Solubility of Liquids in Liquids

Binary Solutions

It is very common for two or more liquids to be mixed to make a solution. Therefore, we need to know what liquids can be mixed without precipitation. Examples of pharmaceutical solutions of liquid dissolved in liquids are hydroalcoholic solutions, aromatic waters, spirits, elixirs, lotions, sprays, and some medicated oils that contain a mixture of two or more miscible oils. When two or more liquids are mixed they can be completely miscible, partially miscible, or practically immiscible. Completely miscible liquids mix uniformly in all proportions and hence do not get separated. Partially miscible liquids form two immiscible liquid layers, each of which is a saturated solution of one liquid in the other. Such liquid pairs are called conjugated liquid pairs.

The mutual solubility of partially miscible liquids, being temperature specific, is affected by changes in temperature. For binary phase systems, such as the phenol-water system, the mutual solubility of two conjugate liquid phases increases with an increase in temperature called conjugate temperature, whereas above this temperature they are soluble in any proportions. Other examples of partial miscibility include conjugate liquid pair of nicotine and water, ether and water, and triethanolamine and water. Immiscibility refers to those systems which do not mix at all such as water and liquid paraffin or water and oil. The dielectric constant of a substance also affects the solubility of the substance, Fig. 1.

Effect of Dielectric Constant on Solubility
Figure 1: Effect of Dielectric Constant on Solubility

It is a known fact that the polarity of solvent is dependent on the dielectric constant. Also, remember that LIKE DISSOLVES LIKE. The influence of a foreign substance on a liquid-liquid system is like the idea of the three-component system in the phase rule. Ternary systems are produced by the addition of a third component to a pair of partially miscible liquids to produce a solution. If an added component is soluble in only one of the two components or if its solubility in the two liquids is markedly different, the mutual solubility of the liquid pair is decreased. If the added solute is roughly soluble in both the liquids approximately to the same extent, then the mutual solubility of the liquid pair is increased. This is called blending. An example of this is when succinic acid is added to the phenol-water mixture. The succinic acid is soluble or completely miscible in each phenol and water therefore it causes a blending of the liquids making the mixture one phase.

Ideal Solutions

Dilute solutions consist of a negligible amount of solute compared to pure solvents. These solutions are referred to as ideal solutions. An ideal solution is one in which there is no change in the properties of the components other than dilution when they are mixed to form the solution. No heat is evolved or absorbed during the solution formation. The final volume of the real solution is an additive property of the individual component. In another way, it can be stated as a solution that shows no shrinkage or expansion when components are mixed to form a solution. Ideal solutions are formed by mixing different substances having similar properties and therefore there is complete uniformity of attractive intermolecular forces. For example, when equal amounts of methanol and ethanol are mixed, the final volume of the solution is the sum of the volumes of the methanol and ethanol.

Solutions used in pharmacy consist of a wide variety of solutes and solutions. The basis of solubility and solution theory is based on an ideal solution. In an ideal solution, there is a complete absence of attractive or repulsive forces and therefore the solvent does not affect solubility. The solubility, in this case, depends on temperature, the melting point of solute, and the molar heat of fusion (∆Hf). An ideal solution heat of the solution is equal to ∆Hf. Therefore solubility in an ideal solution can be expressed by,

Solubility of Liquids
Equation (1)

Where Xi2 is the ideal solubility in terms of mole fraction, R is gas constant; T is the temperature of the solution, and To is the temperature (Kelvin) of solute. Equation (1) can be used to calculate molar heat of fusion by plotting the log solubility versus reciprocal of absolute temperature which results in a slope of  ∆Hf/2.303R. Unfortunately, most of the solutions are non-ideal (real) because there may be an interaction between solute and solvent.  In these solutions mixing of solute and solvent can release or absorb heat into or from surroundings, respectively. While describing a non-ideal solution, the activity of the solute must be considered. The activity of solute is defined as the concentration of solute multiplied by the activity coefficient (X2). The activity coefficient is proportional to the volume of solute and the fraction of the total volume occupied by the solvent. On substitution these values in equation (1) we get;

Liquids in Liquids
Equation (2)

As activity approaches unity, the solution becomes more ideal. For example, as a solution become more dilute the activity increases and the solution becomes ideal. The log of activity coefficient (log X2) is the term that considers the work of solubilization, volume of solute, and the volume of solvent. The work of solubilization includes the intermolecular forces of attraction removing molecule from the solid and integrating into the solvent. One more term solubility parameter (γ2) which is a measure of cohesive forces between like molecules is considered for solubility. It is expressed by the following equation.

Equation (3)
Equation (3)
Equation (3)
Equation (3)

Where ∆Hv is the heat of vaporization of solute, V1 is volume/mole of solute as a liquid, V1 is the molar volume of solute and φ12 is the volume fraction of solvent, T is the temperature (Kelvin) and R is gas constant.

Example: The molar heat of fusion and melting point of benzoic acid is 4139 cal/mole and 122°C, respectively. Calculate ideal mole fraction solubility of benzoic acid at 25o C. Given: Gas constant = 8.134 J/K mole.

Solubility of Liquids in Liquids
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