gases

Liquid

Gas

Chloroform mixed with nitrogen 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 hydrogen in palladium

Liquid

Solid

Amalgam of mercury with sodium

Solid

Solid

Copper dissolved in gold

Aqueous Solution

If water is used as a solvent, the solution is called aqueous solution and if not, the solution is called non-aqueous solution.

(B) Depending upon the amount of solute dissolved in a solvent we have the following types of solutions:

(i) Unsaturated solution

A solution in which more solute can be dissolved without raising temperature is called an unsaturated solution.

(ii) Saturated solution

A solution in which no solute can be dissolved further at a given temperature is called a saturated solution.

(iii) Supersaturated solution

A solution which contains more solute than that would be necessary to saturate it at a given temperature is called a supersaturated solution.

Solubility

The maximum amount of a solute that can be dissolved in a given amount of solvent (generally 100g) at a given temperature is termed as its solubility at that temperature.

Concentration of Solutions

The concentration of a solution is defined as the relative amount of solute present in a solution. On the basis of concentration of solution there are two types of solutions.

(i) Dilute solution (ii) Concentrated solution.

Methods of Expressing Concentration of Solutions :

(i) Percentage by mass (w/w %): It is defined as the amount of solute present in 100 g of solution.

ww% =mass of solutemass of solution×100

(ii) Volume percentage (V/V %) is defined as:

VV%=Volume of the component Total volume of solution×100

(iii) Mass by volume (w/V) is defined as the weight of solute present in 100 mL of solution.

wV% = weight of solutevolume of solution ×100

(iv) Parts per million (ppm) is defined as the parts of a component per million parts (106) of the solution. It is widely used when a solute is present in trace quantities.

ppm =no of parts of the componenttotal no of parts of all the components ×106

(v) Mole fraction (χ) is defined as the ratio of the number of moles of a component to the total number of moles of all the components. For a binary solution, if the number of moles of A and B are nA and nB respectively, the mole fraction of A will be

χA =nAnA+nB and χB =nBnA+nB

 χA+χ B=1

(vi) Molarity (M) is the number of moles of solute present in 1L (dm3) of the solution.

M =number of moles of solutevolume of solution in L

Also,

M =Percent by mass × density × 10Molar mass of solute

When molarity of a solution is 1 M, it is called a molar solution. 0.1 M solution is called a decimolar solution while 0.5 M solution is known as semi molar solution

(vii) Molality (m) is the number of moles of solute per kilogram of the solvent.

m=number of moles of solutemass of solvent in kg

When solvent used is water, a molar (1 M) solution is more concentrated than a molal (1 m) solution. (Why?)

(viii) Normality (N) is the number of gram equivalents of solute present in 1 L of solution.

N= number of grams equivalents of solutevolume of solution in L

Equivalent weight (also known as gram equivalent) is the mass of one equivalent, that is, the mass of a given substance which will

The mole equivalents of an acid or base are calculated by determining the number of H+ or OH- ions per molecule:

Eq.mass of an acid= Molar mass of the acidBasicity

Eq.mass of a base= Molar mass of the baseAcidity

Eq.mass of a salt= Molar mass of the saltTotal positive valency of metallic atoms

Number of gram equivalents of solute =Mass of solute in gramsEquivalent mass of solute

Relationship between molarity and normality

For an acid solution, n is the number of H+ ions provided by a formula unit of acid (i.e. basicity).

For a basic solution, n is the number of OH+ ions provided by a formula unit of base (i.e. acidity).

Also,

(ix) Formality (F) is the number of formula weights of solute present per litre of the solution.

F =moles of solutevolume of solution in L

(x) Mass fraction of any component in the solution is the mass of that component divided by the total mass of the solution.

mass fraction =mass of solutemass of solution

Dilution Law

Solubility of a Solid in a Liquid

Effect of temperature

The solution being in dynamic equilibrium, must follow Le Chateliers Principle.

Effect of pressure

Pressure does not have any significant effect on solubility of solids in liquids. It is so because solids and liquids are highly incompressible and practically remain unaffected by changes in pressure.

Solubility of a Gas in a Liquid

Effect of Pressure – Henry’s Law

The law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of liquid or solution.

The most commonly used form of Henry’s law states

“the partial pressure (p) of the gas in vapour phase is proportional to the mole fraction (χ) of the gas in the solution”

and is expressed as

Where, KH. is a proportionality constant called Henery’ constant.

Applications of Henry’s Law

  1. In manufacture of soft drinks and soda water, CO2 is passed at high pressure to increase its solubility.

  2. In case of deep sea diving, increased pressure increases the solubility of atmospheric gases in blood. When the divers come towards surface, the pressure gradually decreases. 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 minimise the painful effects (bends) accompanying the decompression of deep sea divers, O2 is diluted with less soluble He gas as breathing gas.


  3. At high altitudes, the partial pressure of O2 is less than that at the ground level. This leads to low concentrations of O2 in the blood of climbers which causes anoxia.

Effect of Temperature

Dissolution of gases in liquids is an exothermic process. Hence the solubility of gases in liquids decreases with rise in temperature. Thus, aquatic species are more comfortable in cold water [more dissolved O2] rather than warm water.

Vapour Pressure of Liquid-Liquid Solutions – Raoult’s Law

For a solution of two volatile liquids, the vapour pressure of each liquid in the solution is less than the respective vapour pressure of the pure liquids and the equilibrium partial vapour pressure of the liquid is directly proportional to its mole fraction.

In case of a binary solution, containing two liquids 1 and 2 with mole fractions χ1 and χ2, for component 1 and 2 respectively,

The proportionality constant is obtained by considering the pure liquid.

When χ1 = 1 then k = po1, where po1 is the vapour pressure of pure component 1 at the same temperature.

Hence, p1 = po1 χ1

Similarly, for component 2

where po2 is the vapour pressure of pure component 2 at the same temperature.

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According to Dalton’s law of partial pressures, the total pressure (ptotal) over the solution phase in the container will be the sum of the partial pressures of the components of the solution. Or,

Substituting the values of p1 and p2, we get

Konowaloff Rule

At any fixed temperature, the vapour phase is always richer in the more volatile component as compared to the solution phase.

In other words, mole fraction of the more volatile component is always greater in the vapour phase than in the solution phase.

The composition of vapour phase in equilibrium with the solution is determined by the partial pressure of components. If y1 and y2 are the mole fractions of the component 1 and 2 respectively in the vapour phase then, using Dalton’s law of partial pressure, then

Raoult’s Law and Henry’s Law

Raoult’s Law - The vapour pressure of a volatile component in a given solution is given by,

[Raoult’s law gives the partial vapour pressures of components in terms of solutbility of components]

Henry’s Law - Solubility of gas is given by,

Hence Raoult’s law is a special case of Henry’s law in which KH becomes po1.

Raoult’s Law for Solutions of Solids in Liquids

Raoult’s law in its general form can be stated as,

For any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.

If component 1 is the solvent then,

Since the other component is solid p2 = 0

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Ideal solutions

The solutions which satisfy the following conditions called ideal solutions.

  1. Solution must obey Raoult‟s law, i.e.,

      p1 = po1 χ1 and p2 = po2 χ2


  2. ΔmixH = 0 (No energy evolved or absorbed)

  3. ΔmixV = 0 (No expansion or contraction on mixing)

Some solutions behave like nearly ideal solutions are,

Non-ideal solutions

Those solutions which show deviation from Raoult’s law, are called non-ideal solution.

For such solutions, ΔmixH ≠ 0 and ΔmixV ≠ 0

The vapour pressure of such a solution is either higher or lower than that predicted by Raoult’s law.

If it is higher, the solution exhibits positive deviation if it is lower, it exhibits negative deviation from Raoult’s law.

Non-ideal solutions showing positive deviation

In such a case, the A – B interactions are weaker than A – A or B – B interactions and the observed vapour pressure of each component and the total vapour pressure are greater than that predicted by Raoult‟s law.

For such solutions

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Examples

Explanation

Non-ideal solution showing negative deviation

In such a case, the A – B interactions are stronger than A – A or B – B interactions and the observed vapour pressure of each component and the total vapour pressure are lesser than that predicted by Raoult’s law.

For such solutions

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Examples

Explanation

Azeotropic mixture

The binary mixtures which are having the same composition in liquid and vapour phase and boil at a constant temperature are called Azeotropic mixtures.

In such cases, it is not possible to separate the components by fractional distillation.

  1. Minimum boiling azeotropes are formed by those liquid pairs which show large positive deviation from ideal behaviour. Such azeotropes have boiling points lower than either of the components, e.g., C2H5OH (95.57%) + H2O (4.43%) by mass.

  2. Maximum boiling azeotropes are formed by those liquid pairs; which show negative deviation from ideal behaviour. Such azeotropes have boiling points higher than either of the components. e.g., H2O (20.22%) + HCl (79.78%) and HNO3 (68%) + H2O (32%) by mass.

Colligative properties

(colligative: Latin - co means together, ligare means to bind)

Colligative properties are those properties of solution which depend only on the number of solute particles in a solution irrespective of their nature.

Explanation

The vapour pressure of solution decreases when a non-volatile solute is added to a volatile solvent.

We know that evaporation is a surface phenomenon. The fraction of molecules changing from liquid phase to gaseous phase depends on the number of molecules of the solvent at the surface.

When a non-volatile solid is added to a solvent, the concentration of solvent molecules, at the surface, decreases. As a result, the number of molecules changing from liquid phase to gas phase decreases and vapour pressure decreases.

Some of the important colligative properties of solutions

  1. Relative lowering of vapour pressure of the solvent

  2. Depression of freezing point of the solvent

  3. Elevation of boiling point of the solvent and

  4. Osmotic pressure of the solution.

Relative lowering of vapour pressure

It is the ratio of lowering in vapour pressure to vapour pressure of pure solvent. The relative lowering in vapour pressure of solution containing a nonvolatile solute is equal to the mole fraction of solute in the solution.

For a solute (2) in solvent (1), we have,

Hence

 p1o - p1p1o = χ2=n2n1+n2

For dilute solutions n2 << n1

Therefore,

p1o - p1p1o= n2n1

Or,

p1o - p1p1o= W2×M1W1×M2

Where, W2 and W1 = mass of solute and solvent respectively. M2 and M1 = molecular weight of solute and solvent respectively.

 M2= W2×M1W1×p1op1o - p1

From the above expression we can find the molecular weight of an unknown solute dissolved in a given solvent.

Elevation in boiling point (ΔTb)

Boiling point of a liquid is the temperature at which its vapour pressure becomes equal to the atmospheric pressure. As the vapour pressure of a solution containing a nonvolatile solute is lower than that of the pure solvent, its boiling point will be higher than that of the pure solvent.

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The increase in boiling point is known as elevation in boiling point and is given by,

It has been found experimentally that for dilute solutions the elevation of boiling point (ΔTb) is directly proportional to the molal concentration of the solute in a solution.

where; m = molality of the solution.

Kb is called the molal elevation constant or ebullioscopic constant. The unit of Kb is K kg mol-1

Calculation of Molecular Mass of Solute

If W2 gram of solute of molar mass M2 is dissolved in W1 gram of solvent, then molality, m of the solution is given by

m=W2/M2W1/1000=W2×1000M2×W1 

So,  ΔTb = Kbm=Kb×W2×1000M2×W1

Or,  M2 =Kb×W2×1000ΔTb×W1

For water, Kb = 0.52 K kg mol-1

Depression in Freezing Point (ΔTf)

Freezing point of a liquid is the temperature at which vapour pressure of the solvent in its liquid and solid phase become equal. As the vapour pressure of solution containing non-volatile solute is lower than that of pure solvent, solid form gets separated out at a lower temperature.

This decrease in freezing point of a liquid is known as depression in freezing point.

Kf is called the molal depression constant or Cryoscopic Constant constant. The unit of Kf is K kg mol-1

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Calculation of molecular mass using depression in freezing point

m=W2/M2W1/1000=W2×1000M2×W1 

So,  ΔTf = Kf m=Kf×W2×1000M2×W1

Or,  M2 = Kf m=Kf×W2×1000ΔTf×W1

For water, Kf = 1.86 K kg mol-1

Kf=R×M1×Tf2ΔfusH×1000

Kb=R×M1×Tb2ΔvapH×1000

Where ΔfusH and ΔvapH are molar enthalpies of fusion and vapourisation of the solvent, respectively.

Ethylene glycol is usually added to water in the radiator to lower its freezing point. It is called antifreeze solution.

[Common salt (NaCl) and anhydrous CaCl2 are used to clear snow on the roads because they depress the freezing point of water.]

Osmotic pressure (π)

Osmosis is the phenomenon of spontaneous flow of the solvent molecules through a semipermeable membrane from pure solvent to solution or from a dilute solution to concentrated solution.

Some natural semipermeable membranes are animal bladder, cell membrane etc. Cu2[Fe(CN)6] is an artificial semipermeable membrane which does not work in non-aqueous solutions as it dissolves in them.

Osmosis may be

  1. Exosmosis - outward flow of water or solvent from a through semipermeable membrane.

  2. Endosmosis - inward flow of water or solvent from a through a semipermeable membrane.

The hydrostatic pressure developed on the solution which just prevents the osmosis of pure solvent into the solution through a semipermeable membrane is called osmotic pressure.

For dilute solutions, it has been found experimentally that osmotic pressure is proportional to the molarity, C of the solution at a given temperature T. Or,

Here π is the osmotic pressure and R is the gas constant.

π = n2VR T 

Here V is volume of a solution in litres containing n2 moles of solute.

If W2 grams of solute, of molar mass, M2 is present in the solution, then

n2 =W2M2

Hence,

π = W2V×M2R T 

 M2=  W2R TπV

where R = gas constant, T = temperature

Note: Osmotic pressure method is the best method for determining the molecular masses of polymers since observed value of any other colligative property is too small to be measured with reasonable accuracy.

Types of solutions based on osmosis

On the basis of osmotic pressure, the solution can be

  1. Hypertonic solution

    A solution is called hypertonic if its osmotic pressure is higher than that of the solution from which it is separated by a semipermeable membrane.

    When a plant cell is placed in a hypertonic solution, the fluid from the plant cell comes out and cell shrinks, this phenomenon is called plasmolysis.

(ii) Hypotonic solution

A solution is called hypotonic if its osmotic pressure is lower than that of the solution from which it is separated by a semipermeable membrane.

(iii) Isotonic solution

Two solutions having same osmotic pressure at a given temperature are called isotonic solutions. These solutions have same molar concentration. 0.91% solution of pure NaCl is isotonic with human RBC‟s.

Isotonic solutions have same molar concentration, e.g., if x % solution of X is isotonic with y % solution of Y, this means molar concentration of X = Molar concentration of Y,

x100×1000Mx=y100×1000My

xMx= yMy

In case the solution is not dilute,

x/(1-x)Mx= y/(1-y)My

Reverse osmosis

When the external pressure applied on the solution is more than osmotic pressure, the solvent flows from the solution to the pure solvent, which is called reverse osmosis. Desalination of sea water is done by reverse Osmosis.

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Cellulose acetate is permeable to water but impermeable to impurities and ions present in sea water.

Abnormal molecular masses

When there is dissociation of solute into ions, the experimentally determined molar mass is always lower than the true value.

Similarly, using freezing point and boiling point method also, the experimentally determined molar mass is again lower than the true value.

van’t Hoff factor (i)

These observed values are corrected by multiplying the experimentally determined values by van‟t Hoff factor (i).

It is the ratio of observed value of colligative property to the calculated value of colligative property.

i =observed value of colligative propertycalculated value of colligative property

or

i =normal molecular massobserved molecular mass

or

i =number of particles afterassociation or dissociation  number of particles initially

So to correct the observed value of molar mass, van‟t Hoff factor (i) must be included in different expressions for colligative properties.

p1o - p1p1o = i χ2

Degree of dissociation (α) and van’t Hoff factor (i)

  1. If one molecule of a substance A gets dissociated into n particles or molecules

      A → nP

    And if α is the degree of dissociation then

      Total number of moles A P
      Initially 1 0
      At equilibrium 1 - α n α

    Therefore

    Total number of moles at equilibrium= 1  α + nα = 1+n-1α

    i =number of particles after association or dissociation  number of particles initially

    i =1+n-1α1

    or α =i-1n-1

Degree of association (α) and van’t Hoff factor (i)

If n molecules of a substance A associate to form An

A → Ann

And if α is the degree of association then

Therefore

Total number of moles at equilibrium=1-α+an

i =number of particles after association or dissociation  number of particles initially

i =1-α +α/n1

or α =i-11/n-1

Note: