Raoult’s Law  

• Vapour Pressure

Consider a pure liquid in a beaker is covered with a jar. Some molecules on the liquid surface evaporate and fill the vacant space available to them. The molecules in the vapour phase move randomly in the vacant space, during this motion, they strike the surface of the liquid  and condensed. This process of evaporation and condensation go on and an equilibrium is established between evaporation and condensation. The pressure exerted by vapours over the liquid surface at equilibrium is called vapour pressure of the liquid.

If solute is non volatile solid or liquid the vapour pressure of solution is equal to partial vapour pressure of solvent in the solution and if the solute is volatile solid or liquid, then vapour pressure will be equal to the sum of partial vapour pressure of solute and that of solvent.

• Statement of The Roults Law

“The partial vapour pressure of any component in the solution is directly proportional to its mole fraction”. P_A = KX_A  

X_A  =   Mole fraction of A in solution

For pure liquids X_A = 1

Then K = P⁰_A Where P⁰_A  is the vapour pressure of component A in pure state

Hence, P_A  = X_AP⁰_A 

Similarly for component B , P_B = X_BP⁰_A

Roults law  is applied for a solution of liquid in liquids 

Refer to the following video for Raoult’s Law

Raoult’s Law in Combination with Dalton’s Law of Partial Pressure

Assuming that vapours of a liquid is behaving like an ideal gas, then according to Dalton’s law of partial pressure, the total pressure P_T is given by

P_T = P_A + P_B

or P_T = X_AP⁰_A + X_BP⁰_B = X_AP⁰_A +(1- X_A)P⁰_B 

Composition of the Vapour:

The composition of the liquid and vapour that are in mutual equilibrium are not necessarily the same, the common sense suggest that the vapour pressure should be richer in the more volatile component. This expectation can be confirmed as follows: 

Let the mole fractions of A and B in vapour phase be Y_A and Y_B, then from Dalton’s law,

Condensation of vapours of solution:

When the vapours of solution (containing liquids A and B) is condensed, the composition of liquids A and B in the condensate remains same. The vapours over condensate can again recondensed and the composition of A and B in condensate (2) remains same as it was in vapour phase over condensate (2).

Raoult’s Law as a special case of Henry’sLaw

According to Raoult’s law,  p_i  = x_i p_i⁰. ...(i)

In the solution of a gas in a liquid, one of the components is so volatile that it exists as a gas and we have already seen that its solubility is given by

According to Henry’s law   p = K_H x ….......(ii)
If we compare the equations for Raoult’s law and Henry’s law, it can be seen that the partial pressure of the volatile component or gas is directly proportional to its mole fraction in solution. Only the
proportionality constant K_H differs from p₁⁰.

Thus, Raoult’s law becomes a special case of Henry’s law in which K_H becomes equal to p₁⁰

Partial pressure of immiscible liquids  

Let ‘A’ and ‘B’ be the two volatile and immiscible liquids; p_A and p_B be the partial pressures of ‘A’ and ‘B’ respectively.  

Then

where m_A and m_B are molar concentrations of ‘A’ and ‘B’ respectively.  

Where W_A, W_B are weights of ‘A’ and ‘B’ and M_A, M_B are molecular weights of ‘A’ and ‘B’ respectively.  

Ideal and Non – Ideal Solutions

The solutions which obey Raoult’s law at all compositions of solute in solvent at all temperature are called ideal solutions.

Ideal solutions can be obtained by mixing two components with identical molecular size, structure and they should have almost same inter molecular attraction e.g., two liquids A and B form an ideal solution when A –A  and B–B molecular attractions will be same and hence A–B molecular atrraction will be almost same as A–A and B–B molecular attraction.

An ideal solution should have following characteristics

• It should obey Raoult’s law i.e., P_A = X_A and P_B = X_B  

• H_mixing = 0, i.e. no heat should be absorbed or evolved during mixing

• V_mixing  = 0, i.e. no expansion or contraction on mixing ?

Examples of  Ideal solutions

• Ethyl chloride and ethyl bromide

• n–hexane and n–heptane

• CCl₄ and SiCl₄

The solution which deviate from ideal behaviour are called  non ideal solution  or real solutions and they do not obey Raoult’s law over entire range of composition.

It has been found that on increasing dilution, a non ideal solution tend to be ideal.

For non ideal solutions,

• P_A  X_AP⁰_A, P_B ¹ X_BP⁰_B i.e, they do not obey Raoult’s law

• H_mixing  0,

• V_mixing  = 0

Here we may have two cases 

Case 1:

Such a solution show positive deviation from Raoult’s Law and the observed boiling point of such solutions is found to be less than the calculated value. e.g. cyclohexane and ethanol. In ethanol the molecules are held together due to hydrogen bonding,  when cyclohexane is added to ethanol the molecules of cyclohexane tend to occupy the space between ethanol molecules due to which some hydrogen bonds break due to which inter molecular attraction between cyclohexane and ethanol is reduced and hence show higher vapour pressure.

Examples of solutions showing positiveedeviation:

• Acetone + Ethanol

• Acetone- Benzene

• Water + Methanol

• Water + Ethyanol

Case 2:

Solutions of above type show negative deviation from Raoult’s law and their observed boiling point is found to be higher than the calculated value eg.  When acetone and chloroform are mixed together a hydrogen bond is formed between them which increases inter molecular attraction between them and hence decreases the vapour pressure

Examples of solutions showing negative deviation:

• Acetone + Aniline

• Chloroform + Diethyl ether

• Chloroform + Benzene 

• Water + HCl

Condition for forming non-ideal solution showing positive deviation

Two liquids A & B on mixing form this type of solutions when

• A-B attractive force should be weaker than A-A and B-B attractive force.

• “A” and “B” have different shape, size and character.

• “A” and “B” escape easily showing higher vapour pressure than the expected value.

Condition for forming non-ideal solution showing negative deviation

Two liquids A & B on mixing form this type of solutions when

• A-B attractive force should be greater than A-A and B-B attractive force.

• “A” and “B” have different shape, size and character.

• Escaping tendency of both “A” and “B” is lower showing lower vapour pressure than expected ideally. 

Azeotropes

The non-ideal solutions showing large deviations from Roult’s law cannot be purified by distillation.

A solution at certain composition which continues to boil at constant temperature without change in the composition of the solution is called an Azeotrope or Constant boiling mixture.

Azeotropes with minimum vapour pressure and Minimum boiling point:

When liquid in a solution do not have great chemical affinity for each other their higher escape tendencies increase the vapour pressure much more than expected on the basis of Roult’s Law. In many cases the deviation are so extreme as to lead to a maximum in the curve. The point of maximum vapour pressure means that the boiling point at this composition will be minimum and constant.

Azeotropes with minimum vapour pressure and Maximum  boiling point:

When liquids in solution show –ve deviation from ideality, their escape tendencies and hence the vapour pressure decreases than expected on the basis of Roult’s Law. In many cases, the maximum in the temperature composition curve is obtained. The point of minimum vapour pressure in the curve means that the boiling point of this composition will be maximum and constant.

Comparison Between Ideal and Non-ideal Solutions    

Theory of Fractional Distillation

Consider the distillation of a mixture of composition x. The vapour given off has the composition x₁. The composition of residual liquid will shift towards A. In the mean time the composition of the distillate shifts towards C. ultimately by repeated fractional distillation, the mixture of composition C will be obtained as distillate and pure liquid A will be left as residue. It will never be possible to have pure B.

When a mixture of composition y is distilled, the vapour given off has the composition y₁, i.e., the composition of residual liquid will shift towards B. Ultimately the mixture of composition C will be obtained as distillate and pure liquid B will be left as residue. It will never be possible to have pure A.

There are several quid pairs which form minimum boiling point azeotropes. Some examples are given in the following table.

 

 liquid and vapour phases have been shown in Fig. 5.4. The curves meet at point C. At this point both liquid and vapour phases have same composition. The constant-boiling mixture has maximum boiling point.

Consider distillation of a mixture of composition x. The vapour coming off is richer in A as indicated by composition x₁. The composition of the residual liquid shifts towards C. As the distillation proceeds, the composition of the distillate moves towards A and that of residue towards. C.

Similarly, a mixture of composition lying between B and C, say y, on distillation will gie vapour richer in B as indicated by composition y₁. The composition of residual liquid shifts towards C and distillate towards A on repeated distillation.

It is never possible to separate a mixture completely into the pure components A and B. It mainly gives a constant boiling mixture (azeotropes) which can never be separated by distillation.

There are several liquid pairs which form maximum boiling point azeotrope. Some examples are tabulated below:

Question 1: Enthalpy of mixing  for an  ideal solution is 

a. 0

b. -ve

c. +ve

d. may be positive or negative depending on the nature of liquids

Question 2: For pure liquids X_A =

a. 0

b. 1

c. 0.1

d. 0.5

Question 3: Which of the followings is not an ideal solution?

a. Ethyl chloride and ethyl bromide

b. n–hexane and n–heptane

c. CCl₄ and SiCl₄

d. Acetone and Aniline

Question 4: Which of the following solutions does not  show positive deviation? 

Acetone  and  Ethanol

Toluene and Benzene

Water and  Methanol

Water and Ethyanol

Related Resources

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• Look here for reference books of chemistry

• You can also refer methods of expressing concentration of solution

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