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Ideal solution
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In chemistry, an ideal solution or ideal mixture is a solution in which the enthalpy of solution (or "enthalpy of mixing") is zero; the closer to zero the enthalpy of solution is, the more "ideal" the behavior of the solution becomes. Equivalently, an ideal mixture is one in which the activity coefficients (which measure deviation from ideality) are equal to one.
The concept of an ideal solution is fundamental to chemical thermodynamics and its applications, such as the use of colligative properties.
Physical origin
Ideality of solutions is analogous to ideality for gases, with the important difference that intermolecular interactions in liquids are strong and can not simply be neglected as they can for ideal gases.
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Encyclopedia
In chemistry, an ideal solution or ideal mixture is a solution in which the enthalpy of solution (or "enthalpy of mixing") is zero; the closer to zero the enthalpy of solution is, the more "ideal" the behavior of the solution becomes. Equivalently, an ideal mixture is one in which the activity coefficients (which measure deviation from ideality) are equal to one.
The concept of an ideal solution is fundamental to chemical thermodynamics and its applications, such as the use of colligative properties.
Physical origin
Ideality of solutions is analogous to ideality for gases, with the important difference that intermolecular interactions in liquids are strong and can not simply be neglected as they can for ideal gases. Instead we assume that the mean strength of the interactions are the same between all the molecules of the solution.
More formally, for a mix of molecules of A and B, the interactions between unlike neighbors (UAB) and like neighbors UAA and UBB must be of the same average strength i.e. 2UAB=UAA+ UBB and the longer-range interactions must be nil (or at least indistinguishable). If the molecular forces are the same between AA, AB and BB, i.e. UAB=UAA=UBB, then the solution is automatically ideal.
If the molecules are almost identical chemically, e.g. 1-butanol and 2-butanol, then the solution will be ideal. Since the interaction energies between A and B are the same, it follows that there is no overall energy (enthalpy) change when the substances are mixed. The more dissimilar the nature of A and B, the more strongly the solution is expected to deviate from ideality.
Formal definition
An ideal mix is defined as a mix that satisfies:
where is the fugacity of component and is the fugacity of as a pure substance.
Since the definition of fugacity in a pure substance is:
Where is the molar free energy of an ideal gas at a temperature and a reference presure
which might be taken as or the presure of the mix to ease operations.
If we derivative this last equation with respect to at constant we get:
but we know from the Gibbs potential equation that:
These last two equations put together give:
Since all this, done as a pure substance is valid in a mix just adding the subscript to all the intensive variables and
changing to , standing for Partial molar volume.
Applying the first equation of this section to this last equation we get
which means that in an ideal mix the volume is the addition of the volumes of its components.
Prociding in a similar way but derivative with respect of we get to a similar result with enthalpies
derivative with respect to T ang remembering that we get:
which in turn is .
Meaning that the enthalpy of the mix is equal to the sum of its components.
Since and :
It is also easily verifiable that
Finally since
Which means that
and since
then
At last we can calculate the entropy of mixing since
and
Consequences
Since the enthalpy of mixing (solution) is zero, the change in Gibbs free energy on mixing is determined solely by the entropy of mixing. Hence the molar Gibbs free energy of mixing is
or for a two component solution
where m denotes molar i.e. change in Gibbs free energy per mole of solution, and is the mole fraction of component .
Note that this free energy of mixing is always negative (since each is positive and each must be negative) i.e. ideal solutions are always completely miscible.
The equation above can be expressed in terms of chemical potentials of the individual components
where is the change in chemical potential of on mixing.
If the chemical potential of pure liquid is denoted , then the chemical potential of in an ideal solution is
Any component of an ideal solution obeys Raoult's Law over the entire composition range:
where
is the equilibrium vapor pressure of the pure component
is the mole fraction of the component in solution
It can also be shown that volumes are strictly additive for ideal solutions.
Non-ideality
Deviations from ideality can be described by the use of Margules functions or activity coefficients. A single Margules parameter may be sufficient to describe the properties of the solution if the deviations from ideality are modest; such solutions are termed regular.
In contrast to ideal solutions, where volumes are strictly additive and mixing is always complete, the volume of a non-ideal solution is not, in general, the simple sum of the volumes of the component pure liquids and solubility is not guaranteed over the whole composition range.
See also
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