A solution is a homogeneous mixture of two (or more) substances, the composition of
which may vary between certain limits. A solution consisting of two components is called binary solution. The component which is present in large quantity is called solvent and the component which is small in quantity is called solute. If both components are in same physical state.
Type of Solutions:
All the three states of matter (gas, liquid or solid) may behave either as solvent or solute. Depending on the state of solute or solvent, mainly there may be the following seven types of binary solutions.
S.No. | Solute | Solvent | Example |
1 | Gas | Gas | Air |
2 | Gas | Liquid | Aerated water (CO_{2} + H_{2}O) |
3 | Gas | Solid | Hydrogen in palladium |
4 | Liquid | Liquid | Alcohol in water, benzene in toluene |
5 | Liquid | Solid | Mercury in zinc amalgam |
6 | Liquid | Gas | CO_{2} dissolved in water |
7 | Solid | Liquid | Sugar in water, common salt in water |
8 | Solid | Gas | Smoke |
9 | Solid | Solid | Various alloys |
VAPOUR PRESSURE
RAOULT'S LAW
“The partial vapour pressure of any component in the solution is directly proportional to its mole fraction”.
For a binary solution of two components A and B,
P_{A } = P^{°}_{A }X_{A}
P_{B} = P^{°}_{B }X_{B}
Where,
Limitations of Raoult’s Law:
Raoult’s Law in Combination with Dalton’s Law of Partial Pressure:
P_{T} = X_{A} P^{0}_{A} + X_{B} P^{0}_{B} = P^{0}_{B} + (P^{0}_{A }-P^{0}_{B}) X_{A}
Where
P_{T} = Total Vapour Pressure of the Solution.
IDEAL AND NON-IDEAL SOLUTIONS
Ideal Solutions:
An ideal solution is the solution in which each component obeys Raoult’s law under all conditions of temperatures and concentrations.
Properties of Ideal solutions:
(i) ΔH_{mixing} = 0, i.e. no heat should be absorbed or evolved during mixing
(ii) ΔV_{mixing} = 0, i.e. no expansion or contraction on mixing
(iii) Intermolecular attractive forces between the A-A and B-B are nearly equal to those between A-B.
Examples: Ethyl chloride and Ethyl bromide, n–hexane and n–heptane , CCl_{4 }and SiCl_{4}
Non-Ideal Solutions:
When a solution does not obey Raoult’s law over the entire range of concentration, then it is called non-ideal solution.
For non ideal solutions,
(i) ΔH_{mixing } ≠ 0
(ii) ΔV_{mixing} ≠ 0
Here we may have two cases
1. Positive Deviation:
(i) Solvent-Solute(A-B) type of force is weaker than Solute-Solute(B-B) & Solvent-Solvent(A-A) forces.
(ii) The vapour pressure is higher than predicted by the law.
(iii) ΔH_{mixing} > 0
(iv) ΔV_{mixing} > 0
Examples: Ethanol and Acetone, Carbon disulphide and Acetone
2. Negative Deviation:
(i) Solvent-Solute(A-B) type of force is stronger than the other two.
(ii) The vapour pressure is lower than predicted by the law.
(iii) ΔH_{mix} < 0
(iv) ΔV_{mix } < 0
Examples: Phenol and Aniline, Chloroform and Acetone
etc
COLLIGATIVE PROPERTIES
The properties of dilute solutions which depend only on number particles of solute present in the solution and not on their identity are called colligative properties (denoting depending upon collection).
Lowering of Vapour Pressure by a Non-Volatile Solute
The relative lowering of vapour pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute present in the solution.
Here w_{1} and w_{2} are the masses and M_{1} and M_{2} are the molar masses of the solvent and solute respectively.
Elevation of Boiling Point by a Non-Volatile Solute :
Since the addition of a non-volatile solute lowers the vapour pressure of the solvent, the vapour pressure of a solution is always lower than that of the pure solvent, and hence it must be heated to a higher temperature to make its vapour pressure equal to atmospheric pressure.
where M_{1} = molecular weight of solute and w_{2} and w_{1} are weights of solute and solvent
K_{b}:
It is defined as the elevation in boiling point when the molality of the solution is unity.
The unit of K_{b} is K kg mol^{–1}
Determination of K_{b}:
where: R = Gas constant (8.314 JK/mol),
T_{f} = Freezing temperature in K,
M_{1} = Molar mass of solvent in Kg/mol,
Δ_{vap}H = Enthalpy of vapourisation of solvent in J/mol.
Depression of Freezing Point by a Non-Volatile Solute:
where M_{1} = molecular weight of solute and w_{2 }and w_{1} are weights of solute and solvent
K_{f}:
It is defined as the depression in freezing point when the molality of the solution is unity. The unit of K_{f} is K kg mol^{-1}
Determination of K_{f}:
where : R = gas constant (8.314 JK/mol),
T_{f} = freezing temperature in K,
M_{1} = Molar mass of solvent in Kg/mol,
Δ_{fus}H = enthalpy of fusion of solvent in J/kg
Osmosis and Osmotic Pressure:
πV = nRT
where
π = Osmotic pressure
V = volume of solution
n = no. of moles of solute that is dissolved
R = Gas constant
T = Absolute temperature
Isotonic Solutions: Two solutions having same osmotic pressure at a given
temperature are called isotonic solutions.
The solution with lower concentration or lower osmotic pressure is known as “Hypotonic” with respect to more concentrated solution.
The solution with higher concentration or higher osmotic pressure is known as “Hypertonic” with respect to dilute solution.
ABNORMAL MOLECULAR WEIGHT AND VAN'T HOFF FACTOR
Van't Hoff Factor:
Van't Hoff, in order to account for all abnormal cases introduced a factor i known as the Van't Hoff factor, such that
Degree of Association:
The fraction of the total number of molecules which combine to form bigger molecule
Let a be the degree of association, then,
The number of unassociated moles = 1 - α
The number of associated moles = α/n
Total number of effective moles = 1- α + α /n
Obviously, i < 1
Degree of Dissociation:
The fraction of the total number of molecules which dissociates in the solution, that is, breaks into simpler molecules or ions.
KCl ↔ K^{+} + Cl^{-}
Thus, the total number of moles after dissociation = 1 - α + α + α = 1 + α
Hence, i = (1 + α)/1
i = 1 + α = 1+ (2–1)α
In general, i = 1+ (n–1)α,
Where, n = number of particles ( ions) formed after dissociation
From the above formula, it is clear that i > 1