Raoult's law is a law of thermodynamics established by French chemist
François-Marie Raoult in 1882. It states that the partial vapor pressure of each
component of an ideal mixture of liquids is equal to the vapor pressure of the
pure component multiplied by its mole fraction in the mixture.
Mathematically, Raoult's law for a single component in an ideal solution is
stated as where is the partial vapor pressure of
the component in the gaseous mixture, is the vapor pressure of the pure
component , and is the mole fraction of the component in the mixture.
Once the components in the solution have reached equilibrium, the total vapor
pressure of the solution can be determined by combining Raoult's law
with Dalton's law of partial pressures to give
If a non-volatile solute is dissolved into a solvent to form an ideal
solution, the vapor pressure of the final solution will be lower than that
of the pure solvent. Principle
Raoult's law is a phenomenological law that assumes ideal behavior based on the
simple microscopic assumption that intermolecular forces between unlike
molecules are equal to those between similar molecules: the conditions of an
ideal solution. This is analogous to the ideal gas law, which is a limiting law
valid when the interactive forces between molecules approach zero, for
example as the concentration approaches zero. Raoult's law is instead valid if
the physical properties of the components are identical. The more
similar the components are, the more their behavior approaches that described
by Raoult's law. For example, if the two components differ only in isotopic
content, then Raoult's law is essentially exact.
Comparing measured vapor pressures to predicted values from Raoult's law
provides information about the true relative strength of intermolecular
forces. If the vapor pressure is less than predicted, fewer molecules of each
component than expected have left the solution in the presence of the other
component, indicating that the forces between unlike molecules are stronger.
The converse is true for positive deviations.
For a solution of two liquids, A and B, Raoult's law predicts that if no other
gases are present, then the total vapor pressure above the solution is equal to
the weighted sum of the "pure" vapor pressures of the two components, and .
Thus the total pressure above the solution of A and B would be
Since the sum of the mole fractions is equal to one,
This is a linear function of the mole fraction , as shown in the graph.
Thermodynamic considerations Raoult's law was originally discovered
as an idealised experimental law. Using Raoult's law as the definition of an
ideal solution, it is possible to deduce that the chemical potential of each
component of the liquid is given by where is the chemical potential of
component i in the pure state. This equation for the chemical potential may
then be used to derive other thermodynamic properties of an ideal
solution. However, a more fundamental
thermodynamic definition of an ideal solution is one in which the chemical
potential of each component is given by the above formula. Assuming also that
the vapor mixture acts as an ideal gas, it is then possible to re-derive
Raoult's law as follows. If the system is at equilibrium, then
the chemical potential of the component i must be the same in the liquid
solution and in the vapor above it. That is,
Assuming the liquid is an ideal solution, and using the formula for the
chemical potential of a gas, gives: where is the fugacity of the vapor of
and indicates the reference state. The corresponding equation for pure in
equilibrium with its vapor is: where * indicates the pure component.
Subtracting the equations gives us which re-arranges to
The fugacities can be replaced by simple pressures if the vapor of the solution
behaves ideally i.e. which is Raoult's Law.
= Ideal mixing = An ideal solution would follow Raoult's
Law, but ideal solutions do not exist. The fact that the vapor above the liquid
is taken to be ideal is the least of our worries. Interactions between gas
molecules are typically quite small, especially if the vapor pressures are
low. The interactions in a liquid however are very strong. For a solution
to be ideal we must assume that it does not matter whether a molecule A has
another A as neighbor or a B molecule. This is approximately true only if the
two species are almost identical chemically. One can see that from
considering the Gibbs free energy change of mixing:
This is always negative, so mixing is spontaneous. However the expression is,
apart from a factor –T, equal to the entropy of mixing. This leaves no room
at all for an enthalpy effect and implies that must be equal to zero and
this can only be true if the interactions U between the molecules are
indifferent. It can be shown using the Gibbs–Duhem
equation that if Raoult's law holds over the entire concentration range x = 0–1
in a binary solution then, for the second component, the same must also
hold. If deviations from the ideal are not too
large, Raoult's law is still valid in a narrow concentration range when
approaching x = 1 for the majority phase. The solute also shows a linear
limiting law, but with a different coefficient. This law is known as
Henry's law. The presence of these limited linear
regimes has been experimentally verified in a great number of cases. In a
perfectly ideal system, where ideal liquid and ideal vapor are assumed, a
very useful equation emerges if Raoult's law is combined with Dalton's Law.
where is the mole fraction of component in the solution and is its mole
fraction in the gas phase. This equation shows that, for an ideal solution where
each pure component has a different vapor pressure, the gas phase is
enriched in the component with the higher pure vapor pressure and the
solution is enriched in the component with the lower pure vapor pressure. This
phenomenon is the basis for distillation.
= Non-ideal mixing = Raoult's Law may be adapted to non-ideal
solutions by incorporating two factors that account for the interactions
between molecules of different substances. The first factor is a
correction for gas non-ideality, or deviations from the ideal-gas law. It is
called the fugacity coefficient. The second, the activity coefficient, is a
correction for interactions in the liquid phase between the different
molecules. This modified or extended Raoult's law
is then written: Real solutions
Many pairs of liquids are present in which there is no uniformity of
attractive forces, i.e., the adhesive and cohesive forces of attraction are
not uniform between the two liquids, so that they deviate from the Raoult's law
applied only to ideal solutions. = Negative deviation =
If the vapor pressure of a mixture is lower than expected from Raoult's law,
there is said to be a negative deviation. This is evidence that the
adhesive forces between different components are stronger than the average
cohesive forces between like components. In consequence each component is
retained in the liquid phase by attractive forces that are stronger than
in the pure liquid so that its partial vapor pressure is lower.
For example, the system of chloroform and acetone has a negative deviation
from Raoult's law, indicating an attractive interaction between the two
components that has been described as a hydrogen bond. The system hydrochloric
acid - water has a large enough negative deviation to form a minimum in the vapor
pressure curve known as a azeotrope, corresponding to a mixture that
evaporates without change of composition.
= Positive deviation = When the cohesive forces between like
molecules are greater than the adhesive forces between dissimilar molecules, the
dissimilarities of polarity leads both components to escape solution more
easily. Therefore, the vapor pressure is greater than expected from the Raoult's
law, showing positive deviation. If the deviation is large, then the vapor
pressure curve shows a maximum at a particular composition and form a
positive azeotrope. Some mixtures in which this happens are benzene and
methanol, carbon disulfide and acetone, and chloroform and ethanol.
Electrolytes solutions The expression of the law for this case
includes the van 't Hoff factor. See also
Atomic theory Azeotrope
DECHEMA model Dühring's rule
Henry's law Köhler theory
Solubility References
Chapter 24, D A McQuarrie, J D Simon Physical Chemistry: A Molecular
Approach. University Science Books. E. B. Smith Basic Chemical
Thermodynamics. Clarendon Press. Oxford