RAOULT’S LAW

RAOULT’S LAW

source : chemwiki.ucdavis.edu

RAOULT’S LAW

Lowering of vapour pressure-

The molecules of liquid are in a state of constant motion in all directions, some of these molecules have higher kinetic energy than others. Some molecules which are present at the surface of a liquid may leave the surface & go into vapour state. The pressure exerted by the vapours of a liquid on its surface is known as vapour pressure of that liquid.

Vapour pressure of a liquid depends upon temperature & is independent of amount of liquid & vapours present in the system.

When a nonvolatile solute is dissolved in a liquid, the escaping tendency of liquid molecules is lowered hence  vapour pressure of liquid is lowered. This difference of vapour pressure is called lowering of vapour pressure.

Lowering of vapour pressure= p-ps

p=vapour pressure of pure solvent

ps= vapour pressure of pure solution

Relative  lowering of vapour pressure = p-ps/p

Raoult’s Law-

According to Raoult’s law,

“The relative lowering of vapour pressure of solvent is equal to the mole fraction of the solute.”

Let, No. of moles of solute = n

No. of moles of solvent = N

Total moles = n+N

Vapour pressure of pure solvent= p

Vapour pressure of solution =Ps

lowering of vapour pressure= p-ps

Relative lowering of vapour  pressure= p- ps/p

So, According to Raoult’s Law,

p- ps/p =n / n+N

Limitation of Raoult’s Law-

Raoult’s law is followed by dilute solutions

1- The mole fraction of the solute in a given solution remains constant at all temperatures

2- Lowering of vapour pressure is a colligative property.

For solute that dissociates or associated in solution, Vant Hoff factor (i) is defined as-

Vant Hoff factor (i) = no.of solute particles after dissociation or association / no. of solute particles dissolved

The term ‘n’ is replaced by ( i * n).

3. Molecular weight of solute can be calculated by using Raoult’s law as follows-

p- ps/p =n / n+N

n =w/m ; N =W/M

p /p-ps =n+N/n

(p /p-ps) -1 = (n+N/n ) -1

ps/p-ps =N/n

p-ps /ps =n/N

n=w/m : N =W/M

p-ps /ps =wM/mW

m =w. M.ps /W(p-ps)

When dissociation or association takes peace, then ‘n’ is replaced by i × n

m=i.w.M.ps /W(p-ps)

4. Consider a solution of two liquids A & B, their vapour  pressures in pure state be p₁ & p₂, their vapour pressures in solution be ps₁ & ps₂, their no. of moles in solution be n₁ & n₂.

According to Raoult’s law

p- ps/p =n / n+N

1 – (ps /p) =n / n+N

ps/p =1 – (n / n+N )

ps/p =N/n+N

ps = p (N/n+N )

Vapour pressure of solution = vapour pressure  of pure solvent × mole fraction of solvent

ps₁ = p₁ ( n₁/n₁+n₂)

ps₂ = p₂ ( n₂/n₁+n₂)

Vapour pressure of solution = ps₁+ps₂

=  p₁ [ n₁/(n₁+n₂)] +  p₂[ n₂/(n₁+n₂)]

= ( p₁.n₁ + p₂.n₂) /(n₁+n₂)

=  p₁ [n₁ +( p₂ .n₂/p₁)]/  (n₁ + n₂)

If p₂ >p₁, the vapour pressure of solution will be greater than the vapour pressure of A & lesser than vapour pressure of  B.

If p₂<p₁, the vapour pressure of solution will be less than the vapour pressure of A & greater than the vapour pressure of B.