Ideal solution

In activity coefficients (which measure deviation from ideality) are equal to one.^[2]

The concept of an ideal solution is fundamental to colligative properties.

Physical origin

Ideality of solutions is analogous to 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 (U_AB) and like neighbors U_AA and U_BB must be of the same average strength i.e. 2U_AB=U_AA+ U_BB 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. U_AB=U_AA=U_BB, then the solution is automatically ideally.

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 solutions are mixed. The more dissimilar the nature of A and B, the more strongly the solution is expected to deviate from ideality.

Consequences

Since the enthalpy of mixing (solution) is zero, the change in entropy of mixing. Hence the molar Gibbs free energy of mixing is

ΔG_m,mix = RT	∑	x_ilnx_i
	i

or for a two component solution

Δ G m,mix = R T (x A ln x A + x B ln x B)

where m denotes molar i.e. change in Gibbs free energy per mole of solution, and $x i$ is the mole fraction of component $i$ .

Note that this free energy of mixing is always negative (since each $x i$ is positive and each $ln x i$ 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

ΔG_m,mix =	∑	x_iΔμ_i,mix
	i

where $Δμ i,mix = R T ln x i$ is the change in chemical potential of $i$ on mixing.

If the chemical potential of pure liquid $i$ is denoted $\mu_i^*$ , then the chemical potential of $i$ in an ideal solution is

$\mu_i = \mu_i^* + \Delta \mu_{i,\mathrm{mix}} = \mu_i^* + RT \ln x_i$

Any component $i$ of an ideal solution obeys Raoult's Law over the entire composition range:

$\ P_{i}=(P_{i})_{pure} x_i$

where

$(P_i)_{pure}\,$ is the equilibrium vapor pressure of the pure component

$x_i\,$ 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 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.

References

^ A to Z of Thermodynamics Pierre Perrot ISBN 0198565569
^ International Union of Pure and Applied Chemistry. "ideal mixture". Compendium of Chemical Terminology Internet edition.

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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Ideal_solution". A list of authors is available in Wikipedia.

Ideal solution

Physical origin

Consequences

Non-ideality

See also

References