Raoult law states that. "in the case of a solution of volatile liquids, the partial vapour pressure of each component (A & B) of the solution is directly proportional to its mole fraction.
According to Raoult's law,
P_A \(\alpha\) X_A 
p_A = K X_A
When xA = 1, k = \({ p }_{ A }^{ 0 }\)
Where \({ p }_{ A }^{ 0 }\) is the vapour pressure of pure component 'A' at the same temperature
"The relative lowering of vapour pressure of an ideal solution containing the nonvolatile solute is equal to the mole fraction of the solute at a given temperature".

Derivation:
when sodium chloride is added to the water, the vapour pressure of the salt solution is lowered. The vapour Pressure of the solution is determined by the number of molecules of the solvent present in the surface at any time and is proportional to the mole fraction of the solvent.
P_solution \(\infty \) X_A
Where X_A is the mole fraction of the solvent
P_solution  = K X_A
When X_A = 1, K = P⁰ solvent
\({ P }_{ solvent }^{ 0 }\) is the partial pressure of pure solvent
P_solution = \({ P }_{ solvent }^{ 0 }\) X_A
\(\frac { { P }_{ solution } }{ { P }_{ solvent }^{ 0 } } ={ X }_{ A }\)
\(1-\frac { { P }_{ solution } }{ { P }_{ solvent }^{ 0 } } 1-{ X }_{ A }\)
\(\frac { { P }_{ solvent }^{ 0 }-{ P }_{ solution } }{ { P }_{ solvent }^{ 0 } } ={ x }_{ B }\)
Where X_B the mole fraction of the solute
( \(\because\) X_A + A_B = 1, X_B = 1 - X_A)
The above expression gives the relative lowering of vapour pressure. Based on this expression, Raoult's law can also be stated as "the relative lowering of vapour pressure of an ideal solution containing, the nonvolatile solute is equal to the mole fraction of the solute at a given temperature".

The amount of dissolved oxygen in water decreases with rise in water's temperature. Cold water has more dissolved oxygen per unit area than warm water. So they are more comfortable is cold water during winter. During summer the warm water contain less dissolved oxygen.

ppm = \({mass\ of\ dissolved\ solid\over mass\ of\ water}\times 10^6\)
\({5\times 10^{-3}\ g\over 1.05\times 10^{3}\ g}\times 10^6=\) 4.76 ppm.

The solubility of a substance at a given temperature is defined as the amount of the solid that dissolves in 100 g of the solvent at a given temperature to form a saturated solution.

If the water is not the solvent, the solution is non- aqueous solution. (Benzene, CCI₄, ether etc., act as solvent in these solutions).

Solution is a homogeneous mixture of two or more substances. If the water is the solvent in the solution, then it is an aqueous solution.

For an ideal dilute solution, the properties, namely, relative lowering of vapour pressure, elevation of boiling point, depression in freezing point and osmotic pressure do not depend on the chemical nature of the solute but depends only on the number of solute· particles (ions/molecules) present in the solution. These four properties are known as colligative properties.

Van't Hoff found out that for dilute solutions, the osmotic pressure is directly proportional to the molar concentration ofthe solute and the temperature of the solution. He proposed the following equation to calculate osmotic pressure which is now called as van't Hoff equation.
\(\pi\) = cRT
Here, 
c = Concentration of the solution in molarity
T = Temperature
R = Gas constant

A solution of potassium chloride in water deviates from ideal behavior because the solute dissociates to give K⁺ and CI^- ion which form strong ion-dipole interaction with water molecules.
\(\mathrm{KCl}_{(3)}+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{K}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})\)

In solution, acetic acid exists as a dimer by forming intermolecular hydrogen bonds, and hence deviates from Raoult's law.

This law states that "in the case of a solution of volatile liquids, the partial vapour pressure of each component (A & B) of the solution is directly proportional to its mole fraction".
According to Raoult's law,
P_A \(\alpha\) X_A
P_A = K X_A
when X_A = 1, K p p⁰
where p⁰ _A is the vapour pressure of pure component 'A' at the same temperature.
Therefore, pA = \({ p }_{ A }^{ 0 }x_{ A }\)

Two solutions having same osmotic pressure at a given temperature are called isotonic solutions.

Molality : It is the number of moles of the solute present one kg of the solvent
Molality = \(\frac { No.of \ moles\ of \ solute }{ Mass\ of\ the\ solvent\ (in\ kg) } \) 

Generally the change in pressure does not have any significant effect in the solubility of solids and liquids as they are not compressible. However, the solubility of gases generally increases with increase of pressure.
Consider a saturated solution of a gaseous solute dissolved in a liquid solvent in a closed container. In such a system, the following equilibrium exists.
Gas (in gaseous state) = Gas (in solution)
According to Le-Chatelier principle, the increase in pressure will shift the equilibrium in the direction which will reduce the p.ressure. Therefore, more number of gaseous molecules dissolves in the solvent and the solubility increases.

Henry's law states that, "the partial pressure of the gas in vapour phase is directly proportional to the mole fraction(x) of the gaseous solute in the solution at low concentrations".
Henry's law can be expressed as,
\(\rho \)_solute \(\alpha\) X _{solute in solution}
P_solute = K_Hx _{solute in solution}
Explanation: Here, P_solute represents the partial pressure of the gas in vapour state which is commonly called as vapour pressure. x _solute in solution represents the mole fraction of solute in the solution. K_H is a empirical consiint with the dimensions of pressure. The value of 'K_H' depends on the nature of the gaseous solute and solvent. The above equation is a straight-line in the form of y = mx. The plot partial pressure of the gas against its mole fraction in a solution will give a straight line as shown in fig The slope of the. straight line gives the value of K_H.

Limitation of Henry's law:
i) Henry's law is applicable at moderate temperature and pressure only.
ii) Only the less soluble gases obeys Henry's law.
iii) The gases reacting with the solvent do not obey Henlry s law For example, ammonia or HCI reacts \Mith water and hence does not obey this law.
\(\mathrm{NH}_3+\mathrm{H}_2 \mathrm{O} \leftrightarrows \mathrm{NH}_4^{+}+\mathrm{OH}^{-}\)
(iv) The gases obeying Henry's law should not associate or dissociate while dissolving in the solvent.