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# CHEMISTRY FORM FIVE TOPIC 4: RELATIVE MOLECULAR MASSES IN SOLUTIONS What is a solution homogeneous?

RELATIVE MOLECULAR MASSES IN SOLUTIONS:- A solution is a uniform mixture of two or more substances.

The substance which are mixed to form solution are also termed as components

Example of solution

##### The solution formed can be

i) Solution of liquid in liquid

ii) Solution of solid in liquid

iii) Solution of gas in liquid

iv) Solution of gas in gas

#### SOLUTION OF LIQUID IN LIQUID

This is the solution formed when two or more liquids are mixed to form a uniform homogeneous mixture.

When the solution of liquid in liquid is formed the liquids are to be miscible.

When the solution is formed the saturated vapour pressure depends on the composition of the components.

The composition of the components is also depends on the mole fraction of such component.

Example

What is mole fraction?

Mole fraction Is the ratio of number of a liquid to the total number of moles of all liquid present in the container.

Consider the solution formed by mixing liquid A and B

Then

Let : nA be number of moles of liquid A

nB be number of moles of liquid B

Total number of moles = nA + nB

nT = nA + nB

Then to get mole fraction:
ΧA = mole fraction of A
XB = mole fraction of B

When expressed in decimal

When expressed in percentage

The mole fraction can also be calculated interns of partial pressure ie If the liquid to be mixed are A and B

#### RAOULT’S LAW OF PARTIAL PRESSURE

The Raoult’s law of partial pressure states that

“The saturated vapour pressure of each component in a mixture is equal to the product of mole fraction of that component and its pure vapour pressure”

#### ASSUMPTIONS OF RAOULT’S LAW

For the Raoult’s law to be feasible the following assumptions are to be considered.

1. i) Intermolecular forces of attraction should be equal to the intermolecular forces of attraction.
2. ii) After mixing the component there must be no change in volume.

iii) There must be No change in temperature.

1. iv) The liquids must be miscible.
2. v) The liquid should not react.

CONCLUSION

The solutions that do obey all assumption of Raoult’s law are called IDEAL SOLUTION. While the liquid which deviate from the assumption of Raoult’s law are termed  as NON – IDEAL SOLUTION/REAL SOLUTION.

#### IDEAL SOLUTION

In an Ideal solution the cohesive forces between its molecules. In an ideal or perfect solution, the cohesive forces would be just the same as those existing in the separate components of the solution.

A solution made from A and B would only be ideal if the forces existing in the solutions of  A and B were just the same as those existing in pure A and pure B.

Ideal solutions are rare, but they are most likely same to occur with mixtures of two almost identical chemicals e.g. hexane and heptane. Most solutions deviate considerably from the ideal because the interactions within the solution are different from those in the pure liquids.

Ideal solution depends on:

1) Vapour pressure of Ideal solution

2) Boiling point of Ideal solution

#### 1. VAPOUR PRESSURE OF IDEAL SOLUTIONS OF TWO LIQUIDS

The vapour in equilibrium with a mixture of two liquids is a mixture of two vapours, and the total vapour pressure is the sum of the two partial vapour pressure. All three pressures vary with temperature and with the composition of the solution.

The  change with the composition for ideal solution at a fixed temperature, is describe by Raoult’s law (1886) which state that the partial vapour pressure of A in a solution, at a given temperature, is equal to the  vapour pressure of pure A, at the same temperature, multiplied by the mole fraction of A in the solution.

In an Ideal solution components A and B will have just the same tendency to pass into the vapour phase as they have in pure A and pure B because the internal forces within the pure liquids and the solution are like.

There will however  be relatively fewer particles of A in a solution containing both A and B than in a pure A, so that the partial vapour pressure of A above the solution might be expected, ideally to be proportional to the mole fraction of A in the solution. Similarly the partial vapour pressure of B above the solution would be proportional to the mole fraction of B.

The total vapour pressure above the solution would be equal to the sum of the partial vapour pressures of A and B.

This is illustrated in the figure below. The vapour pressure of pure B is 50 but it is only 25 when the mole fraction of B in a solution with A, is 0.5.

Similarly the vapour pressure of a pure A is 60, but only 30 at a mole fraction of 0.5. The total vapour pressure of a mixture of A and B at a mole fraction of 0.5 will therefore be 25 plus 30, i.e 35, Numerical result of this type are given only by ideal solutions eg. hexane and heptane or bromoethane and idoethane.

#### VAPOUR PRESSURE COMPOSITION DIAGRAM FOR NON – IDEAL SOLUTION

What is non ideal solution?

Non ideal solution is the solution which do not obey some or not all assumption of Raoult’s law

Non Ideal solution are of two types:

i) Positive deviation from Raoult’s law

ii) Negative deviation from Raoult’s law

##### i) POSITIVE DEVIATION FROM RAOULT’S LAW

The positive deviation is observed when the saturated vapour pressure of the solution is greater than the expected one (ideal).

This is due to the large number of molecules that escape from liquid phase to vapour phase.

The large number of molecules escape is due to the fact that intramolecualar forces of attraction is greater than intermolecular forces of attraction.

Vapour pressure composition diagram/positive deviation from Raoult’s law.

##### ii) NEGATIVE DEVIATION FROM RAOULT’S LAW

The negative deviation is observed when the saturated vapour pressure of the solution is less than the expected one (ideal)

This is due to the less number of molecules that escape from liquid phase to vapour phase

The small number of molecule that escaped is due to the fact that intermolecular forces of attraction is less than the intramolecular forces of attraction

Vapour pressure composition diagram/negative deviation from Raoult’s law

#### (2) BOILING POINT COMPOSITION DIAGRAM

The shape of the boiling point diagram depends on the nature and the degree of deviation from Raoult’s law of the two liquids concerned. There are three important type of diagram:

i) No maximum or minimum

This type corresponds with the vapour pressure composition diagrams. Any deviation from Raoult’s law is relatively small.

ii) A maximum boiling point

Corresponding with vapour pressure composition diagrams and a large negative deviation from Raoult’s law.

iii) A minimum boiling point

Corresponding with vapour pressure composition diagrams and a large positive deviation from Raoult’s law.

Boiling point composition diagrams with no maximum or minimum

Boiling point composition diagram with no maximum or minimum
A diagram of this type is given by methanol water mixtures. The liquid line shows the way in which boiling point of methanol water mixture varies with composition at fixed pressure.

For liquid mixture of any one composition the water vapour with which it is in equilibrium will be richer in the more volatile component i.e. in methanol. The liquid line has therefore an associated vapour line. The vapour pressure composition diagram corresponding with this Boiling point composition diagrams as shown above.

When a mixture of methanol and water containing 50 per cent of each is boiled, it will boil at temperature T. The vapour coming from it will have a composition represented by A, and on condensing, this liquid is boiled again, it will now boil at temperature t1, giving a vapour of a composition B, and this will condense into a liquid whose composition is also B.

By repeating this boiling condensing boiling point process, pure methanol could be obtained, but the method would be tedious, and the same result can be obtained in one operation by fractional distillation using a fractionating column.

Idealized and simplified representation of the fractional distillation of a mixture of methanol 10% and water 90% using fractionating column.

A simple and effective column for laboratory use consists of along glass tube packed with short lengths of a glassing tubing, glass beads or specially made porcelain rings. The aim is to obtain a large surface area, and there are many patent designs of column.

Industrially, a fractionating tower is used. Such a tower is divided into a number of compartments by means of trays set one above the other. These trays contain central holes, covered by bubbles caps, to allow vapour to pass up the tower and overflow pipes to allow liquids to drop down.

At each point in a column or at each plate in a tower, an equilibrium between liquid and vapour is setup and this is facilitated by an upward flow of vapour and downward flow of liquid, a large surface area slow distillation. It also preferable to maintain the various levels of the column or tower at a steady temperature so that external lagging or an electrical heating jacket is often used.

A fractionating tower

These state of affairs existing in an idealized and simplified distillation of a mixture of a methanol and water, containing 10 per cent by mass of methanol as shown in the figure above. The figure shows five liquid vapour equilibria which are setup at different temperatures in the fractionating column.

The purpose of the fractionating column is to facilitate the setting up of this equilibria.
Mixtures of varied compositions can be drawn off from different points on the column or tower as is done, for instance in the fractional distillation of crude oil in a refinery.

#### BOILING POINT COMPOSITION DIAGRAM WITH MAXIMUM

The vapour pressure composition diagram for nitric acid water mixtures shows a minimum and the corresponding boiling point composition diagram, with a maximum is shown.
On distilling a mixture of nitric acid and water containing less than 68.2 per cent nitric acid, the distillate will consist of pure water and the mixture in the flask will become more and more concentrated until it contain 68.2 per cent nitric acid .

At this stage, the liquid mixture will boil at a constant temperature because the liquid and the vapour in equilibrium with it have the same composition, i.e. 68.2 per cent nitric acid.
Mixtures containing more than 68.2 percent nitric acid will give a distillate of a pure nitric acid until the residue in the flask reaches the 68.2 percent nitric acid.

Thereafter the distillate will 68.2 percent nitric acid be as before. A mixture with this type of boiling point composition curve cannot be completely separated by the fractional distillation.

It can only be separated into a one component and what is known as the constant boiling mixture, maximum boiling point mixture, or azeotropic mixture.
Maximum boiling point of mixtures are also obtain from mixtures of water with hydrofluoric, hydrobromic, hydrochloric, sulphuric and methanoic acids.

#### BOILING POINT COMPOSITION DIAGRAM WITH A MINIMUM

Ethanol and water give a vapour pressure composition diagram with a maximum. The corresponding boiling point composition diagram, with a minimum is shown in figure below. It is not possible to get a complete separation of ethanol and water by fractional distillation.

A mixture containing more than 95.6 percent ethanol can be separatedinto pure ethanol and a minimum boiling point mixture, with a composition of 96.5 percent ethanol. A mixture containing less than 96.5 percent ethanol can be separated int pure water and the same water and the same boiling point mixture.

Water with propanol or pyridine and ethanol with tri-chloromethane or methyl benzene, also give minimum boiling point mixtures.

#### SEPARATION OF AZEOTROPIC MIXTURES

An azeotropic mixture may have either a maximum or a minimum boiling point but at any one pressure, it has a fixed composition.

It is a unusual for this composition to correspond with that of any sample chemical formula for the mixture, and there is definitely no compound formation because the composition of the mixture does not depend on pressure.

Moreover, the mixture can be separated into its component parts fairly easily. Such separation can be brought about by the following methods.

a) By distillation with a third component

The azeotropic mixture of ethanol and water contains 95.6 percent of alcohol at normal atmospheric pressure. If benzene is added distillation yields, first a ternary azeotropic mixture of ethanol, water and benzene, then a binary azeotropic mixture of ethanol and benzene, and finally absolute ethanol.b) By chemical methods

Quicklime may be used to remove the water from an azeotropic mixture of ethanol and water. Concentrated sulphuric acid will remove aromatic or unsaturated hydrocarbons from mixtures with saturated hydrocarbons in the refining of petrols and oils.c) Absorption
Charcoal or silica gel may absorb one of the components.d) Solvent extraction
One component can be extracted by a solvent.

##### PARTIALLY MISCIBLE LIQUIDS

Critical Solution temperature.

Phenol and water are completely miscible, forming one solution, above 66oC, but two immiscible solutions may from below that temperature, depending on the composition of the mixture. One of the solutions will be a solution of phenol in water, the other a solution of water in phenol.

They called conjugate solutions

The effect of composition and temperature is shown in a temperature-composition diagram below. The temperature above which phenol and water are always completely miscible is known as the upper critical solution temperature. At any point above the curve there will only be one layer, i.e. one solution. Below the curve, two layers will-always form and the curve will give the compositions of the two conjugate solutions making up the two layers.

A mixture of 50 per cent phenol and 50 per cent water, for example, at 50 °C, will form two layers whose compositions are given by A and B. The line YZ is known as a tie-line. The ratio YX/XZ is equal to the ratio of the mass of the phenol layer (of composition B) to that of the mass of the aqueous layer (of composition A).

The complete miscibility of phenol and water with increasing tempera­ture comes about because their mutual solubilities increase as the temperature does. The curve in Fig.(a) can be regarded as made up of two halves, one being the solubility curve of water in phenol and the other the solubility curve of phenol in water.

With triethylamine and water the mutual solubilities decrease as the temperature is increased. This leads to a temperature-composition dia­gram with a lower critical solution (or consolute) temperature of I8,5°C (Fig. (b)). A 50:50 mixture will be completely miscible at 10 °C but will separate into two layers, with compositions C and D, at 50 °C.

Mixtures of nicotine and water are very unusual as they have both an upper (208 °C) and a lower (61 °C) critical solution temperature.

Conjugate solutions have the same total vapour pressure and the same vapour composition; that is why they can coexist together.

#### REVIEW QUESTIONS

1. Some solution are ideal while others are not briefly explain what do you understand by this statement
2. How do ideal gases differ from ideal solution?
3. Define the following

i) Mole fraction of that liquid

ii) Ideal solution

iii) Briefly explain how Raoult’s law becomes feasible

Vapour pressure of methyl alcohol and ethyl alcohol at 20oc are 94 mmHg and 44mmHg respectively. If 20g of ethyl alcohol and 100g of ethyl alcohol are mixed. Calculate

a) Partial pressure of each in a mixture

b) Total pressure of the mixture

c) % composition of each alcohol in a mixture

Define the following terms

i) Vapour pressure

ii) Partial Vapour pressure

6.a) Define the following

i) Ideal solution

ii) Non ideal solution

b) State the Raoult’s law partial pressure Answer

i) Ideal solution are these solution that do obey all assumption of Raoult’s law of partial pressure

ii) Non ideal solution are these solution that do not obey some or all assumption of Raoult’s law of partial pressure

i) Raoult’s law of partial pressure states that “The saturated vapour pressure of each component in a mixture is equal to the product of mole fraction of that component and its pure vapour pressure”

7.a) ii) Raoult’s law

ii) Partition law

b) The ideality of a solution is approached when it is made more dilute explain

c) 10 g of methanol give an ideal solution when mixed with 50g of ethanol. If the vapour pressure of methanol and ethanol at the same temperature are 6265 Pa and 2933 Pa respectively

Calculate

i) The partial pressure exerted by each component in the mixture

ii) The component of the vapour

8.a) State

i) Boyl’s law

ii) Charles’s law

b) SO2 used in manufacture of sulphuric acid is obtained from sulphide ore

4 Fe2(s) + 11O2(g) 2Fe2O3(s) + 8 SO2(g)

Find the mass of oxygen in grams reacting when 75 litres SO2 is produced at 1000C and 1.04 atm.

1. What is azeotropic mixture?

Azeotropic mixture is the mixture of two different components with constant vapour pressure and boiling point and it cannot be separated by fractional distillation.

1. What is azeotropic point

Azeotropic point is the point in temperature composition graphic which shows the azeotropic temperature and its composition

1. What is azeotropic temperature?

Azeotropic point is the temperature is the temperature at which azeotropic mixture tend to boi

The temperature composition graph of non ideal solution shows some deviations from ideal behaviour deviation

i) Positive deviation

ii) Negative deviation

iii) Boiling point composition diagram which undergo Positive deviation

a) Define the following terms

i) Azeotropic mixture

ii) Azeotropic point

iii) Boiling point

iv) Azeotropic composition

b) Liquid Q and R from a non ideal solution. If liquid Q boil at 100oC and R boil at 43% less than that of Q. On boiling the azeotropic mixture was formed at 56% composition by mass liquid Q and boil at 51oC

i) Plot the temperature composition graph

ii) What type of deviation is shown by your graph?

a) What do you understand by the following terms

i) Non ideal solution

ii) Azeotropic solution

b) How does non ideal solution deviate from ideal solution?

c) The mixture container the following water and nitric acid which boil at 86oC . The composition of azeotropic is 68% by mass nitric acid

i) Plot the boiling point curve which represent above data

ii) Account for the distillated and residue on distilling the mixture contain 50% by mass water

iii) Account for the distillated and residue on distilling the mixture contains 78% by mass HNO3. If azeotropic temperature is 12oC

iv) Is the deviation positive or negative? Why?

v) 20% by mass HNO3 . Account for the distillated at the point.

i) Raoult’s law states that

The saturated vapour pressure of a component in a mixture is equal to the product of mole fraction of that components and its partial vapour pressure

ii) Partition law state that

When a solute is added to two immiscible solvents it distribute itself between the two solvent until the ratio of concentration of solute in one solute to another is constant, provided that solute remains in the same molecular state in both solvent and temperature is constant

b) The ideality of a solution is approached when it is made more dilute because the attractive or repulsive forces between solvent and solute molecules become weaker and cause the gas to obey assumption Raoult’s law .

As a solution become more dilute

* In start stronger forces, grater deviation from Raoult’s law , solution become more constant

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