Solution Sample calculation: Consider the second set of data. T = 378 K; P A = 125.
3 kPa; P B =
55.6 kPa.
Using Eq. (8.51),
101.3 = 55.6 + xA(125.3 – 55.6)
Therefore, xA = 0.656.
Using Eq. (8.54), we see
yA = 0.656 125.3/101.3 = 0.811
Relative volatility is
a = PSA/PSB = 125.3/55.6 = 2.25
These calculations are repeated for other temperatures. The results are tabulated below:
T, K 371.4 378 383 388 393 398.6
xA 1.000 0.656 0.487 0.312 0.157 0
yA 1.000 0.811 0.674 0.492 0.279 0
a 2.28 2.25 2.17 2.14 2.08 2.02
(a) Plot of T versus x and y gives the boiling point diagram
(b) Plot of y against x gives the equilibrium diagram
(c) The average of the last row gives a = 2.16. Use this value of a in Eq. (8.55) to get the equation
for the equilibrium curve.
8.10 NON-IDEAL SOLUTIONS
We have seen that the partial pressure of a component in an ideal solution varies linearly with
concentration in the solution. If the solution behaves ideally, the different molecules should be
chemically similar. In that case, the molecules of a particular substance, when brought into solution
with other components, would not experience any difference in the environment surrounding them
from that existed in their pure state. The intermolecular forces in the pure state of the substance and
that in the solution would then be approximately of the same order of magnitude. Therefore, the
fugacity (or the partial pressure) of a substance, which is a measure of the tendency of the substance
to escape from the solution, is not affected by the properties of the other components in the solution. It
depends only on the number of molecules of the substance present, or its concentration. In short, the
components in an ideal solution obey Raoult’s law. But for non-ideal solutions, the partial pressures
do not vary linearly with composition, as shown in Fig. 8.11 for the case of carbon disulphide–
acetone system.
The non-ideal behaviour of liquid mixtures arises due to the dissimilarity among molecules. The
dissimilarities arise from the difference in the molecular structure or from the difference in the
molecular weight. The non-ideal behaviour of light hydrocarbons such as methane, ethylene, etc., in
mixtures of heavier paraffin or crude oil is due to the difference in the molecular weights. In contrast,
it is a type of intermolecular attraction called hydrogen bonding, that is responsible for the non-ideal
behaviour resulting from the difference in the molecular structure. Molecules, which contain atoms
such as oxygen, chlorine, fluorine or nitrogen, tend to be polar. When the electrons in the bonds
between these atoms and hydrogen are not equally shared, a dipole is created. The electrons tend to
be closer to the larger atoms, which become negatively charged compared to hydrogen which
becomes the positive end of the dipole. In a solution of polar substances, the molecules tend to
arrange themselves so that the charge deficiency of the hydrogen atoms is compensated by an
intermolecular bond with a ‘donor’ or negatively charged atom. These hydrogen bonds have energies
of the order of several kJ/mol. Because of hydrogen bonding, bimolecular complexes between like or
unlike molecules are formed, and even chain-like or three-dimensional aggregates between a large
number of molecules are sometimes formed. The formation or destruction of hydrogen bonding during
mixing leads to very large heat effects and drastic changes in the thermodynamic properties.
Non-ideal behaviour falls into one of the following two types: positive deviation from ideality and
negative deviation from ideality. The positive deviation from ideality results when the actual partial
pressure of each constituent is greater than it should be if Raoult’s law were obeyed. Solutions in
which intermolecular forces between like molecules are stronger than those between unlike
molecules, show appreciable positive deviation from ideality. On mixing the constituents which form
a solution exhibiting positive deviation from ideality, there is an absorption of heat. This can be
proved easily if we recognise the experimental observation that most solutions tend to exhibit ideal
behaviour as temperature is increased. For a solution showing positive deviation, for each
component is greater than its mole fraction xi, and as temperature is increased it becomes equal to xi ,
because the solution tends to ideality as temperature is increased. It means that for a system of given
composition for which deviation from Raoult’s law is positive, the ratio decreases with
increasing temperature. That is
Comparing Eq. (8.58) with Eq. (8.59) we see that /RT2 < 0, which means . The total
enthalpy of the solution is , whereas the enthalpy of the system before mixing is
S niHi. Since the former is greater than the latter, there is absorption of heat during mixing. Examples
of solutions showing positive deviation from ideality are oxygen–nitrogen, ethanol–ethyl ether,
water–ethanol, carbon disulphide–acetone, benzene–cyclohexane, acetonitrile–benzene,
n-hexane–nitroethane, etc.
For solutions exhibiting negative deviation from ideal behaviour, the partial pressures are less than
those given by Raoult’s law. By a derivation similar to the one presented in the preceding paragraph,
it can be shown that when solutions showing negative deviation are formed from pure constituents
there is evolution of heat. At the molecular level, appreciable negative deviation reflects stronger
intermolecular forces between unlike than between like pairs of molecules. Examples are
chloroform–ethyl ether, chloroform–benzene, hydrochloric acid–water, phenol–cyclohexanol,
chloroform–acetone, etc.
The general nature of the vapour pressure curves showing positive and negative deviation are shown
in Fig. 8.12. Figures 8.12(a) and (b) refer to constant temperature conditions. The uppermost curves
give the total vapour pressure as function of liquid composition. The corresponding curves, as a
function of the vapour composition lie below it, so that the vapour is rich in the more volatile
component.
8.10.1 Azeotropes
Azeotropes are constant boiling mixtures. The word ‘azeotrope’ is derived from Greek word meaning
‘boiling without changing’. When an azeotrope is boiled, the resulting vapour will have the same
composition as the liquid from which it is produced. Whereas, the equilibrium temperature of an
ordinary solution varies from the bubble point to the dew point, the boiling point of an azeotrope
remains constant till the entire liquid is vaporised. The azeotropes are formed by solution showing
large positive or negative deviation from ideality. If the vapour pressures of the constituents of a
solution are very close, then any appreciable positive deviation from ideality will lead to a maximum
in the vapour pressure curve and negative deviations from ideality under the same conditions leads to
a minimum in the vapour pressure curve. Even if an appreciable difference exists in the vapour
pressures of the pure components, the chances for the occurrence of maximum or minimum in the
vapour pressures should not be overruled if the deviation from ideal behaviour is quite high. At the
composition at which there exists a maximum or minimum in the vapour pressure curve, a minimum or
maximum, as the case may be, exists in the boiling point diagrams. The mixture is said to form an
azeotrope at this composition under the given temperature and pressure and it will distil without
change in composition, because the vapour produced has the same composition as the liquid.
Minimum-boiling azeotropes. Solutions showing positive deviation from ideality in certain
cases may lead to the formation of azeotropes of the minimum-boiling type. The P-x-y, T-x-y and x-y
curves for the minimum-boiling azeotropes are shown in Fig. 8.13.
