The Henry's law states that the mass of a gas dissolved per unit volume of the solvent at a given temperature is proportional to the pressure of the gas in equilibrium with the solution.
\( m \propto p \\ \mathrm{m}=\mathrm{kp} \)
where k is proportionality constant.

\(\triangle { T }_{ b }={ K }_{ b }\times m={ K }_{ b }\times \frac { { W }_{ B } }{ { M }_{ B } } \times \frac { 1000 }{ { W }_{ A } } \)
\(\\ \Rightarrow \ \triangle { T }_{ b }=0.52\times \frac { 0.52 }{ 180 } \times \frac { 1000 }{ 80.2 } =\frac { 270.4 }{ 14436 }\)
\( =0.0187\)
Boiling point of solution = 373 + 0.0187
= 373.0187 K

When non-volatile solute is added to solvent, its vapour pressure decreases, therefore, at a lower temperature, vapour pressure of solid and solution becomes equal, i.e. depression in freezing point takes place as shown in diagram.

(i) Mole fraction (x): It is the ratio of number of moles of a particular component to the total number of moles of all the components.
For example, mole fraction of a component A,
\({ X }_{ A }=\frac { { n }_{ A } }{ { n }_{ A }+{ n }_{ B } } \)
where \({ n }_{ A }\ and \ { n }_{ B }\)  are the number of moles of components 'A' and 'B' respectively.
(ii) Isotonic solutions: Two solutions are said to be isotonic when they exert the same osmotic pressure because they have same molar concentration. All intravenous injections must be isotonic with body fluids.
(iii) van't Hoff factor (i): The ratio of the experimental value of a colligative property to the theoretical value (calculated on the basis of normal behaviour of solute) is known as van't Hoff factor.
Experimentally determined
 \(i=\frac { value \ of \ the \ colligative \ property }{ \ \ Calculated \ value \ of\ the\\ \ \ colligative \ property } \)
(iv) Ideal solution: Those solutions which obey Raoult's law are called ideal solutions. When the forces of attraction between A-A, B-B are similar to A-B, then A and B will form ideal solution.

Molality is more accurate than molarity because molarity does not depend on temperatures mass does not change with temperature.

Osmotic pressure.

Given, M₂ (ethylene glycol) = 62 g mol^-1
W₁ = 5.50 kg = 5500 g. \(\Delta T_f\)= 10K
[0⁰​​C - (- 10° C)= 10° C = 10 K]
and K_f = 1.86 K kg mol^-1
\(\Delta T_f=\frac{K_f W_2 1000}{M_2W_1}\)
\(W_2=\frac{\Delta T_f M_2 W_1}{K_f 1000}\)
\(=\frac{10 K \times 62 g mol{-1}\times 5500 g}{1.86 K kg mol^{-1}\times 1000}\)
W₃ = 1833.33 g = 1.833 kg

(a) Osmosis is the flow of solvent from solution of lower concentration to higher concentration through a semi-permeable membrane.
Osmotic pressure is the excess pressure which must be applied to a solution to prevent the passage of solvent through a semi-permeable memberane.
It has been found experimentally that for n moles of the solute dissolved in V litres of the solution, the osmotic pressure (π) at temperature T is
πV=nRT
Where R is a gas constant.
or \(\pi={n\over V}RT\)
= C RT
Where Cis the molar concentration ofthe solution.For a solution at given tempeature, both R and T are constant, so that
π ∝ C
Thus, osmotic pressure depends upon the molar concentration ofsolution and therefore, is a colligative property.
(b) \(ΔT_b={iK_b\times1000\times W_2\over W_1\times M_2}\)
NaCI dissociates as:
NaCI ⇾ Na⁺ + Cl^-
i = 2
W₂ = 1.5.0g, W₁ = 250.0 g, M₂ = 58.44 g mol^-1 K_b = 0.512 K kg mol^-1
\(\Delta T_b={2\times 0.512\times1000\times15.0\over 250.0\times58.44}\)
= 1.05 °C
Boiling point of solution = 100 + 1.05
= 101.5° C

Alcohol is polar compound. It can form H-0bound with water molecule. That is why alcohols are miscible with water in all proportion. They also have dipole-dipole interactions due to which there is the force of attraction between alcohol and water molecules.