Concept of Binary Liquid Solutions:

You must have heard of the binary compounds. What are they? These are the compounds which are comprised of just two elements. These elements could be a metal and a non-metal and they can as well be metals. In the case of binary liquid solution make an attempt to describe what it implies. The binary liquid solutions are the liquid solutions comprised of two liquids. Whenever two liquids 'A' and 'B' are mixed totally there are three possibilities:

1) Liquid 'A' is completely miscible with liquid 'B' in all the proportions (example: water and ethanol, toluene and benzene and so on).

2) Liquids 'A' and 'B' are just partially miscible in one other (example: water and phenol).

3) Liquids 'A' and 'B' are completely immiscible with one other (example: water and palm oil).

Completely miscible liquids:

The orange juice and carbonated water are the two liquids you can simply find out at a grocery store. Whenever you mix both the liquids altogether the best orange juice fizz drink is formed. Did you identify the recipe for making this drink is a great illustration of a chemical property termed as miscibility.

Miscibility signifies to the capability of a liquid to completely dissolve in the other liquid solution. A dissimilar layer among the two liquids will not form whenever you have a solution which is labeled miscible. Whenever a distinct layer does form in a mixed solution this is termed as immiscibility. For illustration: a kind of immiscible liquid is water and oil. Whenever mixed altogether, oil will basically 'sit on top' of water ensuing in the formation of a very perceptible layer.

In chemistry, you can make use of this concept of forming a layer whenever you would like to state the difference between the miscible and immiscible liquids. A water curve, termed as a meniscus, will form whenever two liquids are immiscible. Therefore, miscible liquids will not contain a meniscus.

Miscibility basically signifies how completely two or more liquids dissolve in one other. It is qualitative instead of quantitative observation - miscible, partly miscible and not miscible. (To state precisely how miscible two liquids were, a scientist would make use of the bigger concept of solubility, generally in a specific weight or volume per litre of solution.) The two completely miscible liquids will make a homogeneous (that is, uniform) solution in any amount. Water and ethyl alcohol, for illustration, are completely miscible whether the solution is 1% water and 99% ethyl alcohol, 50% of both, or 1% ethyl alcohol and 99% water. Whenever first mixed, miscible liquids frequently illustrate oily bands - termed as striations - in the bulk of the solution; these disappear whenever mixing is complete.

Similar to any other solubility phenomenon, the miscibility based on the forces of attraction between the molecules of the various liquids. The rule of thumb 'Like dissolves like' implies that liquids having similar molecular structures, in specific similar polarity, will probable dissolve in one other. (The Polarity signifies the extent to which the partial positive and negative charges appear on the molecule, as the kind and arrangement of its component atoms.) Both the water and ethyl alcohol encompass very polar hydroxyl groups (-OH) on their molecules, and thus both experience the strong intermolecular attraction termed as 'hydrogen bonding'. Hexane, on the other hand, is not miscible by water as its molecular structure includes no polar groups of any type which would be attracted to the water molecules.

Raoult's Law:

Raoult's law defines that the vapor pressure of a solvent above a solution is equivalent to the vapor pressure of the pure solvent at similar temperature scaled via the mole fraction of the solvent present.

Raoult's Law is represented by:

P_solution = Χ_solvent P^o_solvent

Here,

P_solution is the vapor pressure of solution.

Χ_solvent is the mole fraction of solvent.

P^o_solvent is the vapor pressure of pure solvent.

In the year 1880s, French chemist Francois-Marie Raoult discovered that whenever a substance is dissolved in the solution, the vapor pressure of the solution will usually decrease. This observation based on two variables:

A) The mole fraction of the quantity of dissolved solute present and

B) The original vapor pressure (that is, pure solvent).

At any specific temperature for a particular solid or liquid, there is a pressure at which the vapor made up above the substance is in dynamic equilibrium with its liquid or solid form. This is the vapor pressure of substance at that temperature. At equilibrium, the rate at which the solid or liquid evaporates is equivalent to the rate which the gas is condensing back to its original form. All the solids and liquids encompass a vapor pressure, and this pressure is constant apart from of how much of the substance is present.

The vapor pressure of the solution (P_total) is the sum of the partial pressures of the components, that is, for the solution of two volatile liquids having vapor pressures P_A and P_B.

P_total = P_A + P_B = (P^o_A x X_A) + (P^o_B x X_B)

On the other hand, Raoult's law might be defined as 'the relative lowering of vapor pressure of a solution having a non-volatile solute is equivalent to the mole fraction of the solute in the solution'.

Relative lowering of vapor pressure is stated as the ratio of lowering of vapor pressure to the vapor pressure of the pure solvent. This is determined by the Ostwald-Walker method.

Therefore, according to the Raoult's law,

(P^o - P)/P^o = n/(n+N) = (w/m)/[(w/m) + (W/M)]

Here, 

P = Vapor pressure of the solution

P^o = Vapor pressure of the pure solvent

n = Number of moles of the solute

N = Number of moles of the solvent

w and m are the weight and molecular weight of solute

W and M are the weight and molecular weight of the solvent

Example of Raoult's law:

Assume we have 100 mL of water and 100 mL of ethylene glycol in two dissimilar containers. If the vapor pressure of pure water is 500 mmHg, we would like to compute the new vapor pressure of the solution which is made up by mixing the two substances altogether. This is a direct application of the Raoult's law.

Limitations of Raoult's law:

a) The Raoult's law is applicable only to very dilute solutions.

b) Raoult's law is applicable to solutions having only non-volatile solute.

c) Raoult's law is not applicable to solutes that associate or dissociate in the particular solution.

Ideal solutions:

A solution which obeys Raoult's law at all concentrations and at all temperatures is termed as an ideal solution. The two liquids A and B on mixing form an ideal solution, if:

a) The molecules of A and B encompass similar structure and polarity, and

b) The intermolecular attractions between A and A, B and B, and A an B are similar.

The theory of an ideal solution is basic to chemical thermodynamics and its applications, like the use of Colligative properties. The ideal solution or ideal mixture is a solution in which the enthalpy of solution (ΔH_solution = 0) is zero; with the closer to zero the enthalpy of solution, the more 'ideal' the behavior of the solution becomes. As the enthalpy of mixing (that is, solution) is zero, the change in Gibbs energy on mixing is determined solely through the entropy of mixing (ΔS_solution).

Some of the illustrations of nearly ideal liquid mixtures are:

a) Ethylene bromide and ethylene chloride

b) Benzene and toluene

c) n-hexane and n-heptane

d) n-butyl chloride and n-butyl bromide

e) Carbon tetrachloride and silicon tetrachloride

Non Ideal Solutions:

Most of the completely miscible liquid pairs form the non-ideal solutions. These solutions don't obey the Raoult's law. They either exhibit positive deviation (that is, whenever the vapor pressure of the solution is higher than that of the ideal solution of similar concentration) or negative deviation (that is, when the vapor pressure of the solution is lower than that of the ideal solution of similar concentration) from the Raoult's law.  In such solutions,

P_A = P^o_AxA

P_B = P^o_BxB

If the components of a non-ideal solution are mixed, a considerable change in the volume and enthalpy is observed. Therefore the features of non-ideal solutions are as shown below:

a) They don't obey the Raoult's law.

b) ΔH_mix > 0

c) ΔV_mix > 0

Liquid Pairs Showing Deviation from Raoult's Law:

=> Illustrations of solutions exhibiting the negative deviation.

a) Pyridine and formic acid (or acetic or propanoic acid): One of the components is basic and the other one is acidic.

b) Mixture of halomethane (example: chloroform) having an oxygen or nitrogen compound (example: a ketone, ether, amine or ester): In this case, there takes place a partial association among the molecules via the hydrogen bonding.

c) The aqueous solution of a strong volatile acid like halogen acids, nitric acid and perchloro acids: In this case, non-volatile ions are made up by the interaction of ions of the acid with water.

=> Illustrations of solutions exhibiting the positive deviation.

a) Carbon tetrachloride and heptane at 323 k: This solution exhibits the small deviations from Raoult's law as both the constituents are non-polar and comprise low forces of attraction.

b) Ethyl ether and acetone at 293 K and 303 K: Deviations here are bit bigger as the components vary appreciably in the intermolecular attraction forces.

c) Heptane and ethyl alcohol at 323 K: This solution exhibits very big deviations as the two liquids differ appreciably in all the above four factors, that is, polarity, chain-length, intermolecular forces of attraction and the association of alcohol in the liquid state.

Ideal Solutions of Volatile Solutes:

Whenever two volatile liquids make an ideal solution, each will form a contribution to the overall vapor pressure which is directly proportional to the vapor pressure of the pure liquid and to its mole fraction in the solution. This is merely Raoult's law again, and it as well gives an operational definition for the ideal solution: an ideal solution is one which follows the Raoult's law.

In case of Raoult's law for volatile solute, we have to compute both the partial pressure applied by the vapor of the volatile solute and the vapor pressure of the solvent. The vapor pressure of the mixture is simply associated to the vapor pressure of pure substance present in the solution, whenever the two substance whose molecules are very similar from a liquid solutions. The sum of both vapor pressures will provide the total vapor pressure of the solution. For illustration: we mix 1 mole of benzene to the 1 mole of toluene.

The mole fraction of benzene (X_b) and the mole fraction of toluene (X_t) are equivalent to 0.5. The measured vapor pressure of the mixture is less than the average vapor pressure of the benzene and toluene at that temperature 79.6°C.

Measured vapor pressure of the mixture = 516 mm Hg

Vapor pressure of toluene = 290 mm Hg

Vapor pressure of benzene = 744 mm Hg

The average vapor pressure = 744 + 290 = 517 mm Hg

Raoult's law is utilized to illustrate the behavior of the substance. Here benzene and toluene acts as same as how they act in the pure liquids.

The rate at which benzene molecules get away from the surface of the solution will be half the rate at which they would escape from the pure liquid, as there are only half as most of the benzene molecules in the mixtures as in pure benzene. In similar manner partial vapor pressure of the benzene in mixture will be one half of the vapor pressure of the pure benzene, in other hand partial vapor pressure of the toluene in mixture will be one 

P_b = 1/2 P_b* and P_t = 1/2 P_t*

Here,

P_b = Partial pressure of benzene

P_t = Partial pressure of toluene

P_b* = vapor pressure of benzene

P_t* = vapor pressure of toluene

The total vapor pressure of solution is:

P = P_b + P_t

P = 1/2 P_b* + 1/2 P_t*

P = (P_b* + P_t*)/2

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