solutions class 12

8/12/2019 Solutions class 12

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In this chapter we will study about:

a. Types of solutions

b. Units of concentrations of solutions

c. Solid solutions

d. Vapour pressure of liquidse. Raoults law

f. Relative lowering of vapour pressure

g. Ideal and non-ideal solutions

h. Azeotropic mixtures

i. Colligative properties

j. Elevation in boiling points

k. Depression in freezing points

l. Osmosis and osmotic pressure


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Solution is a single phase homogeneous system, containing two or more substances.The component of a solution forming the larger proportion is referred to as solvent;

while the other component which is present in minor proportion in solution is called

solute. The composition of the solution may vary within wide limits. Examples of

solutions are common salt in water, alcohol in water, sugar in water etc.

TYPES OF SOLUTIONS

Solutions may exist in any one of the three physical states solid, liquid or gaseous. Any

state of matter viz., gas, liquid or solid may act as a solute or a solvent. Depending upon

the physical state of solute and the solvent, there are nine types of solutions possible.

These are given in the table.

Solvent Solute Example

Gas Gas mixture of gases, air

Gas Liquid water vapours in air (humidity)

Gas Solid sublimation of solid (e.g., camphor) into a gas, dust or smoke

particles in air

Liquid Gas CO2 dissolved in water

Liquid Liquid Mixture of miscible liquids, i.e., alcohol in water.

Liquid solid salt in water, sugar in water

Solid Gas phenomenon of adsorption of gases over metals ; hydrogen over

palladium

Solid Liquid mercury in copper, mercury in gold

Solid solid homogeneous mixture of two or more metals (alloys , e.g., copper

in gold, zinc in copper), coloured stones, gems etc.

The most important types of solutions are those which are in the liquid phase and may

be categorised as:

1. Solid in liquid solutions

2. Gas in liquid solutions and

3. Liquid in liquid solutions

SOLID IN LIQUID SOLUTIONS

The solubility of a solid in a liquid at any temperature is defined as the maximum

amount of solid (solute) in grams which can dissolve in 100 g of the liquid (solvent) to

form the saturated solution at that temperature.

Factors that affect the solubility of a solid

I. Nature of the solute and the solventSolid dissolves in a liquid which is chemically similar to it. This is expressed by

saying 'like dissolves like''. This statement implies that ionic compounds dissolve

in polar solvents like water and are very little soluble or almost insoluble in non-

polar solvents like benzene, ether etc. Similarly non-polar compounds are soluble

in non-polar solvents like benzene, ether, carbon tetrachloride etc. and are very

little soluble in water.

Common salt (an ionic compound) is more soluble in water than sugar (a covalent

compound) . Their solubilities in water are 5.3 moles per litre and 3.8 moles perlitre respectively.


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Iodine (a covalent substance) is more soluble in alcohol or carbon tetrachloride

(covalent liquids) than in water.

The reason for the behaviour observed above may be explained as follows:

For ionic compounds being soluble in polar solvents, the solubility is on accountof the fact that there are strong electrostatic forces of attraction between the

ions of the crystal and the polar solvent molecules ; the negative ions being

attracted by the positive poles of the polar solvent molecules and positive ions by

the negative poles of the solvent molecules.

Thus, the water molecules pull the ions of the crystal apart and the electrostatic

forces of attraction existing between the ions of the crystal are cut off. Further,

the ions are surrounded by water molecules which act as an envelope around the

ions and prevent the recombination of the ions. The ions thus moving freely inthe solution are said to be hydrated. Energy is required for splitting of the ionic

compound into ions (called lattice energy) and energy is given out when ions get

hydrated (hydration energy). A substance dissolves if there is net evolution of

energy. Lowering of energy occurs if hydration energy is greater than the lattice

energy. For non-polar compounds being soluble in non-polar solvents, the

solubility is due to similar solute-solute, solute-solvent and solvent-solvent

interactions.

II. Temperaturevarious ionic substances are divided into following categories

a. Those whose solubility increases continuously with increase of temperature.

Most of the substances like NaNO3, NaCl, and KCl etc. fall into this category.

The reason for this behaviour is that in case of all such substances, the process

of dissolution is endothermic, i.e.,

Solute + Solvent Solution

Applying Le Chatelier's principle, as the temperature is increased, equilibrium

will shift in a direction in which the heat is absorbed i.e., in the forward dir;consequently more of the solute passes into the solution.

b. Those whose solubility decreases continuously with increase in temperature.

There are a few substances like ceric sulphate, lithium carbonate, sodium

carbonate monohydrate (Na2CO3 . H2O) etc. whose solubility decreases

with increase of temperature. Obviously it is due to the fact that the process

of dissolution of these substances is exothermic i.e., accompanied by

evolution of heat.

GAS IN LIQUID SOLUTIONS Henry's Law

Gases dissolve in liquids to form true solutions. Such solutions are examples of two

component systems. The solubility of a gas depends on:

(a) the temperature of the solution

(b) the pressure of the gas over the solution,

(c) the nature of the gas, and

(d) the nature of the solvent.

Substances which have similar chemical characteristics are readily soluble in each otherthan the substances which have different chemical characteristics.


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The solubility of different gases in the same solvent (say water) varies considerably. It

has been observed that gases like nitrogen , oxygen etc. dissolve to a small extent than

the gases like ammonia, sulphur dioxide , hydrogen chloride etc. The solubility of latter

gases with water to form ammonium hydroxide, sulphurous acid respectively.NH3 + H2O NH4

++ OH

SO3 + H2O H2SO3HCl + H2O H3O

++ Cl

The solubility of a gas is usually determined by measuring the volume rather than the

mass that dissolves. It is frequently expressed in terms of Busen absorption coefficient

() which is defined as the volume of the gas at STP (273 K and 1 atm pressure) dissolved

by unit volume of the solvent at the given temperature under a partial pressure of 1

atmosphere of the gas. If Vo is the volume of the gas that dissolves reduced to STP , V isthe volume of the solvent and p the partial pressure of the gas in atmosphere, then the

absorption coefficient , is given by :

= Vo / V p

Effect of temperature on solubility

Gases generally dissolve in a liquid with evolution of heat. Hence Le-Chatelier's principle

predicts that an increase in temperature result in a decrease in solubility of gas. It is for

this reason that gases are readily expelled from solutions on boiling. However, there are

certain gases such as hydrogen and inert gases in non-aqueous solvents where thesolubility increases with increase in temperature. At constant pressure variation of

solubility with temperature is given by: =

where S is the solubility in mol dm3

of the gas in the solvent and H is the enthalpy of

the solution. If H is regarded as temperature independent then integration of the

above equation within limits gives:

InS

S =

H

RT T ( T T

where S2 and S1 are the solubilities at T2 and T1 respectively.

Effect of pressure on solubility Henry's Law

Le Chatelier's principle predicts that the increase of pressure on solubility of a gas should

increase. Consider a system at equilibrium, containing a gas in contact with its solution

in a given solvent. On increasing the pressure, the volume of the gas will be reduced and

hence an increase in solubility will result from an increase of pressure.

William Henry in 1803 made a systematic investigation of the solubility of a gas in a

liquid and observed the following law known as Henry's law. The law states that themass of a gas dissolved by unit volume of a solvent at constant temperature is directly

proportional to the pressure of the gas with which it is in equilibrium. If X2 is the mole

fraction of the gas dissolved by unit volume of the solvent at equilibrium pressure P ,

then :

X2 P

or X2 = K'H P

P = KH X2 (i)

Where, KH is a proportionality constant known as Henry's law constant. The magnitudeof KH depends on the nature of the gas, solvent and units of pressure.


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Equation (i) is an equation of a straight line passing

through the origin. Thus a plot of solubility of the

gas against equilibrium pressure at a given

temperature gives a straight line passing throughthe origin. This shows the validity of Henry's law.

Different gases have different KH values at the same

temperature. This suggests that KH is a function of

the nature of gas. The following TABLE gives KHvalues of some common gases at specified

temperatures.

Values of Henry's Law constant (KH) for some selected gases in water

Gases Temperature (K) K H(bar)He 293 144.97

H2 293 69.16

N2 293 76.48

N2 303 88.84

O2 293 34.86

O2 393 46.82

It is obvious from equation (1) that higher the value of KH at a given pressure, lower is

the solubility of the gas in the liquid. It can be seen from the TABLE that KH value forboth N2 and O2 increases with increase of temperature indicating that solubility of gases

decreases with increase of temperature. It is due to this reason aquatic species are more

comfortable in cold waters than warm waters.

Applications of Henry's law

Henry's law finds several applications in industry and explains some biological

phenomena. Notable among these are:

1. To increase the solubility of CO2 in soft drinks and soda water, the bottle is sealed

under high pressure.2. To minimise the painful effects accompanying the decompression of deep sea

divers, oxygen diluted with less soluble helium gas is used as breathing gas.

3. In lungs where oxygen is present in air with high partial pressure, haemoglobin

combines with oxygen to form oxyhaemoglobin. In tissues where partial pressure

of oxygen is low, oxyhaemoglobin releases oxygen for utilization in cellular

activities.

Limitations of Henry's law

Henry's law is applicable only if the following conditions are satisfied.1. The pressure should be low and the temperature should be high i.e., the gas

should behave like an ideal gas.

2. The gas should not undergo compound formation with the solvent or association

or dissociation in the solvent.

For example, the law is not applicable in the case of dissolution of ammonia in

water, because it undergoes compound formation followed by dissociation.

NH3 (g) + H2O (l) NH4OH (aq)

NH4OH (aq) NH4+

(aq) + OH

(aq)similarly, the law is not applicable to the dissolution of HCl gas in water because it


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undergoes dissociation after dissolution.

HCl(g) + aq H+(aq) + Cl

(aq)

SOLUBILITY OF SOLIDS IN LIQUIDSThe solubility of solids in liquids varies greatly with the nature of the solid and liquid,

temperature and to a much lesser degree the pressure of the system. When a solid

(solute) is dissolved in a liquid solvent at a given temperature, the dissolution continues

until the solution attains a certain maximum concentration. The solution at this stage is

said to be saturated solution at that temperature. The maximum amount of solute that

can be dissolved by the solvent at a particular temperature is called its solubility.

Thus, solubility of a substance at a given temperature is defined as the amount of solid

that dissolves in 100 g of the solvent at a given temperature to form a saturatedsolution.

The solubility is also expressed as molar solubility which gives the molar concentration

of a substance in a saturated solution. For example, if the concentration of glucose in its

saturated solution at 20C is 6 mol L1

. Thus, the concentration of the solute has the

highest value in a saturated solution. In other words, a saturated solution represents the

limit of solute's solubility in a given quantity of solvent. The temperature has a marked

effect on the solubility of a solid in a solvent. The solubility may increase or decrease

with increase in temperature.Thus, in General:

a. If solute dissolves with absorption of heat (endothermic process), the solubility

increases with rise in temperature.

b. If the solute dissolves with evolution of heat (exothermic process), the solubility

decreases with rise in temperature.

However, for some substances the solubility behaviour is not regular. For example, the

solubility of sodium sulphate

(Na2SO4) increases up to a certain temperature and then decreases as temperature isfurther raised. The temperature corresponding to the break in solubility curve is known

as the transition temperature. For example, the solubility curve of sodium sulphate

shows a sharp break at 32.8C. This is due to change in one solid form into another solid

form. For example in the case of Na2SO4 10 H2O, at 32.8C, there is an equilibrium

between solid decahydrate Na2 SO4 10 H2O and anhydrous Na2SO4. Below this

temperature, only sodium sulphate decahydrate (Na2SO4 10 H2O) exists while above this

temperature, anhydrous sodium sulphate (Na2SO4) exists.

The effect of pressure on the solubility of solids in liquids is generally very small. Forexample, a change of 500 atm in pressure increases the solubility of sodium chloride in

water only by 2.3%.

LIQUID IN LIQUID SOLUTIONS

When two liquids are mixed, the mixture may be of the following types:

1. The two components may be almost immiscible

In this case; one of the liquid is polar, while the other is non-polar nature. For

example benzene and water.


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2. The miscibility of the component may be partial

if the intermolecular attraction of one liquid is different from intermolecular

attraction of the other, there may be partial miscibility of the two liquids. For

example ether and water.3. The two components may be completely miscible

In this case, the liquids are of the same nature, i.e., they are either polar (like

alcohol and water) or non-polar (like benzene and hexane).

Cause of Miscibility of Liquids

Chemically alike substances dissolve in one another more freely as compared to others.

For example, alkanes are miscible in all proportions with one another. Alkanes however

are, not miscible with water because they cannot form H-bonds with water molecules.

1. Dipole-Dipole interactions also play an important role in forming liquid solutions.2. Molecular sizes of liquids which are mutually soluble are also approximately the

same.

UNITS OF CONCENTRATIONS OF SOLUTIONS

The concentration of a solution may be defined as the amount of solute present in the

given quantity of the solution. It is usually expressed in any one of the following ways.

Mass Percentage

The mass percentage of a component in a given solution is the mass of the componentin 100 g of the solution. If mA and mB are the masses of the two components A and B

respectively, in a binary solution, then:

Mass percentage of A =m 100

m m

Volume Percentage

Volume percentage is defined as the volume of the component per 100 parts by volume

of solution. If VA mL is the volume of one component A and VB mL is the volume of the

second component B, then:

Volume percentage of A =V 100

V V

Parts per million (ppm)

When a solute is present in very minute amounts, the concentration is expressed in

parts per million abbreviated as ppm. It is the parts of a component per million parts of a

solution. It is expressed as:

Parts per million =mass of solute 10

Mass of solution

This mode is generally used to express very low concentration such as hardness of water

or concentration of chlorine in public supply of potable water. The concentration of

atmospheric pollutants in cities is often expressed in terms of

mg mL1

.


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Molarity (M)

It is the number of moles of the solute dissolved per litre of the solution. If n B moles of

solute are present in V litres of solution, then:

Molarity = nV

= number of moles of solutevolume in litres of solution

= ( )

( )

A solution having molarity one is called molar solution. Such a solution contains

one mole of solute per litre of solution.

Molarity is expressed in mole dm3

.

Molarity of a solution changes with change in temperature.

Molality (m)

It is the number of moles of the solute dissolved per 1000 g (= 1 kg) of the solvent.

Molality(m)=number of moles of solute

weight of solvent in kg

=number of moles of solute x 1000

weight of solvent in gm

If nB is the number of moles of solute and WA is the weight of the solvent in grams, then

molality of the solution is:

( )=1000

A solution containing one mole of solute per 1000 g of solvent has molality equal

to one is called a molal solution.

Molality is expressed in units of moles per kilogram ( mol kg1

).

Molality is considered better for expressing the concentration as compared to

molarity because the molarity changes with temperature because of expansionor contraction of the liquid with temperature. However, molality does not change

with temperature because mass of the solvent does not change with change in

temperature.

Normality (N)

It is the number of gram equivalents of the solute dissolved per litre of solution.

( )=

A solution having normality equal to one is called a normal solution. Such asolution contains one gram equivalent of solute per litre of solution.

A decinormal solution contains 0.1 g equivalents of solute per litre of solution.

A seminormal solution contains g equivalents per litre.

A centinormal solution contains 0.01 g equivalents per litre.

Relationship between Normality and Molarity of solution

The molarity and normality of the solution are related as:

=


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For acids, Normality = Molarity x Basicity of acid

Basicity is the number of H+

ions furnished by each molecule of acid in aqueous

solutions.

For bases, Normality = Molarity Acidity of a base. Acidity is the number of OH

ions furnished by each molecule of base in solutions.

Mole fraction (X)

Mole fraction of any component in a solution is the ratio of the number of moles of that

component to total number of moles of solute plus solvent in solution.

Let us suppose that a solution contains n A moles of solvent and n B moles of solute:

=+

=+

The sum of the mole fractions must be equal to 1 i.e.,

+ =+

++

= 1

Thus, if the mole fraction of one component is known, that of the other can be

calculated. For example,

XA = 1 XBor XB = 1 XA

Formality (F)

Formality of a solution may be defined as the number of gram formula masses of ionic

solute dissolved per litre of the solution.

( )=

Formality is used to express the concentration of the ionic solids which do not

exist as molecules but exist as network of ions.

A solution containing one gram formula mass of the solute per litre of solution

has formality equal to one and is called formal solution.

Formality of a solution changes with change in temperature.

SOLID SOLUTIONS

Solid solutions are formed by mixing two solid components. Solid solutions are of two

types: substitutional solid solutions and interstitial solid solutions. In substitutional solid

solutions, atoms, molecules or ions one substance takes the place of similar species of

other substance in its crystal lattice.

(a) Substitutional solid solution in which particles of the solute replace particles in the

host lattice (solvent). Brass, bronze, Monel metal and steel are familiar examples of this

type of solid solution.

Interstitial solid solutions constitute the other type and are formed by placing atoms of

one kind into voids or interstices that exist between atoms in the host lattice.

(b) Interstitial solid solution in which the solute particles fit in spaces between particles of

the host lattice (the solvent)

Tungsten carbide WC, an extremely hard substance, is an example of interstitial solidsolution. Here tungsten atoms are arranged in a face-centred cubic pattern with carbon


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atoms surrounded by six tungsten atoms at the vertices of an octahedron. Tungsten

carbide has many industrial uses in making of cutting and grinding tools.

VAPOUR PRESSURE OF LIQUIDSWhen a liquid is kept in an open vessel, its fastest moving molecules escape into the free

space as gas or vapour. This process in which liquids automatically evaporate is known

as evaporation. If the liquid is in the open vessel, evaporation continues, till the entire

liquid changes into vapour form. If the liquid is kept in a closed vessel, evaporation

starts. However, some of the vaporised molecules possessing low energies, are likely to

be attracted on striking the surface of the liquid. This process of conversion of vapour

molecules into liquid phase is known as 'condensation of vapour''. Thus in a closed

vessel, two opposing processes of evaporation and condensation take placesimultaneously, till a state of dynamic equilibrium is attained. At this point, the relative

amounts of the liquid and the vapour become constant, the molecules in the vapour

phase exerts pressure, called equilibrium vapour pressure or simply vapour pressure.

Thus, vapour pressure of a liquid at a given temperature is defined as the pressure of the

vapour in equilibrium with the liquid at that temperature. The vapour pressure of a liquid

may be determined by using static method (Fig) in which the liquid is caused to

evaporate in vacuum and the depression of mercury column, at equilibrium state, is

noted as vapour pressure.Every pure liquid exerts a vapour pressure in the space above it The vapour pressure of a

liquid depends on:

Nature of liquid: Liquids, which have weak intermolecular forces are volatile and

have greater vapour pressure.

For example, dimethyl ether has greater vapour pressure than ethyl alcohol.

Temperature: Vapour pressure increases with increase in temperature. This is due

to the reason that with increase in temperature more molecules of the liquid can

go into vapour phase.

Lowering of Vapour pressure

Consider the addition of a small amount of a non-volatile solute to the liquid (solvent) to

form a solution. In such a case the vapour pressure of the solution is because of solvent,

as solute is non-volatile. It is found that the vapour pressure of the solution is less than

that of pure solvent.

Explanation: The lowering of vapour pressure can be explained on the basis of the

surface area of the liquid from which evaporation occurs. In the case of solution, a partof the liquid surface is occupied by solute particles; therefore evaporation of liquid will

take place from a lesser surface area. In other words, the particles

(or molecules) of the liquid will now have a less tendency to change into vapours. This

will, therefore, result in lowering of vapour pressure.

RAOULT'S LAW

Raoult carried out a series of experiments to study the vapour pressure of a number of

binary solutions. On the basis of the results of experiments, he proposed ageneralisation called Raoult's law, which states that: the vapour pressure of a solution


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containing non-volatile solute is directly proportional to the mole fraction of the solvent.

In case of solution containing two components A (volatile solvent) and B (non-volatile

solute) , the vapour pressure of the solution is given by :

Vapour pressure of solution Vapour pressure of solvent in solution PA Mole fraction of solvent XA

PA XAPA = k XA

where k is a proportionality constant. For pure liquids, XA= 1; then k becomes equal to

the vapour pressure of the pure solvent which is denoted by Po

A . Thus,

PA = Po

A XAPsolution = Ppure solvent mole fraction of solvent

In a solution of two miscible volatile liquids A and B, the partial vapour pressure PA of aliquid is proportional to its mole fraction XA and the partial vapour pressure PB of liquid B

is proportional to its mole fraction XB . Thus,

PA XAPA = P

oA XA

Also,

PB= Po

B XBWhere, P

oA and P

oB are the vapour pressures of pure

components A and B respectively. The relationship iscalled Raoult's

Law. It states that for a solution of two or more miscible

volatile liquids, the partial vapour pressure of each

component of the solution at a particular temperature is

directly proportional to its mole fraction.

According to Raoult's law a plot of PA against XA should

give a straight line passing through

Po

A when XA = 1 (shown by broken lines I in Fig )Similarly , a plot of PB against XB is a straight line passing

through Po

B when XB = 1

( broken line II in Fig ). The total vapour pressure, P

exerted by the solution is the sum of

PA and PB as required by Daltons Law of partial pressures.

P = PA + PAor P = P

oA XA + P

oBXB

= P

o

A(1 XB) + P

o

BXB ( Since XA + XB = 1 )= P

oA P

oA XB + P

oB XB

= (Po

B Po

A)XB + Po

A .. (1)

Similarly, by putting XB = 1 XA , we can arrive at the following relation :

P = (Po

A - Po

B)XA + Po

B . (2)

Since Po

A and Po

B are constants at a particular temperature, therefore equations (1) and

(2) reveal that the total pressure P is linear function of XB ( or XA ) . This means that a plot

of P vs XB or P vs XB should be a straight line. The variation of

P with mole fraction is given by the solid line III in the graph.The solutions which obey Raoult's law are called ideal solutions. For such solutions, the


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vapour pressure of the solution always lies between the vapour pressures of the pure

components.

RELATIVE LOWERING OF VAPOUR PRESSUREWhen a non-volatile solute is added to a solvent, the vapour pressure of the solution

decreases. Let XA be the mole fraction of the solvent, XB the mole fraction of the solute

and Po

A be the vapour pressure of the pure solvent and P be the vapour pressure of

solution. Since the solute is non-volatile, there will be no contribution of solute to the

vapour pressure and the vapour pressure of the solution will be only due to the solvent.

Therefore, in such cases, the vapour pressure of the solution (P) will be equal to the

vapour pressure of the solvent (PA), over the solution, i.e., P = PA

But according to Raoult's law, the vapour pressure of the solvent is given as:PA = P

oA XA

or P = PA = Po

A XA . (1)

Since XA is always less than one, the vapour pressure of the solution is always less than

Po

A , i.e., vapour pressure of the pure solvent.

But for a binary solution,

XA + XB = 1 or XA = 1 XBSubstituting in equation (1) we get:

PA = Po

A (1 XB)= P

oA P

oA XB

Po

A - PA = Po

A XB

Here Po

A PA (difference in vapour pressure of pure solvent and solution) represents the

lowering in vapour pressure on the formation of a solution. Now, by dividing the

lowering in vapour pressure with the vapour pressure of pure solvent, i.e., (Po

A PA ) /P

oA , we get the relative lowering in vapour pressure. This is also an alternate statement

of Raoult's law. Thus, the Raoult's law in its modified form may be sated as:

The relative lowering of vapour pressure of a solution containing a non-volatile solute is

equal to the mole fraction of the solute in solution.

According to equation (3) , the relative lowering in vapour pressure depends only on the

molar concentration of the solute (mole fraction ) and is independent of its nature.

Therefore, relative lowering of vapour pressure is a colligative property.

IDEAL AND NON-IDEAL SOLUTIONS

The binary solutions may be of two types:

1. Ideal solutions

2. Non-ideal solutions

Ideal Solutions

An ideal solution may be defined as the solution which obeys Raoult's law over the

entire range of concentration and temperature and during the formation of which no

change in enthalpy and no change in volume takes place.


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The condition for the formation of ideal solution are:

It should obey Raoult's law , i.e.,

PA = Po

A XA and PB = Po

B XB Hmixing = 0 Vmixing= 0

There is no solution which behaves strictly as an ideal solution. However, the solutions in

which solvent-solvent and solute-solute interactions are almost the same type as

solvent-solute interactions behave nearly as ideal solutions. This type of solutions are

possible if molecules of solute and solvent are almost of the same size and have identical

polarity. For example, solutions of following pairs almost behave as ideal solutions.

1. n-Heptane and n-hexane

2. Chlorobenzene and bromobenzene3. Ethyl bromide and ethyl iodide

4. Carbon tetrachloride and silicon tetrachloride.

In such solutions, the interactions between molecules remain almost of the same type

before and after mixing, therefore such solutions are not accompanied by any change in

enthalpy or volume, i.e., Hmixing = 0 and Vmixing= 0. For such solutions, the vapour

pressure of the solution is always intermediate between the vapour pressures of pure

components A and B, i.e., Po

A and Po

B .It may be noted that although most of the

solutions show deviation from ideal behaviour, yet they behave as ideal solutions whenthe concentration of the solution is very low. In other words, most of the dilute solutions

behave as ideal solutions.

Non-Ideal Solutions

The solutions which do not obey Raoult's law are called non-ideal solutions. Therefore

for such solutions:

PA Po

A XA and PB Po

B XBIn non-ideal solutions, there is a noticeable change in the volume and heat energy when

the two components are mixed. Most of the real solutions are non-ideal because theydeviate from ideal behaviour to more or less extent. Thus for

non-ideal solutions:

i) PA Po

A XA and PB Po

B XB i.e., none of the components obey Raoult's law.

ii) Hmixing 0

iii) Vmixing 0

The non-ideal solutions are classified into two types:

1. Solutions showing positive deviations.

2. Solutions showing negative deviations.Non-ideal Solutions showing Positive deviations

Consider binary solutions of two components A and B. If

A B interactions in the solution are weaker than A A

and

B B interactions in the two liquids forming the solution,

then the escaping tendency of A and B types of

molecules from the solution becomes more than from

the pure liquids. As a result, each component of thesolution has a partial vapour pressure greater than


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expected on the basis of Raoult's law. The total vapour pressure will be greater than the

corresponding vapour pressure expected in the case of ideal solution of the same

composition. The boiling points of such solutions are lowered. This type of behaviour of

solution is described as positive deviation from Raoul's law. Mathematically, it may berepresented as:

PA> Po

A XA and PB> Po

B XBThe positive deviations have been shown in Fig in which dotted lines show the ideal

behaviour upon mixing, while, the thick lines exhibit the actual behaviour.

A few examples of solution showing positive deviations are:

1. cyclohexane and ethyl alcohol

2. carbon disulphide and acetone

3. acetone and benzene4. chloroform and carbon tetrachloride

For solutions with positive deviations, there is an intermediate composition for which

the vapour pressure of the solution is maximum and the boiling point is minimum. At

this composition, the solution distils at constant temperature without change in

composition. A solution which distils without change in composition at a particular

temperature is called azeotrope or azeotropic mixture. The azeotrope in solutions with

positive deviations is called minimum boiling azeotropes.

Explanation for positive deviationsConsider a solution of ethyl alcohol and cyclohexane. In alcohol, the molecules are held

together due to hydrogen bonding as shown below:

When cyclohexane is added to ethyl alcohol, the

molecules of cyclohexane tend to occupy the spaces

between ethyl alcohol molecules. Consequently some

hydrogen bonds in alcohol molecules break and the

attractive forces in alcohol molecules are weakened.

For such solutions, there is an increase in volume i.e.,Vmixing is positive and there is also absorption of certain amount of energy to overcome

the hydrogen bonding i.e., Hmixing is positive. There is also a slight increase in vapour

pressure on mixing.

NON-IDEAL SOLUTIONS SHOWING NEGATIVE DEVIATIONS

In such deviations, the A B interactions are stronger than A A and B B interactions

in the two liquids forming the solution Due to stronger A B interactions, the escaping

tendency of A and B types of molecules from the solution becomes less than from pureliquids. Consequently, each component of the solution has a partial vapour pressure less

than expected on the basis ofRaoult's law. As a result, the total vapour pressure

becomes less than the corresponding vapour pressure expected in the case of ideal

solution. The solutions are said to have negative deviations from Raoult's law as:

PA< Po

A XA and PB< Po

B XBThe negative deviations have been shown in Fig 9 in which dotted lines show the ideal

behaviour upon mixing, while the thick lines show the actual behaviour. A few solutions

showing negative deviations are:1. Acetone and chloroform


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2. Chloroform and nitric acid

3. Chloroform and benzene

For solutions with negative deviations, there is an

intermediate composition for which vapour pressure ofthe solution is minimum and hence boiling point is

maximum. At this composition, the solution distils at

constant temperature without change in composition. So

it is an azeotrope. The azeotrope in solutions with

negative deviation is called maximum boiling azeotrope.

Explanation for negative deviations

Consider a solution of acetone and chloroform. When

acetone and chloroform are mixed, there are newattractive forces due to intermolecular hydrogen bonding.

Thus the attractive forces become stronger and the escaping tendency of each liquid

from the solution decreases.

For such solutions, there is a decrease in volume upon mixing, i.e., Vmixing is also

negative and due to the energy released on account of hydrogen bonding Hmixing is also

negative. The vapour pressure of the solution is also less than what is expected for an

ideal solution.

Examples for non-ideal solutions showing positive and negative deviations are given in

the following TABLE.

Solutions showing positive

deviations

Solutions showing negative

deviations

CH3COCH3 + CS2 CH3COOH + C5H5N

(CH3)2CO + C2H5OH CHCl3 + (CH3)2CO

C6H6 + (CH3)2CO CHCl3 + C6H6CCl4 + CHCl3 CHCl3 + (C2H5)2O

CCl4+ C6H5CH3 H2O + HClH2O + C2H5OH H2O + HNO3CH3CHO + CS2 (CH3)2CO + C6H5NH2

AZEOTROPIC MIXTURES

When a binary solution of volatile liquids is boiled, its vapours, in general do not have

the same composition of the components as that in solution. The mole fraction of the

more volatile component is higher in vapours. This forms the basis of fractionaldistillation. But many binary solutions at definite compositions behave like pure liquids


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because their vapours have same composition of the two components as in solution.

Such solutions are called azeotropic mixtures or azeotropes. Thus azeotropes are

defined as the mixture of liquids which boil at constant temperature like pure liquid and

possess same composition of components in liquid as well as in vapour phase.Azeotropes are called constant boiling mixtures because whole of the azeotrope

changes into vapour state at constant temperature and their components cannot be

separated by fractional distillation. Azeotropes are of two types:

1. Minimum boiling azeotropes

2. Maximum boiling azeotropes

Minimum boiling azeotropes

These azeotropes are formed by those liquid pairs which show positive deviation from

ideal behaviour. Such azeotropes have boiling points lower than either of thecomponents. Some examples are given below :

Components mass %

of B

Boiling point (K)

A B B A B zeotrope

H2O C2H5 OH 95.57 373 351.3 351.1

H 2O C3H7 OH 71.67 373 370 350.72

CHCl3 C2H5 OH 67 334 351.3 312.2

(CH3)2CO CS2 6.8 329.3 320 312.2

Maximum boiling azeotropes

Azeotropes are formed by those liquids which show negative deviation from ideal

behaviour. Such azeotropes have boiling points higher than either of the components.

Some examples are given below :

Components mass % of B Boiling point (K)

A B B A B zeotrope

H2 O HCl 20.3 373 188 383H2O HNO3 58.0 373 359 393.5

H2O HClO4 71.6 373 383 476

Note

Mole fraction of a component in vapour phase may be calculated as:

=

Mole fraction of compound B in vapour phase=

COLLIGATIVE PROPERTIES

The dilute solutions of non-volatile solutes exhibit certain characteristic properties

which do not depend upon the nature of the solute but depend only on the number of

particles (molecules or ions) furnished by the solute, i.e., on the molar concentration ofthe solute. These are called colligative properties. The properties of a solution which


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depend only on the number of solute particles but not on the nature of the solute are

called colligative properties. Some of the colligative properties are :

1. Relative lowering of vapour pressure

2. Elevation of boiling point3. Depression of freezing point

4. Osmotic pressure

Relative Lowering of Vapour Pressure

When a non-volatile solute is added to a solvent, the vapour pressure of the solution

decreases. Let XA be the mole fraction of the solvent A , XB the mole fraction of the

solute B and Po

A be the vapour pressure of the pure solvent and

P be the vapour pressure of solution.

Since the solute is non-volatile, there will be no contribution of solute to the vapourpressure and the vapour pressure of the solution will only be due to the solvent.

Therefore, in such cases, the vapour pressure of the solution (P) will be equal to the

vapour pressure of the solvent (PA) , over the solution, i.e.,

P = PABut according to Raoult's law, the vapour pressure of the solvent is given as :

PA = Po

A XAor P = PA = P

oA XA (1)

Since XA is always less than one, the vapour pressure of the solution is always less thanP

oA i.e., vapour pressure of the pure solvent. But for a binary solution :

XA + XB = 1 or XA = 1 XBSubstituting in equation (1) we get :

PA = Po

A (1 XB)

PA = Po

A Po

A XBP

oA PA = P

oA XB

or,

Hence Po

A PA (difference in vapour pressure of pure solvent and solution) represents

the lowering of vapour pressure on the formation of a solution. Now by dividing the

lowering in vapour pressure with vapour pressure of pure solvent,

i.e., (Po

A PA ) / Po

A , we get the relative lowering in vapour pressure. This is also an

alternate statement of

Raoults law. Thus, the Raoult's law in its modified form may be stated as:Relative lowering in vapour pressure of an ideal solution (dilute solution) is equal to the

mole fraction of the solute at a given temperature. According to Equation (3), the

relative lowering in vapour pressure depends only on the molar concentration of the

solute (mole fraction) and is independent of its nature. Therefore, relative lowering of

vapour pressure is a colligative property.

Calculation of Molecular mass from Relative Lowering of Vapour pressure

Molecular mass of non-volatile substance can be determined from relative lowering ofvapour pressure. A known mass


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(WB) of the solute is dissolved in a known mass of the solvent (W A ) , to prepare a dilute

solution and relative lowering of vapour pressure is determined experimentally.

Knowing the molecular mass of the solvent (MA ), the molecular mass of solute (MB) can

be determined as shown under :

Relative lowering of vapour pressure is given by :

For dilute solutions, WB/ MB


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non-volatile solute with solvent respectively. It is evident from the plot that at each

temperature the vapour pressure of the solution is lower than that of the pure solvent

and thus the vapour pressure curve for the solution runs below that of the pure solvent.

At temperature To , the vapour pressure of the pure solvent becomes equal to theatmospheric pressure and thus , To is the boiling point of the pure solvent. The vapour

pressure of the solution at To is much less than the atmospheric pressure and therefore ,

it is necessary to heat the solution to a higher temperature, T1 , in order that its vapour

pressure becomes equal to the atmospheric pressure. Thus T1 is the boiling point of the

solution. Thus it is clear that the solution boils at a higher temperature than the pure

solvent. Evidently, (T1 To) or (Tb) is the elevation in boiling point. Since its magnitude is

determined by the vapour pressure lowering, the elevation in boiling point is also

proportional to the solute concentration. Thus,Tb P XB

For dilute solutions, WB/ MB


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relation:

Where MA = Molecular mass of the solvent ,

R = Universal gas constant

Tb = Boiling point of pure solvent

Hvap= Enthalpy of vaporisation of solvent.

The Molal Elevation constant Kb for different solvents are given in the following TABLE.

Solvent Boilig point (K) Kb (K kg mol1

)

Water 373 0.52

Carbontetrachloride 353.3 2.53Carbon disulphide 319.4 2.34

Chloroform 334.4 3.63

Ethyl alcohol 351.5 1.20

Ether 307.8 2.02

cetic acid 391.3 3.07

Camphor 481.3 5.95

Nitrobenzene 483.8 5.24

Calculation of Molecular mass of an unknown solute from Elevation in Boiling point

To calculate the molecular mass of an unknown non-volatile compound, a known mass

(say WB g) of it is dissolved in a known mass (say WA g) of some suitable solvent and

elevation in boiling point (Tb) is determined. Let MB be the molecular mass of the

compound. Then:

Knowing Kb, WB, WA and Tb the molecular mass of the compound can be calculated

from the above relation.

The method of determining molecular mass by the study of elevation in boiling point is

known as Ebullioscopic method.

DEPRESSION IN FREEZING POINT

Freezing point is the temperature at which the solid

and the liquid states of the substance have the same

vapour pressure. It has been found that when a non-

volatile solute is added to a solvent, the

freezingpoint of the solution is always lower than

that of the pure solvent. This is illustrated in Fig. In

the above Fig, the curve BC gives the vapour pressure


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of the pure solvent. We know that the addition of a non-volatile solute lowers the

vapour pressure and the curve AB gives the vapour pressure curve of the solution at

different temperatures. The curve AB corresponds to the vapour pressure of solid

solvent at different temperatures. The temperature corresponding to the point B, wherethe solid and liquid solvent meet

(i.e., solid and liquid states have the same vapour pressure) represents the freezing

point temperature of pure solvent (To). The temperature corresponding to the point A'

where the solid solvent and liquid solution meet (i.e., solid and liquid states have the

same vapour pressure) represents the freezing point temperature of the solution (T1).

Since T1 is less than To, this shows that the freezing point of the solution is less than that

of pure solvent and the depression in freezing point (Tf) is given as:

Tf= To T1It has been determined experimentally that the depression in freezing point of a solution

is proportional to the molal concentration of the solution, i.e.,

Tf m

or Tf= Kfm .. (5)

where Kf is the molal depression constant. It is also called molal cryoscopic constant. If

m = 1 ; Tf= Kf .

Thus Molal depression constant is defined as the depression in freezing point for 1 molal

solution, i.e., a solution containing 1 g mole of the solute dissolved in 1000 g of solvent.As Kf is constant; Tf m

Thus, the depression in freezing point temperature is directly proportional to the molal

concentration of the solute

(i.e., number of molecules) and therefore, it is a colligative property. Kf is related to the

molar enthalpy of fusion as :

where MA= Molecular mass of solvent

R = Universal gas constant

Tf= freezing point of the pure solvent

Hfusion= Enthalpy of fusion of the pure solvent.

The molal depression constants of some solvents are given in the following TABLE

Solvent Freezing point (K) Kf(K kg mol1

)

cetic acid 289.6 3.90

Benzene 278.6 5.12Camphor 452.0 39.7

Carbondisulphide 164.2 3.83

Carbon tetrachloride 250.5 31.8

Chloroform 209.6 4.70

Ether 156.9 1.79

Ethyl alcohol 155.7 1.99

Naphthalene 353.3 6.80

water 273.0 1.86Nitrobenzene 278.7 7.00


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DETERMINATION OF MOLECULAR MASS FROM DEPRESSION IN FREEZING POINT

To calculate the molecular mass of an unknown non-volatile compound, a known mass

(WB g) of it is dissolved in a known mass (say WA g) of some suitable solvent and

depression in freezing point ( Tf) is determined. Let MB be the molecular mass of thecompound. Then molality of the solution:

Knowing Kf , WB , WA and Tfthe molecular mass of the compound can be calculated

from the above relation.

Antifreeze Solutions

Water is used in radiators as cooling liquid. If the vehicle is to be used at high altitudes

where the temperature is

sub-zero, water would freeze in the radiators. To avoid the difficulty, a solution of

ethylene glycol in water is used in radiators. This solution has freezing point lower thanzero. Freezing point can be lowered to the desired extent by changing the

concentration.

Experimental Determination of Depression in Freezing Point

Depression in freezing point is measured by Beckmann method. A known weight of the

solvent is taken in a freezing point tube (Fig ).

It is cooled, with constant stirring to about 0.5 0 below its

freezing point (super cooling). Then on vigorous stirring, the

temperature of the solution rises to the freezing point, whichbecomes constant. The freezing point temperature is also

indicated by the appearance of crystals of the solvent. After re-

melting of the solvent, a known weight of the solute is added

and freezing point of the solution is determined. The difference

between the freezing point of the pure solvent and of the

solution gives the depression in freezing point. Knowing the

value of the mass of the solute, the mass of solvent, depression

in freezing point and molal depression constant for the solvent, we can calculate themolecular mass of the solute.

OSOMOSIS AND OSMOTIC PRESSURE

This was studied for the first time by Abbe Nollet in 1748. Let

us consider an aqueous solution of sugar placed in an

inverted thistle funnel having a semipermeable membrane

such as animal bladder or parchment paper, attached to its

bottom. The thistle funnel is lowered into a beakercontaining water. The membrane is such that it allows only


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the molecules of the solvent and not the solute to pass through it. Thus there will be

movement of water molecules through pure solvent(less concentrated) into solution

(more concentrated). As a result, water passes into the thistle funnel and level of

solution in the thistle funnel rises gradually (Fig) . This process is known as osmosis.Thus, the phenomenon of the flow of solvent through a semipermeable membrane from

pure solvent to the solution is called osmosis . Osmosis can take place between the

solutions of different concentrations. In such cases, the solvent molecules move from

the solution of low solute concentration to that of higher solute concentration.

The flow of the solvent through the semipermeable membrane will continue till the

equilibrium is reached when the hydrostatic pressure of the liquid column exactly

balances the tendency of water to pass inward through the semipermeable membrane.

The hydrostatic pressure set up as a result of osmosis is a measure of the osmoticpressure of the solution. Thus the osmotic pressure of a solution at a particular

temperature may be defined as the excess pressure that builds up when the solution is

separated from the solvent by a semipermeable membrane. It is denoted by .

The osmotic pressure can be defined in another way. In order

to understand this, let us consider the phenomenon of

osmosis in a special type of apparatus as shown in Fig. The

apparatus consists of a chamber divided into water-tight

compartments ( S and W) by semipermeable membrane andfitted with water-tight pistons. On putting the solution in

compartment S and water in compartment W, the piston P'

will be displaced upwards due to the movement of water

from W to S. To stop this movement of water, we have to

apply mechanical pressure on the solution side. The pressure

just sufficient to stop osmosis will be the osmotic pressure. Thus osmotic pressure may

be defined as the excess pressure on the solution side to prevent the passage of solvent

into it through a semipermeable membrane. If the pressure applied on the solution isgreater than the osmotic pressure, then the solvent starts passing from the solution into

solvent. This is called reverse osmosis. The phenomenon of reverse osmosis is generally

used for purification of sea water or hard water. Sea water which is a dilute solution of

many undesirable salts is placed in contact with pure water through a semipermeable

membrane. Pressure greater than osmotic pressure is applied on sea water. This causes

movement of pure water from sea water to pure water side.

Semipermeable Membrane

Semipermeable membrane is one which allows only the solvent to pass through it.Various substances which serve as semipermeable membranes are parchment paper,

animal membranes and cellophane. In nature, plant cells and cells in animal body are

surrounded by semipermeable walls. These are however very weak and or not perfectly

semipermeable.

In the laboratory, an artificial membrane of copper ferrocyanide is generally employed.

In order to make it strong enough to withstand very high pressures, copper ferrocyanide

is deposited in the walls of a porous pot as follows.

A porous pot thoroughly cleaned by washing it successively with acid solution, water,alkali and finally distilled water. After washing, it is soaked in distilled water for a few


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hours or distilled water is forced through its pores under pressure. This removes any air

present in its pores. The porous pot is filled with 2.5% solution of copper sulphate and

then placed in a trough containing 2.5% solution of potassium ferrocyanide. An electric

field is applied by dipping platinum electrodes inside and outside the porous pot. TheCu

2+and [Fe(CN)6]

4ions move towards the oppositely charged electrodes and form a

gelatinous deposit of copper ferrocyanide in the pores of the porous pot.

2 Cu2+

+ [Fe(CN)6]4

Cu2 [Fe(CN)6]

Importance of Osmosis

Osmosis is a process of prime importance in living organisms. The salt concentration in

blood plasma due to different species is equivalent to 0.9% of aqueous sodium chloride

has by mass. If blood cells are placed in pure water, water molecules rapidly move into

the cell. The movement of water molecules into the cell dilutes the salt content. Theblood cells as a result of this transfer of water molecules , swell and burst. Hence care is

always taken to ensure that solutions that flow into the blood stream are of the same

osmotic pressure as that of blood. Sodium ion Na+

and potassium ion K+

are responsible

for maintaining proper osmotic pressure balance inside and outside of the cells of

organism. Osmosis is also critically involved in the functioning of kidneys.

Isotonic Solutions

Two solutions having equal osmotic pressure are called isotonic solutions. A solution

having osmotic pressure greater than some other solution is said to be hypertonic withrespect to the other solution. A solution having lower osmotic pressure relative to some

other solution is called hypotonic. A 0.91% solution of sodium chloride solution often

called saline water is isotonic with human blood corpuscles. In this solution, the

corpuscles neither shrink nor swell. Consequently, medicines are mixed with saline

water before being injected into the veins.

LAWS OF OSMOTIC PRESSURE

van't Hoff showed the existence of a close analogy between gases and solutions. Heobserved that the osmotic pressure of a dilute solution was equal to the pressure which

the solute would have exerted as a gas at the same temperature of the solution and

occupied a volume equal to that of the solution. He established that a dilute solution

behaves like an ideal gas and the different gas laws are applicable to dilute solutions or

ideal solutions. Using the data on the study of osmotic pressure , van't Hoff put forward

the laws of osmotic pressure . They are :

1. van't Hoff -Boyle Law

It states that at constant temperature(T) , the osmotic pressure( p .) of a dilutesolution is directly proportional to the molar concentration of the solute ( C) , i.e.

C

2. van't Hoff - Charle's Law

It states that at constant concentration, the osmotic pressure () of a dilute

solution is proportional to the temperature in kelvin (T). i.e.,

T

Combining the two laws :

C T = R C T . (6)


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where R is a constant of proportionality known as van't Hoff constantfor

solutions or simply solution constant. But the molar concentration,

C = (n / V) , where n = number of moles of solute.

= (n R T) / Vor . V = n R T . (7)

Equation (7) is the van't Hoff equation for osmotic pressure of solutions. This

equation is similar to the general gas equation , PV = n R T

Osmotic Pressure - A Colligative Property

For a given solvent, the osmotic pressure depends only upon the molar concentration of

the solute but does not depend on its nature. Osmotic pressure is related to the number

of moles of the solute by the following relation :

Here, C = concentration of solution in moles per litre. R = gas constant , T = temperature

n = number of moles of solute V = volume of solution

Equation (8) is called van't Hoff equation .

DETERMINATION OF OSMOTIC PRESSURE - Berkley and Hartley's Method

The apparatus used (Fig ) consists of a

porous pot containing a deposit of copper

ferrocyanide in its walls to act as semi-

permeable membrane. It is fitted into a

gun metal container (outer vessel), which

is provided with a piston and a pressure

gauge. The porous pot is then fitted witha capillary indicator tube on one side and

a solvent reservoir on the other side. The

solution, whose osmotic pressure is to be

measured , is taken in the metal container ; while the solvent is filled in the porous pot .

Solvent from the porous pot tends to move into the solution, through the

semipermeable membrane as a result of phenomenon of osmosis. This is indicated by

the fall in the level of solvent in the capillary tube. Then, suitable external pressure

(which is measured by pressure gauge) is applied on the piston so that the level of thesolvent in the capillary indicator tube remains stationary, i.e., does not rise or fall with

time. The applied pressure at the time of stationary level in the capillary indicator tube

directly gives the osmotic pressure of the solution.

Determination of molecular mass from Osmotic Pressure

According to van't Hoff equation :


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where nB is the number of moles of solute dissolved in V litres of solution.

By applying the above formula, the molecular mass of the solute can be calculated. This

method is especially suitable for the determination of molecular masses of

macromolecules such as proteins and polymers. This is due to the reason that for these

substances the values of other colligative properties such as elevation in boiling point or

depression in freezing point are too small to be measured. On the other hand, osmotic

pressure of such substances are measurable.For getting accurate value of molecular masses

The solute must be non-volatile

The solution must be dilute

The solute should not undergo dissociation or association.

Biological Significance of osmosis

Osmosis plays a significant role in the absorption of water by the plants which is taken in

by the roots. The absorption of water by plants from the soil through the roots and its

movement to different parts of plants due to the process of osmosis. Plants and animalbodies are composed of very large number of cells. The cells contain a fluid (called cell

sap) and the walls of the cells are made up of living cytoplasmic membrane which acts as

a semi-permeable membrane. These membranes allow water to pass through but block

the passages of the enzymes and proteins that have been synthesised in the cell. The cell

saps have generally higher osmotic pressure and, therefore, when the cells come in

contact with water , there is tendency of water to enter into the cell due to osmosis.

Therefore, the osmosis process helps the plants to absorb soil water and push it up to

the stem and other parts of the plants and trees. Plants which grow in marshy lands

have more concentrated saps which develop an osmotic pressure of the order of twenty

five atmospheres. Thus, the plant may absorb excess of water from the soil which might

cause bursting of root hair. Ultimately the plant decays. The addition of fertiliser may

raise the osmotic pressure of the soil water. Consequently, the cell sap is not in a

position to absorb excessive water and the decay of the plant is thus, checked.

The use of salt and sugar as preservatives in pickles and jams has its basis in preventing

growth of fungi and bacteria by osmosis.

ABNORMAL MOLECULAR MASSES

In derivation of colligative properties , it has assumed that the molecular form of the

solute remains unchanged in solution. Furthermore if the solutions are dilute, they

behave ideally. In such cases experimental value of colligative property is in agreement

with theoretically calculated values. However, there are certain substances like solutions

of salts, acids or bases in water or acetic acid in benzene where experimental value

differs considerably from the calculated value. Such solutions are said to be abnormal

solutions. The abnormalities observed in such solutions are of two types :

1. Association of solute molecules

2. Dissociation of solute molecules.


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Association of solute molecules

Certain solutes in solution are found to associate. This

virtually leads to a decrease in the number of molecular

particles in solutions. Thus it results in a decrease in thevalues of colligative properties. The colligative properties are

inversely proportional to the molecular masses. Therefore

higher values are obtained for molecular masses than normal

values of un-associated molecules. For example, acetic acid

dissolved in benzene shows a molecular mass of 120 (normal

molecular mass = 60). Similarly, benzoic acid dissolved in

benzene shows a molecular mass of double of its normal molecular mass. This is

explained by the fact that both acetic acid and benzoic acid form dimers in solution dueto hydrogen bonding.

Dissociation of Solute molecules

A number of electrolytes dissociate in solution to give two or more particles (ions).

Therefore, the number of solute particles , in solutions of such substances , is more than

the expected value. Accordingly such solutions exhibit higher values of colligative

properties. Such colligative properties are inversely proportional to molecular masses,

therefore molecular masses of such substances are calculated from colligative

properties will be less than their normal values.For example, KCl dissociates into K

+and Cl

ions when dissolved in water. So the number

of solute particles in its solution would be double the number of particles if no

dissociation had taken place. Hence it is expected to have molecular mass (on the basis

of colligative properties) equal to half of its normal molecular mass, i.e., 74.5/2 = 37.25.

However, the molecular mass of KCl is found to be 40.3 by studies of depression in

freezing point. The difference in two values is due to the fact that there are strong

attractive forces present in the oppositely changed ions of the strong electrolyte in

solution. These electrical forces hold together a number of the ion pairs. Thus suchelectrolytes are completely dissociated and number of ions formed in solution is not

exactly the double but is somewhat less. Consequently, there is difference in the values

of the molecular masses.

Van't Hoff factor i'

In order to account for the abnormal behaviour of solutions in which solute undergoes

association or dissociation, van't Hoff introduced a correction factor i' which is called

van't Hoff factor and is defined as the ratio of the experimental value of colligative

property to the calculated value of property, i.e.,

Since the colligative property is proportional to the number of solute particles in

solution, hence :

or we may write :


28/29

where M is the molecular mass of the solute , Tb , Tf , P / Po

and are the boiling

point elevation, freezing point depression, relative lowering of vapour pressure and

osmotic pressure of the solution respectively. The subscripts obs' and cal'refer to

experimental and calculated values of the colligative properties.

Introduction of van't Hoff factor modifies the equation for the colligative properties as

follows:

Relative lowering of vapour pressure = (Po

PA) / Po

= iXBElevation in boiling point = Tb = iKb m

Depression in freezing point = Tf= iKfm

Osmotic pressure = = iC R T

From the values of i' it is possible to calculate the degree of dissociation or degree of

association of the substance in solution.

DEGREE OF DISSOCIATION

Consider an electrolyte AxBy which partially dissociate in solution yielding x ions of A

y+

and y' ions of Bx

and is the degree of dissociation i.e., the fraction of the total number

of molecules which dissociates and C be initial concentration of the solute, then the

dissociation equilibrium in solution can be represented as :

The above equation is applicable to any colligative property and provides an important

method for calculating the degree of dissociation. If = 1 , i.e., the dissociation is

complete, i= x + y , the observed colligative property will be (x + y ) times the calculated

value. On the other hand , when no dissociation occurs = 0 and i= 1 ; the calculated

and observed values will be equal.Association of Solute

Consider the association of a solute A into its associated form (A)n according to the

relation :

n A (A)nwhere n ' is the number of solute which combine to form an associated species. IfC is

the initial concentration and the degree of association of the solute, then at

equilibrium the number of moles of the undissociated solute is C (1 ) and that of

associated solute is C ( / n) . The total number of moles in the solution is given by :


29/29

C (1 ) + C ( / n)

or C [(1 ) + / n ]

Hence van't Hoff factor :

If association is complete = 1 : i= 1/ n , the observed value of a colligative property willbe (1/n) times the calculated value and if = 0 ; no association occurs in solution , i.e., i

= 1 and observed and calculated values will be equal.

solutions class 12

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