Solutions B.Sc. 2nd Year Notes

Solutions B.Sc. 2nd Year


Solubility of Gases in Liquids

Gases dissolve in liquids to form homogeneous solutions. The solubility of gas in a liquid depends upon the following factors-
1. The nature of the substance (solute)
2. The nature of the solvent
3. Temperature of the solution
4. Pressure
Some gases like N2, H2, O2 etc. dissolve in water to very small extent whereas the gases like NH3, HCl etc. are highly soluble in water. The most soluble gases are those which chemically react with the liquid solvent.
The solubility of a gases in liquids is greatly influenced by pressure and temperature
1. Effect of temperature: The solubility of a gases decreases with increase in temperature because gases dissolve in a liquid with the evolution of heat (i.e. exothermic process). Therefore, in accordance with Le-Chatelier's principle, the increase in temperature will result in decrease in the solubility of the gas.
2. Effect of pressure: The solubility of gases increases with increase in pressure. This is also in accordance with Le-Chatelier's principle.
Solubility of gas in liquid was explained by Henry's law.
Henry's law stated taht the solubilty of gas increases with incresing the pressure at constant temperature.
Henry's law also stated taht the partial pressure of a gas in vapour phase (p) is proportional to the mole fraction of the gas (X) in a solution.
p ∝ X
or, p =KH X
Where KH = Henry's law constant which depend on the nature of gas and temperature. KH has constant value but different for different gas. KH value increases with increasing the temperature. So, the value of KH is inversely proportional to solubility of gas in liquid.

Raoult’s Law

Raoult’s law stated that relative lowering of vapour pressure is equal to mole fraction of the solute.
if vapour pressure of solvent is P and that of solution is Po, then-
Relative lowering of vapour pressure = (P − Po)/P
if mole fraction of solute is Xsolute then-
(P − Po)/P = Xsolute
if w gm of solute whose molecular mass is m gm dissolve in W gm of solvent whose molecular mass is M then-
mole fraction of solute (Xsolute)-
Xsolute = w/m/(w/m + W/M)
for dilute solutions, w/m is very smaller than W/M. So Xsolute may be written as-
Xsolute = w/m/W/M
Xsolute = w.M/W.m
or, (P − Po)/P = w.M/W.m
or, m = w.M/W.(P − Po)/P
from this equation we can easily calculate the molecular mass of the solute.

Duhem–Margules equation

Duhem–Margules equation is a thermodynamic statement of the relationship between the two components of a single liquid where the vapour mixture is regarded as an ideal gas.
Let consider a binary liquid mixture of two component in equilibrium with their vapor at constant temperature and pressure. Then from Gibbs–Duhem equation is
nAA + nBB = 0 -----(equation-1)
Where nA and nB are number of moles of the component A and B while μA and μB is their chemical potential.
dividing equation-1 by nA + nB we get-
nA/(nA + nA) dμA + nB/(nA + nB) dμB = 0
or, XAA + XAB = 0 -----(equation-2)
Now the chemical potential of any component in mixture is depend upon temperature, pressure and composition of mixture. Hence if temperature and pressure taking constant then chemical potential-
A = (dμA/dXA)T,P . dXA -----(equation-3)
B = (dμB/dXB)T,P . dXB -----(equation-4)
Putting these values in (equation-2), then-
XA(dμA/dXA)T,P . dXA + XB(dμB/dXB)T,P . dXB = 0 -----(equation-5)
we know that sum of mole fraction of all component in the mixture is unity i.e., XA + XB = 1
Hence, dXA + dXB =0
So, equation -5 becomes
XA(dμA/dXA)T,P = XB(dμB/dXB)T,P -----(equation-6)
We know that the chemical potential of any component in mixture is
μ = μo + RTlnP
where P is partial pressure of component. By differentiating this equation with respect to the mole fraction of a component we get-
dμ/dX = RT(dlnP/dX)
so for two component A and B-
A/dXA = RT(dlnPA/dXA)
B/dXB = RT(dlnPB/dXB)
Now substituting these values in equation-6 we get-
XA(dlnPA/dXA) = XB(dlnPB/dXB)
or, (dlnPA/dlnXA)T,P = (dlnPB/dlnXB)T,P -----(equation-7)
Equation-7 is Duhem–Margules equation.

Azeotrope Mixture

An azeotrope mixture is a mixture of two or more liquids whose proportions cannot be changed by simple distillation because when an azeotrope is boiled, the vapour has the same proportions of constituents as the unboiled mixture, because their composition is unchanged by distillation, azeotropes are also called constant boiling point mixtures.
If the constituents of a mixture are completely miscible in all proportions with each other, the type of azeotrope is called a homogeneous azeotrope. For example, any amount of ethanol can be mixed with any amount of water to form a homogeneous solution.
If the constituents are not completely miscible, an azeotrope can be found inside the miscibility gap.
This type of azeotrope is called heterogeneous azeotrope or heteroazeotrope. A heteroazeotropic distillation will have two liquid phases. For example, acetone / methanol / chloroform form an intermediate boiling azeotrope.
Azeotropes, consisting of two constituents are called binary azeotropes such For example, benzene and hexafluorobenzene form a double binary azeotrope. Azeotropes, consisting of three constituents are called ternary azeotropes, For example, acetone / methanol / chloroform. Azeotropes of more than three constituents are also known.
There are two types of azeotropes. One is minimum boiling azeotrope and other is maximum boiling azeotrope. A solution that shows greater positive deviation from Raoult's law forms a minimum boiling azeotrope at a specific composition. For example, an ethanol–water mixture on fractional distillation yields a solution containing at most 97.2% (by volume) of ethanol.
Once this composition has been achieved, the liquid and vapour have the same composition, and no further separation occurs.
A solution that shows large negative deviation from Raoult's law forms a maximum boiling azeotrope at a specific composition. Nitric acid and water is an example of this class of azeotrope. This azeotrope has an approximate composition of 68% nitric acid and 32% water by mass, with a boiling point of 393.5K.
Each azeotrope has a characteristic boiling point. The boiling point of an azeotrope is either less than the boiling point temperatures of any of its constituents (a positive azeotrope), or greater than the boiling point of any of its constituents (a negative azeotrope).
General, a positive azeotrope boils at a lower temperature than any other ratio of its constituents. Positive azeotropes are also called minimum boiling mixtures or pressure maximum azeotropes.
A negative azeotrope boils at a higher temperature than any other ratio of its constituents. Negative azeotropes are also called maximum boiling mixtures or pressure minimum azeotropes.

Steam distillation

Steam Distillation is a Physical method and is applied to separate substances which are steam volatile and are immiscible with water. In steam distillation, steam from a steam generator is passed through a heated flask containing the liquid to be distilled.
The mixture of steam and the volatile organic compound is condensed and collected. The compound is later separated from water using a separating funnel. In steam distillation, the liquid boils when the sum of vapour pressures due to the organic liquid (P1) and that due to water(p2) becomes equal to the atmospheric pressure (P), i.e. P = P1 + P2. Since P1 is lower than P, the organic liquid vaporises at lower temperature than its boiling point. Thus, if one of the substances in the mixture is water and the other, a water insoluble substance, then the mixture will boil close to but below, 373K. A mixture of water and the substance is obtained which can be separated by using a separating funnel. Aniline is separated by this technique from aniline – water mixture.
Applications of Steam Distillation
Steam distillation are widely used in the manufacturing of essential oils, for instance perfumes. This method uses a plant material that consists of essential oils. Mainly orange oil is extracted on a large scale in industries using this method.
Steam distillation is also sometimes used in chemical laboratories as one of many substance separation methods.
Application of steam distillation can be found in the production of consumer food products and petroleum industries. They are used in separation of fatty acids from mixtures.

Fractional distillation

Fractional distillation is applied if the difference in boiling points of two liquids is not more than 25o. In this case simple distillation cannot be used to separate them. The vapours of such liquids are formed within the same temperature range and are condensed simultaneously. In this technique, vapours of a liquid mixture are passed through a fractionating column before condensation.
The fractionating column is fitted over the mouth of the round bottom flask.
Vapours of the liquid with higher boiling point condense before the vapours of the liquid with lower boiling point. The vapours rising up in the fractionating column become richer in more volatile component. By the time the vapours reach to the top of the fractionating column, these are rich in the more volatile component. Fractionating columns are available in various sizes and designs. A fractionating column provides many surfaces for heat exchange between the ascending vapours and the descending condensed liquid. Some of the condensing liquid in the fractionating column obtains heat from the ascending vapours and revaporises. The vapours thus become richer in low boiling component. The vapours of low boiling component ascend to the top of the column. On reaching the top, the vapours become pure in low boiling component and pass through the condenser and the pure liquid is collected in a receiver.
After a series of successive distillations, the remaining liquid in the distillation flask gets enriched in high boiling component. Each successive condensation and vaporisation unit in the fractionating column is called a theoretical plate. Commercially, columns with hundreds of plates are available. One of the technological applications of fractional distillation is to separate different fractions of crude oil in petroleum industry.