CBSE Class 12, Unit-1:Solutions Notes
Raoult's Law for Volatile and Non-Volatile Solutes
Colligative Properties
Relative Lowering of Vapour Pressure
When a non-volatile solute is dissolved in a pure solvent, the vapour pressure of the solvent decreases because the presence of solute molecules reduces the number of solvent molecules that can escape into the vapor phase. Consequently, the vapor pressure of the solution becomes lower than that of the pure solvent at the same temperature.
The relative lowering of vapour pressure can be mathematically expressed as:
Relative Lowering of Vapour Pressure = (po − p)/po
where po is the vapour pressure of the pure solvent, and p is the vapour pressure of the solution, (po − p) is lowering of vapour pressure.
We can also say that the relative loweing of vapour pressure is the ratio of lowering of vapour pressure to the vapour pressure of the pure solvent.
Elevation in Boiling Point
We know that the vapour pressure of solution is always lower than that of the solvent. Therefore, the boiling point of solution is always higher than that of solvent. In other words, when a non-volatile solute is dissolved in the pure solvent, the boiling point increases or elevated. This phenomenon is known as elevation in boiling point.
T2 > T1
and T2 − T1 = ΔTb (Elevation in Boiling Point).
The elevation in boiling point (ΔTb) is proportional to the concentration of the solute in the solution. It can be calculated as-
ΔTb = i × Kb × m
Where, i is the Van't Hoff factor, Kb is the ebullioscopic constant and m is the molality of the solute.
For dilute solution, elevation in boiling point can be calculated by using the given formula-
Where, W is the weight of the solvent, w is the weight of the solute and m is the mass of the solute.
Depression in Freezing Point
When a non-volatile solute is dissolved in the pure solvent, the freezing point decreases. This phenomenon is known as depression in freezing point. When a liquid is cooled by dropping the temperature, the vapour pressure decreases as the quantity of vapour molecules decreases on the surface of the liquid. Unless supercooling occurs, the temperature finally stops decreasing and at the same time a few crystals of crystalline solids are formed and the liquid starts to freeze. At this temperature, both liquid and solid forms have the same vapour pressure. This temperature is called freezing point of liquid.
T2 < T1
and T2 − T1 = ΔT (Depression in Freezing Point).
The depression in freezing point is proportional to the molality of the added solute. The depression in the freezing point of a solution can be described by the following formula.
ΔTf = i × Kf × m
Where, ΔTf is the freezing point depression, i is the Van't Hoff factor, Kf is the cryoscopic constant, and m is the molality.
For dilute solution, depression in freezing point can be calculated by using the given formula-
Where, W is the weight of the solvent, w is the weight of the solute and m is the mass of the solute.
Osmotic Pressure
When two solutions are separated by a semipermeable membrane, then there is a spontaneous flow of the solvent from lower to higher concentration due to osmosis. The pressure that must be applied on the solution of higher concentration to prevent the flow of the solvent from the solution of lower concentration is called osmotic pressure of the solution. It is denoted by π
Osmotic pressure (π) can be expressed mathematically using the van't Hoff equation:
π= i C S T
where, i is the van't Hoff factor, C is the molar concentration of the solute, S is the solution constant (0.082 ltr.atm.K−mol−) and T is the absolute temperature in kelvins
Measurement of Molecular weight of Solute by Osmotic Pressure
We know that PV = nRT for n mole of gas,
Similarly, for n molecules of a solution,
πV = nST
or, πV = (w/m)ST
or, m = wST/πV
where, m is the molecular mass of the solute, w is weight of the solute, V is volume of the solution having w gm of solute, R is solution constant, T is absolute temperature and π is the osmotic pressure.
Abnormal Molecular Weight
Colligative properties are the properties of dilute solutions which depend upon the number of solute particles. Abnormal molecular weight refers to the condition where the molecular mass of a solute, calculated from colligative properties deviates from its expected value. This abnormality arises due to the association or dissociation of solute particles in solution.
We know that elevation in boiling point and depression in freezing point is given by the formula-
ΔT = (1000 x K X w)/m x W
or, ΔT ∝ 1/m
The osmotic pressure (π) is-
π = (w x S X T)/Mm x V
π ∝ 1/m
and the lowering of vapour pressure (ΔP) is-
ΔP/P = wM/mW
or, ΔP ∝ 1/m
Overall we can write as-
Colligative properties ∝ 1/m
or, Number of Solute Particles ∝ 1/Molecular Weight.
Therefore, compounds undergo association or dissociation in solution show abnormal molecular weight.
Solubility of Gas in Liquid
The solubility of gases in liquid is the maximum amount of gas that can dissolve in a given volume of liquid at a particular temperature and pressure. Gases dissolve in liquids to form homogeneous solutions. The solubility of gas in a liquid depends upon the following factors-
1. The nature of the substance (solute)
2. The nature of the solvent
3. Temperature of the solution
4. Pressure
Some gases like N2, H2, O2 etc. dissolve in water to very small extent whereas the gases like NH3, HCl etc. are highly soluble in water. The most soluble gases are those which chemically react with the liquid solvent.
The solubility of a gases in liquids is greatly influenced by pressure and temperature
1. Effect of temperature: The solubility of a gases decreases with increase in temperature because gases dissolve in a liquid with the evolution of heat (i.e. exothermic process).
2. Effect of pressure: The solubility of gases increases with increase in pressure. This is also in accordance with Le-Chatelier's principle.
Solubility of gas in liquid was explained by Henry's law which stated taht the solubilty of gas increases with incresing the pressure at constant temperature.
Henry's law also stated taht the partial pressure of a gas in vapour phase (p) is proportional to the mole fraction of the gas (X) in a solution.
p ∝ X
or, p = KH X
Where KH = Henry's law constant which depend on the nature of gas and temperature.
KH has constant value but different for different gas. KH value increases with increasing the temperature. So, the value of KH is inversely proportional to solubility of gas in liquid.
How does temperature and pressure affect solubility?
Types of Solution
On the basis of physical state of solute and solvent, there are nine types of solutions.
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