CHEMISTRY As LEVEL(FORM FIVE) NOTES – PHYSICAL CHEMISTRY – Relative Molecular Masses in Solutions

PHYSICAL CHEMISTRY – Relative Molecular Masses in Solutions

SOLUTIONS

What is a homogeneous solution?

A solution is a uniform mixture of two or more substances.

The substances which are mixed to form a solution are also termed components.

Example of solution:

The solution formed can be:

• Solution of liquid in liquid
• Solution of solid in liquid
• Solution of gas in liquid
• 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 must be miscible.

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

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

Example

What is mole fraction?

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

Consider the solution formed by mixing liquid A and B.

Then:

Let: n_A be the number of moles of liquid A

n_B be the number of moles of liquid B

Total number of moles = n_A + n_B

n_T = n_A + n_B

Then to get mole fraction:

Χ_A = mole fraction of A

Χ_B = mole fraction of B

When expressed in decimal:

When expressed in percentage:

The mole fraction can also be calculated in terms of partial pressure, i.e., if the liquids to be mixed are A and B:

RAOULT’S LAW OF PARTIAL PRESSURE

Raoult’s law of partial pressure states that:

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

ASSUMPTIONS OF RAOULT’S LAW

For Raoult’s law to be feasible, the following assumptions must be considered:

• Intermolecular forces of attraction should be equal to the intermolecular forces of attraction.
• After mixing, the components must not change in volume.
• There must be no change in temperature.
• The liquids must be miscible.
• The liquids should not react.

CONCLUSION

Solutions that obey all assumptions of Raoult’s law are called IDEAL SOLUTIONS. Liquids that deviate from these assumptions are termed NON-IDEAL SOLUTIONS or REAL SOLUTIONS.

IDEAL SOLUTION

In an ideal solution, the cohesive forces between its molecules are the same as those in the separate components. A solution made from A and B is ideal only if the forces in the solutions of A and B are the same as those in pure A and pure B.

Ideal solutions are rare but most likely occur with mixtures of two almost identical chemicals, e.g., hexane and heptane. Most solutions deviate considerably from ideal because the interactions within the solution differ 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 pressures. All three pressures vary with temperature and composition of the solution.

The change with composition for an ideal solution at a fixed temperature is described by Raoult’s law (1886), which states 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 have 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 alike.

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

The total vapour pressure above the solution equals 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 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., 55. Numerical results of this type are given only by ideal solutions, e.g., hexane and heptane or bromoethane and iodoethane.

VAPOUR PRESSURE COMPOSITION DIAGRAM FOR NON-IDEAL SOLUTION

What is a non-ideal solution?

A non-ideal solution is one that does not obey some or all assumptions of Raoult’s law.

Non-ideal solutions are of two types:

• Positive deviation from Raoult’s law
• Negative deviation from Raoult’s law

i) POSITIVE DEVIATION FROM RAOULT’S LAW

Positive deviation is observed when the saturated vapour pressure of the solution is greater than the expected (ideal) value.

This is due to a large number of molecules escaping from the liquid phase to the vapour phase.

The large number of molecules escaping is because intramolecular forces of attraction are greater than intermolecular forces of attraction.

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

ii) NEGATIVE DEVIATION FROM RAOULT’S LAW

Negative deviation is observed when the saturated vapour pressure of the solution is less than the expected (ideal) value.

This is due to fewer molecules escaping from the liquid phase to the vapour phase.

The small number of molecules escaping is because intermolecular forces of attraction are greater than 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 degree of deviation from Raoult’s law of the two liquids concerned. There are three important types of diagrams:

1. No maximum or minimum
2. A maximum boiling point
3. A minimum boiling point

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

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

iii) A minimum boiling point

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

Boiling point composition diagrams with no maximum or minimum:

A diagram of this type is given by methanol-water mixtures. The liquid line shows how the boiling point of methanol-water mixture varies with composition at fixed pressure.

For a 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., methanol. The liquid line has an associated vapour line. The vapour pressure composition diagram corresponding with this boiling point composition diagram is shown above.

When a mixture of methanol and water containing 50% 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 composition B, and this will condense into a liquid whose composition is also B. By repeating this boiling-condensing process, pure methanol could be obtained, but the method would be tedious. The same result can be obtained in one operation by fractional distillation using a fractionating column.

A simple and effective column for laboratory use consists of a long glass tube packed with short lengths of glass tubing, glass beads, or specially made porcelain rings. The aim is to obtain a large surface area, and there are many patent designs of columns. 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 bubble 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 set up. This is facilitated by an upward flow of vapour and downward flow of liquid, providing a large surface area for slow distillation. It is also preferable to maintain the various levels of the column or tower at a steady temperature, so external lagging or an electrical heating jacket is often used.

A fractionating tower:

These states of affairs exist in an idealized and simplified distillation of a mixture of methanol and water containing 10% by mass of methanol, as shown in the figure above. The figure shows five liquid-vapour equilibria set up at different temperatures in the fractionating column.

The purpose of the fractionating column is to facilitate the setting up of these 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% nitric acid, the distillate will consist of pure water, and the mixture in the flask will become more concentrated until it contains 68.2% 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% nitric acid.

Mixtures containing more than 68.2% nitric acid will give a distillate of pure nitric acid until the residue in the flask reaches 68.2% nitric acid.

Thereafter, the distillate will be 68.2% nitric acid as before. A mixture with this type of boiling point composition curve cannot be completely separated by fractional distillation. It can only be separated into one component and what is known as the constant boiling mixture, maximum boiling point mixture, or azeotropic mixture.

Maximum boiling points of mixtures are also obtained 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 the 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% ethanol can be separated into pure ethanol and a minimum boiling point mixture with a composition of 96.5% ethanol. A mixture containing less than 96.5% ethanol can be separated into pure water and the same boiling point mixture.

Water with propanol or pyridine and ethanol with trichloromethane 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 unusual for this composition to correspond with 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:

1. By distillation with a third component
   The azeotropic mixture of ethanol and water contains 95.6% 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.
2. By chemical methods
   Quicklime may be used to remove 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.
3. Absorption
   Charcoal or silica gel may absorb one of the components.
4. 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 66°C, but two immiscible solutions may form 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 are 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 gives the compositions of the two conjugate solutions making up the two layers. A mixture of 50% phenol and 50% 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 18.5 °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 solutions are ideal while others are not. Briefly explain what you understand by this statement.
2. How do ideal gases differ from ideal solutions?
3. Define the following:
   1. Mole fraction of a liquid
   2. Ideal solution
   3. Briefly explain how Raoult’s law becomes feasible
4. Vapour pressure of methyl alcohol and ethyl alcohol at 20°C are 94 mmHg and 44 mmHg respectively. If 20 g of methyl alcohol and 100 g of ethyl alcohol are mixed, calculate:
   1. Partial pressure of each in the mixture
   2. Total pressure of the mixture
   3. Percentage composition of each alcohol in the mixture
5. Define the following terms:
   1. Vapour pressure
   2. Partial vapour pressure
6. Define:
   1. Ideal solution
   2. Non-ideal solution

   State Raoult’s law of partial pressure.

7. State:
   1. Boyle’s law
   2. Charles’s law
   3. Avogadro’s law

   SO₂ used in the manufacture of sulphuric acid is obtained from sulphide ore:
   
   4FeS₂(s) + 11O₂(g) → 2Fe₂O₃(s) + 8SO₂(g)
   
   Find the mass of oxygen in grams reacting when 75 litres of SO₂ is produced at 100 °C and 1.04 atm.

8. What is an azeotropic mixture?
9. What is an azeotropic point?
10. What is azeotropic temperature?
11. The temperature composition graph of a non-ideal solution shows some deviations from ideal behaviour:
    1. Positive deviation
    2. Negative deviation
    3. Boiling point composition diagram which undergoes positive deviation
12. Define the following terms:
    1. Azeotropic mixture
    2. Azeotropic point
    3. Boiling point
    4. Azeotropic composition

    Liquid Q and R form a non-ideal solution. If liquid Q boils at 100 °C and R boils at 43% less than that of Q. On boiling, the azeotropic mixture was formed at 56% composition by mass of liquid Q and boils at 51 °C.

    1. Plot the temperature composition graph
    2. What type of deviation is shown by your graph?
13. What do you understand by the following terms:
    1. Non-ideal solution
    2. Azeotropic solution

    How does a non-ideal solution deviate from an ideal solution?
    
    The mixture contains water and nitric acid which boil at 86 °C. The composition of the azeotropic is 68% by mass nitric acid.

    1. Plot the boiling point curve which represents the above data
    2. Account for the distillate and residue on distilling the mixture containing 50% by mass water
    3. Account for the distillate and residue on distilling the mixture containing 78% by mass HNO₃. If the azeotropic temperature is 120 °C
    4. Is the deviation positive or negative? Why?
    5. 20% by mass HNO₃. Account for the distillate at the point.
14. Raoult’s law states that:

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

15. Partition law states that:

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

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 assumptions of Raoult’s law.

As a solution becomes more dilute:

• Initially stronger forces cause greater deviation from Raoult’s law; solution becomes more constant.