Introduction:

Some of the liquids, solutions and compounds mix in a good manner, whereas others do not. The miscible liquids are the liquids which are capable to dissolve fully into each other, making a new homogeneous solution. Miscibility is the capability of two different chemical compounds to mix entirely. This is applicable to solids, liquids and gasses.

Defining Homogeneous and Heterogeneous Solutions:

A homogeneous mixture or solution is the substance having uniform composition. Its composition appearance, tastes, or feels the similar all the way through. Illustrations of homogeneous solutions are water, a cup of coffee, a bottle of clear vinegar and vegetable oil. On the other hand, a heterogeneous solution is the mixture or a combination of two dissimilar substances which don't encompass uniform composition. Smog is a heterogeneous combination, where small particles are identifiable in the atmosphere. Other illustrations of heterogeneous solutions are, a bowl of oatmeal and fruit, salad dressing by ground pepper, and a milkshake having fruit bits.

Illustrations of Miscible Liquids:

The miscible liquids join to form homogeneous solutions. Whenever two liquids are combined, it becomes impossible to differentiate one from the other. Rather, the combination becomes a totally different solution. Illustrations of miscible liquids and compounds are alcohol and water, milk and water, wine and water, soda and gin, and vinegar and water.

Definition of Partial Miscibility and Immiscibility:

The immiscible liquids are incapable of mixing entirely. The combination of two immiscible compounds generally outcomes in a heterogeneous mixture, having the compounds still distinguishable from one other. On the other hand, partial miscibility implies the inability of liquids or compounds to mix totally. Immiscible and partially miscible mixtures are frequently characterized by a meniscus line.

Examples of Partially Miscible and Immiscible Liquids:

Illustrations of immiscible liquids are cooking oil and water, milk and oil, gasoline and water, and liquid metals and water. There are as well partially miscible liquids such as honey and water, butanol and water, and potassium chloride and water.

Miscibility and chemical solubility are frequently interchanged by one other. Solubility is the capability of two compounds, one is liquid and the other solid, to join and make a homogeneous solution. Good illustrations of soluble compounds are coffee powder, sugar or salt dissolved in water. Miscibility comprises the combination of two immiscible, partially miscible and miscible liquids.

Partially Miscible Liquid Systems:

Some of the liquid pairs don't give homogeneous solutions at all compositions. These liquid pairs are stated to be partially miscible liquids. Though due  to  increased solubility  by  increase  or decrease  in temperature,  these might become fully  miscible. We can illustrate such a system of liquids phenol and water. Whenever a very small amount of phenol is added to water at room temperature, it dissolves fully to provide a single phase.  Though, if the addition of phenol is continued, a point is reached when phenol doesn't dissolve anymore. At this point, two phases, that is, two liquid layers are made up-one comprising of water saturated with phenol and the other having phenol saturated by water. Moreover, addition of phenol causes water to shift from water-rich layer to phenol-rich layer. When addition of phenol is continued, a point is reached when phenol acts as the solvent for all the water present and the two phases merge with one other to form a single  phase,  that is, solution  of water in phenol. Therefore, on shaking equivalent volumes of phenol and water, two layers are made up - one of phenol in water and the other of water in the phenol.

This has been experimentally found out that at constant temperature, the composition of the two   layers, however different from one other, remains constant as long as the two phases are present.  These solutions of various compositions co-existing with one other are known as conjugate solutions.  The addition of small quantity of phenol or water changes the volume of the two layers and not via compositions. As the temperature is raised, the behavior remains the same apart from that the mutual solubility of the two phases raises. Whenever the temperature reaches 338.8 K, the composition of the two layers becomes similar and afterward the two liquids are completely miscible, that is, at and above 338.8 K, phenol and water dissolve in one other in all proportions and yield merely a single liquid layer on mixing. The variation of mutual solubility of water and phenol by temperature is illustrated in the figure shown below.

Fig: Mutual solubility of water and phenol with temperature

At a specific temperature state 325 K, point A1 symbolizes the composition of water-rich layer and point A2 symbolizes the composition of phenol-rich layer in equilibrium. Between such compositions, all the mixtures will yield two layers of compositions A1 and A2. Outside these compositions, the two liquids are soluble mutually at around 325 K. Similar behavior is seen at other temperatures beneath 338.8 K. We can conclude that the dome-shaped area symbolizes the range of existence of two liquid phases and the area outside the dome symbolizes a single liquid phase. The temperature corresponding to the point B, that is, the temperature at which the solubility becomes complete is termed as the critical solution temperature. As the mutual solubility of phenol and water rises with increase in temperature, the critical solution temperature (CST) lies well above the room temperature. Therefore, these liquid systems are stated to possess an upper critical solution temperature or upper consolute temperature. Therefore, the critical solution temperature for phenol-water system is 338.8 K. At and above 338 8 K phenol and water are fully miscible with one other in all proportions. At this temperature, the composition of the solution is 36.1% phenol and 63.9% water.

Triethylamine Water System:

There are some partially miscible liquid pairs where the mutual solubility is found to raise with decrease in temperature. In the case of triethylamine-water system for illustration, at or below 291.5 K, the two liquids are completely miscible, whereas above this temperature, the two liquids are just partially miscible. The temperature beneath which the two liquids become completely miscible is termed as the lower critical solution temperature as the curve confining the area of partial miscibility shows a minimum. Some other illustrations of this kind are: diethylamine-water (416K) and 1-methyl piperidine-water (321K).

Nicotine Water System:

These systems show an upper and also lower critical solution temperature. In the enclosed area, the two liquids are merely partially miscible and a heterogeneous system exists whereas outside this area, there is only a single layer exists that is, a homogeneous phase is present. The upper or maximum CST is 481 K whereas the lower or minimum CST is 333.8 K.

The CST of this system is influenced by the pressure. On applying the external pressure to system, the upper and the lower CST approach one other until a pressure is reached whenever the two liquids become completely miscible. Other systems of this kind are:

Glycerol-w-toluidine (280K and 393K)

Methyl ethyl ketone-water (279K and 406K)

This is supposed that all partially miscible systems in general exhibit an upper and also a lower critical solution temperature. In most of the cases one of them might not be experimentally realized due to some physical conditions.

There are as well some liquid pairs such as diethyl ether-water which don't exhibit an upper or a lower CST. They are mere partially miscible in one other at all temperatures.

The critical solution temperature is influenced considerably through the presence of foreign substances. If the foreign substance is soluble in just one of the liquids, the mutual solubility is decreased resultant in an increase in the critical solution temperature. For illustration: 0.15M KCl increases the critical solution temperature of phenol-water system by around 12K. On the other hand, if the foreign substance dissolves in both the liquids equally, the mutual solubility is increased and critical solution temperature is lowered. For illustration: 0.083M sodium oleate reduces the CST of phenol-water system to 329.7 K.

Immiscible Liquid pairs:

In case of completely immiscible or nearly completely immiscible liquid pairs, the addition of one liquid to the other does riot influences the properties of either liquid. Therefore, each liquid behaves as if the other is not present. Accordingly, in the mixture of two immiscible liquids, each and every liquid applies its own vapor pressure corresponding to the pure liquid at specific temperature. The total vapor pressure 'P' above the mixture is thus, the sum of the vapor pressures of the two pure liquids at that temperature. Therefore,

P = P°_A P°_B

Here P°_A and P°_B are the vapor pressures of the two pure liquids A and B at that temperature. The pressure applied by each layer and therefore the total pressure don't depend on the actual or relative amounts of the liquids present.

Any system, as we are familiar boils at a temperature if its total vapor pressure becomes equivalent to the external pressure. In this case, as the two liquids altogether can reach any given total pressure at a lower temperature than either liquid alone, it is evident that the mixture would boil at a temperature than either liquid alone, it is obvious that the mixture would boil at a temperature lower than the boiling point of either of the two liquids. Moreover, as at any given temperature there is no change in total vapor pressure having change in composition, the boiling point of all possible compositions of any two immiscible liquids remains constant, as long as the two liquids are present. The temperature increases to T_A or T_B based on whether A or B remains, only if one of the liquids is boiled away.

The relative proportions of two liquids in the distillate can be computed, as the number of moles of each and every component in the vapor phase is proportional to its vapor pressure. At boiling point T, if n_A and n_B are the number of moles of the two liquids A and B in the vapor phase, then

n_A α P^o_A

n_B α P^o_B                                              

Or, n_A/n_B = P^o_A/P^o_B

The composition of vapor remains constant, as P°_A and P°_B are constants at a particular temperature 'T'. If W_A and W_B are the actual weights of the two liquids A and B in the distillate, and M_A and M_B the respective molecular weights, then

P^o_A/P^o_B = (W_A M_B)/(W_B M_A)

Or W_A/W_B = (P^o_A M_A)/(P^o_B M_B)

The above equation associates directly to the ratio of the weights of the two components present in the distillate of the mixture of two immiscible liquids to the molecular weights and vapor pressure of the two pure components.

Illustrations of such pairs comprise water-cyclohexane, water-nitro-benzene, water-bromobenzene and so forth, Distillation of immiscible liquids is used industrially and in the laboratory as it comprises lowering of boiling points of the components. The purification of organic liquids which either encompass very high boiling point or tend to decompose whenever heated to their boiling point can be properly taken out by using the above principle. The other liquid is usually water and the process is termed to as the Steam Distillation.

The immiscible mixture of the liquid and water is either heated directly or through passing the vapors of steam to the liquid and the vapors distilling over are condensed and separated. In this way it is possible to distil numerous organic liquids of high boiling point at temperatures beneath 373K that is the boiling point of water.

Fig: Steam distillation

The apparatus is as illustrated in the figure shown above. Steam from the steam generator is passed to the round-bottom flask having the liquid, state nitrobenzene or bromobenzene to be steam distilled. The tube carrying the steams dips to the liquid and the flask is heated smoothly on a sand bath to shun too much condensation of water into it. The vapors of the organic liquid mixed by steam distil over, condense and collect in the receiver. The organic liquid is then separated from the aqueous layer and at last dried. The proportion by mass of the organic liquid which distils over is associated directly to its vapor pressure and molecular weight. Therefore a higher proportion of the liquid is obtained for liquids having high molecular weights and having a relatively high vapor pressure at about the boiling point of water.

Concept of Distribution Law:

According to the Nernst's Distribution law (in the year 1891) or Partition law, 'If a solute is taken up by two immiscible liquids, in both of which the solute is soluble, the solute distributes itself among the two liquids in such a manner that the ratio of its concentration in the two liquid phases is constant at a particular temperature given by the molecular state of the distributed solute is similar in both the phases'.

That is,

C₁/C₂ = K_D

Here, C₁ and C₂ are the concentrations of the solute in two phases. K_D is termed as the distribution coefficient or partition coefficient.

I) If solute undergoes association in one of the solvents, we encompass:

K_D = C₁/n√C₂ or K_D = n√C₁/C₂

Here 'n' = order of association.

II) If solute undergoes dissociation, we encompass:

K_D = C₁/C₂(1-α) or K_D = C₁(1-α)/C₂

Here α = on degree of dissociation

III) If solute is to be extracted from the solution by other appropriate solvent, we encompass:

Amount left un-extracted = W [K_DV/(K_DV + v₁]ⁿ

Here, W = Initial amount present in solution

V = volume of solution,

v₁ volume of extracting solvent

K_D = Distribution coefficient

n = Number of extraction operations

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