Ideal_solution

In chemistry, an ideal solution or ideal mixture is a solution in which the enthalpy of solution is zeroA to Z of Thermodynamics Pierre Perrot ISBN 0198565569; the closer to zero the enthalpy of solution, 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.International Union of Pure and Applied Chemistry. "ideal mixture". Compendium of Chemical Terminology Internet edition.

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 (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 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.

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

$\backslash Delta\; G\_\{\backslash mathrm\{m,mix\}\}\; =\; RT\; \backslash sum\_i\; x\_i\; \backslash ln\; x\_i$

or for a two component solution

$\backslash Delta\; G\_\{\backslash mathrm\{m,mix\}\}\; =\; RT\; (x\_A\; \backslash ln\; x\_A\; +\; x\_B\; \backslash ln\; x\_B)$

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 $\backslash ln\; x\_i$ 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

$\backslash Delta\; G\_\{\backslash mathrm\{m,mix\}\}\; =\; \backslash sum\_i\; x\_i\; \backslash Delta\backslash mu\_\{i,\backslash mathrm\{mix\}\}$

where $\backslash Delta\backslash mu\_\{i,\backslash mathrm\{mix\}\}=RT\backslash ln\; x\_i$ is the change in chemical potential of $i$ on mixing.

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

$\backslash mu\_i\; =\; \backslash mu\_i^*\; +\; \backslash Delta\; \backslash mu\_\{i,\backslash mathrm\{mix\}\}\; =\; \backslash mu\_i^*\; +\; RT\; \backslash ln\; x\_i$

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

$\backslash \; P\_\{i\}=(P\_\{i\})\_\{pure\}\; x\_i$

where

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

$x\_i\backslash ,$ 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

• Activity coefficient
• Entropy of mixing
• Margules function
• Regular solution

References

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