Vapor Pressure and Raoult's Law

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In 1886 the French chemist Francois Marie Raoult carried out a series of experiments to study the vapor pressure of a number of binary solutions containing non-volatile as well as volatile non electrolyte solutes. On the basis of the results of the experiment he stated a law known as Raoult's law.

It states that,

"In a solution of volatile components, the partial vapor pressure of a component at a given temperature is equal to the mole fraction of that component in the solution multiplied by the vapor pressure of that component in the pure state".

Now, let us consider a mixture of two completely miscible volatile liquids A and B, having the mole fraction x_A and x_B. Suppose at a given temperature their partial vapor pressures are p_A and p_B and the vapor pressure in pure state are:

The total vapor pressure, P exerted by the solution is the sum of P_A and P_B as required by Dalton's law of partial pressures.

P = P_A + P_B

or P = P^o_A c_A + P^o_B c_B

= P^o_A (1-c_B) + P^o_B c_B [because c_A + c_B = 1]

= P^o_A - P^o_A c_B + P^o_B c_B

P = (P^o_B - P^o_A)c_B + P^o_A

Similarly by putting c_B = 1-c_A the vapor pressure of the solution

P = (P^o_A - P^o_B)c_A + P^o_B

fig 3.5

As the values of P^o_A and P^o_B are constants at a particular temperature, it reveals that total pressure is a linear function of c_B or c_A i.e. the plot of P versus c_A or P versus c_B should be a straight line. The variation of P with mole fraction is given by the solid line III in the graph. The solutions which obey Raoult's law are called ideal solutions. For such solutions, the vapor pressure of the solution always lies between the vapor pressure of the pure components.

The vapor pressure of a solution containing non-volatile solute is directly proportional to the mole fraction of the solvent. That is because, there is no contribution towards the vapor pressure of the solution from non volatile component (P_B = 0).

where K is proportionality constant,

Thus, P_A = P^o_A c_A or, P_solution = P_{Pure solvent} x mole fraction of solvent.

In terms of symbols,

But x_A + x_B = 1

or x_A = 1-x_B ……(2)

From equations (1) and (2)

Rearranging

In the above equation p_A^o- p_s represents lowering of vapor pressure and

the mole fraction of the non-volatile solute in the solution.