# Raoult’s law

Raoult’s law (1887)

According to this law, “The relative lowering of vapour pressure is equal to the ratio of the moles of the solute and the total  number of moles in the solution”, i.e., the mole fraction of the solute present in solution.

Thus,

$\dfrac{P- P_s}{P} = \dfrac{n}{n + N}$

where ‘n’ = Number of moles of solute and ‘N’ = Nmuber of moles of solvent.

For very dilute solution, N >> n, the above equation may be written as:

$\dfrac{P- P_s}{P} = \dfrac{n}{N}$

Let ‘w’ be the mass of solute, ‘W’ be the mass of solvent, ‘m’ the molecular mass of solute and ‘M’ the molecular mass of solvent.

Then,

$n =\dfrac{w}{m} \text{and} N = \dfrac{W}{M}$

Hence the above equations may be written as:

$\dfrac{P- P_s}{P} = \dfrac{w/m}{(w / m) + (W / M)} = \dfrac{w / m}{W / M}$ (for N > n)

Thus knowing the relative lowering of vapour pressure, mass of solute and solvent, and molecular mass of solvent, the molecular mass of solute can be calculated.

It is important to note that Raoult’s law is obeyed only by ideal solutions. Hence, “a solution of two or more constituents which obey Raoult’s law at all concentrations and temperatures is called ideal solution”.

On the other hand, a solution which does not obey Raoult’s law is termed as non-ideal solution.

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