Liquid Solution : Raoult’s Law

Colligative properties

Certain properties of dilute solutions containing non-volatile solute do not depend upon the nature of the solute dissolved but depend only upon the concentration i.e., the number of particles of the solute present in the solution. Such properties are called colligative properties. The four well known examples of the colligative properties are

(1)     Lowering of vapour pressure of the solvent.

(2)     Osmotic pressure of the solution.

(3)     Elevation in boiling point of the solvent.

(4)     Depression in freezing point of the solvent.

Since colligative properties depend upon the number of solute particles present in the solution, the simple case will be that when the solute is a non-electrolyte. In case the solute is an electrolyte, it may split to a number of ions each of which acts as a particle and thus will affect the value of the colligative property.

Each colligative property is exactly related to any other and thus if one property is measured, the other can be calculated. The study of colligative properties is very useful in the calculation of molecular weights of the solutes.

 

Lowering of vapour pressure

The pressure exerted by the vapours above the liquid surface in equilibrium with the liquid at a given temperature is called vapour pressure of the liquid. The vapour pressure of a liquid depends on

(1)     Nature of liquid : Liquids, which have weak intermolecular forces, are volatile and have greater vapour pressure. For example, dimethyl ether has greater vapour pressure than ethyl alcohol.

(2)     Temperature : Vapour pressure increases with increase in temperature. This is due to the reason that with increase in temperature more molecules of the liquid can go into vapour phase.

(3)     Purity of liquid : Pure liquid always has a vapour pressure greater than  its solution.

Raoult’s law : When  a non-volatile substance is dissolved in a liquid, the vapour pressure of the liquid (solvent) is lowered. According to Raoult’s law (1887), at any given temperature the partial vapour pressure (pA) of any component of a solution is equal to its mole fraction (XA) multiplied by the vapour pressure of this component in the pure state (pAo). That is,  \[{{p}_{A}}=p_{A}^{0}\times {{X}_{A}}

The vapour pressure of the solution (Ptotal) is the sum of the parital pressures of the components, i.e., for the solution of two volatile liquids with vapour pressures PA and PB.

    \[{{P}_{total}}={{p}_{A}}+{{p}_{B}}=(p_{A}^{0}\times {{X}_{A}})+(p_{B}^{0}\times {{X}_{B}})\]

Alternatively, Raoult’s law may be stated as “the relative lowering of vapour pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution.”

Relative lowering of vapour pressure is defined as the ratio of lowering of vapour pressure to the vapour pressure of the pure solvent. It is determined by Ostwald-Walker method.

Mole fraction of the solute is defined as the ratio of the number of moles of solute to the total numbr of moles in solution.

Thus according to Raoult’s law,

    \[\frac{{{p}^{0}}-p}{{{p}^{0}}}=\frac{n}{n+N}=\frac{\frac{w}{m}}{\frac{w}{m}+\frac{W}{M}}\]

where, p =  Vapour pressure of the solution;  po = Vapour pressure of the pure solvent

n = Number of moles of the solute; N = Number of moles of the solvent

w and m = weight and mol. wt. of solute;  W and M = weight and mol. wt. of the solvent.

 

Limitations of Raoult’s law

  • Raoult’s law is applicable only to very dilute solutions.
  • Raoult’s law is applicable to solutions containing non-volatile solute only.
  • Raoult’s law is not applicable to solutes which dissociate or associate in the particular solution.