This presentation is on the topic " Solutions" for the Chemistry Undergraduate students of Mumbai University

1. Dr. Pravin U. Singare
Department of Chemistry,
N.M. Institute of Science, Bhavan’s College, Andheri
(West), Mumbai 400058
SOLUTIONS

2. Introduction
• A mixture of two liquids is called binary liquid mixture.
• Binary liquid system is prepared by mixing two chemically non reacting liquids.
• Such binary liquid system is of three types
1. Binary liquid system in which two liquids are completely miscible with each other in
all proportions. eg. water + ethyl alcohol system; benzene + toluene system,
2. Binary liquid system in which two liquids are partially miscible with each other in
all proportions. eg. water + phenol system ; triethyl amine + water system.
3. Binary liquid system in which two liquids are completely immiscible with each other
in all proportions. eg. water + benzene system.

3. Completely miscible system
• When two liquid components are completely miscible with each other, the solution mixture thus formed may be
ideal or non -ideal.
What are the conditions for solution to be ideal?
• The solution mixture obtained by mixing liquid component A with liquid component B is said to be ideal
when:
1. the molecules of two liquids attract each other with equal force i.e. the force of attraction between
molecules of liquid A , between molecules of liquid B and between molecules of liquid A & B is
equal (same).
2. there should be no change in volume on mixing of the two liquid components
i.e. V(liquid A) + V (liquid B) = V (solution).
3. on mixing of the two liquid components, heat should neither be evolved or absorbed. In other words,
there should be no enthalpy change on mixing (ΔHmixing = 0).
4. the ideal solution should obey Roult’s Law i.e. the partial vapour pressure of each liquid component
should be directly proportional to the mole fraction of that liquid component present in the solution.
eg. of Ideal solution is benzene + ethylene dichloride system; ethyl bromide + ethyl iodide system; n-butyl
bromide + n-butyl chloride.

4. The solution which do not obey the above conditions for ideal
solution is called non-ideal solution.
eg:- acetone + chloroform system;
HBr + H2O system;
HCl + H2O system;
perchloric acid (HClO4) + H2O system.

5. Roult’s Law
State and Explain Roult’s Law.
• Consider a binary mixture of two liquid components A & B . The total vapour pressure (P)
of the mixture is the sum of partial vapour pressures PA & PB of liquid components A & B
respectively.
P = PA + PB ------- (1)
• According to Roults Law, “the partial vapour pressure of each liquid component is equal
to its mole fraction (X) in the solution multiplied by the vapour pressure (Po) of pure
liquid component.
• If Po
A & Po
B is the vapour pressure of pure liquid component A & B respectively
• XA & XB is the mole fraction of liquid component A & B present in the liquid mixture
• Then according to Roult’s Law
PA = Po
A.XA while PB = Po
B.XB
Then eq (1) will be P = Po
A.XA + Po
B.XB ------- (1)

6. • Blue line is the v.p curve of pure liquid A
• Red line is the v.p curve of pure liquid B
• Thus according to Roult’s Law
PA α XA while PB α XB
• As a result, the graph of partial V.P of
each liquid component against the
mole fraction (X) should be a straight
line passing through the origin.
• The total vapour pressure of a
solution which is the sum of partial
vapour of two liquid components is
also a straight line (as shown by
dotted line in the graph).
• The v.p corresponding to XA= 1 is the
v.p of pure liquid component A (Po
A).
• The v.p corresponding to XB= 1 is the
v.p of pure liquid component B (Po
B).
Vapour
pressure
Vapour
pressure
Mole fraction
B
XB= 1
XA = 0
A
XA= 1
XB = 0
Po
B
Po
A

7. Some important formulas of Roult’s Law
Partial V.P of liquid component A is PA = Po
A.XA
Partial V.P of liquid component B is PB = Po
B.XB
Total v.p of a solution (P) = PA + PB
P = Po
A.XA + Po
B.XB
XA + XB = 1
XA =
𝑛𝐴
𝑛𝐴
+ 𝑛𝐵
=
𝑊𝐴
/𝑀𝐴
𝑊𝐴
𝑀𝐴
+
𝑊𝐵
𝑀𝐵
XB =
𝑛𝐵
𝑛𝐴
+ 𝑛𝐵
=
𝑊𝐵
/𝑀𝐵
𝑊𝐴
𝑀𝐴
+
𝑊𝐵
𝑀𝐵

8. Problem 1. A solution of two liquids A & B exhibit ideal behavior. The mole fraction of A is
0.4 . The v.p. of pure liquid component A is 0.5 bar and that of liquid component B is 0.3 bar.
Calculate the partial v.p. of A & B and hence calculate the v.p. of solution.
Given: XA = 0.4, Po
A = 0.5 bar, Po
B = 0.3 bar
Formulas: XA + XB = 1
PA = Po
A.XA
PB = Po
B.XB
P = Po
A.XA + Po
B.XB
Solution: Since XA + XB = 1
XB = 1- 0.4 = 0.6
PA = Po
A.XA = 0.5 x 0.4 = 0.20 bar
PB = Po
B.XB = 0.3 x 0.6 = 0.18 bar
Total v.p. (P) of solution = Po
A.XA + Po
B.XB
Total v.p. (P) of solution = 0.20 + 0.18 = 0.38 bar

9. Problem 2: At 25oC, v.p of pure CCl4 and SiCl4 are 1.532 x 104 Nm-2 and 3.177x104 Nm-2.
Assuming the mixture behaves ideally calculate total v.p of a mixture containing 1 part by
weight of CCl4 and 3 parts by weight of SiCl4.
Given: Mol. Wt. of CCl4 = 154 & Mol. Wt. of SiCl4 = 170
Solution:
Let us assume that Liquid component A = CCl4 &
Liquid component B = SiCl4
Given: Po
A = 1.532 x 104 Nm-2 , Po
B = 3.177x104 Nm-2,
WA = 1gm, WB = 3gm
MA = 154, MB = 170
Formulas: XA =
𝑊𝐴
/𝑀𝐴
𝑊𝐴
𝑀𝐴
+
𝑊𝐵
𝑀𝐵
XA + XB = 1
PA = Po
A.XA
PB = Po
B.XB
P = Po
A.XA + Po
B.XB
Solution:
XA =
𝑊𝐴
/𝑀𝐴
𝑊𝐴
𝑀𝐴
+
𝑊𝐵
𝑀𝐵
=
1/154
1
154
+
3
170
XA = 0.2690
Since XA + XB = 1
XB = 1- 0.2690 = 0.7310
PA = Po
A.XA = 1.532 x 104 x 0.2690 = 4.121 x103 Nm-2
PB = Po
B.XB = 3.177x104 x 0.7310 = 23.223 x103 Nm-2
Total v.p (P) = Po
A.XA + Po
B.XB
Total v.p (P) = 4.121 x103 + 23.223 x103
Total v.p (P) = 27.344 x103 Nm-2

10. Non –Ideal Solutions
(+ive & -ive deviation from Roult’s Law)
• If the solution mixture of binary liquids do not obey Roult’s law, then such solution
mixture is called non-ideal solution.
eg. Mixture of acetone + CHCl3; HCl +H2O; HClO4 + H2O
• For such non-ideal solution mixture, presence of one liquid affects the vapour pressure
of other liquid.
• The vapour pressure arises due to the escaping tendency of molecules from liquid state
to gaseous (vapour) state.
• Such non-ideal solution mixture show eighter +ive or -ive deviation from Roult’s Law.
• As a result, the vapour pressure graph of non-ideal solution mixture is different from the
vapour pressure graph of ideal solution mixture.

11. +ive deviation
-ive deviation
• The +ive deviation is observed due to decrease in force of
attraction between the molecules of one liquid in presence of
other liquid.
• The force of attraction between the molecules of liquid A
decreases due to presence of liquid B.
• Similarly the force of attraction between the molecules of
liquid B decreases due to presence of liquid A.
• The decrease in force of molecular attraction will result in
increase in escaping tendency of liquid molecules to vapour
phase resulting in increase in vapour pressure.
• As a result, the v.p. of each liquid component will be more
than that of expected or ideal v.p.
• The dotted line in the figure represent ideal v.p.
• eg. Ethyl alcohol + heptane; acetaldehyde + CS2 ; CCl4 +
heptane
• The -ive deviation is observed due to increase in force of
attraction between the molecules of one liquid in presence of
other liquid.
• The force of attraction between the molecules of liquid A
increases due to presence of liquid B.
• Similarly the force of attraction between the molecules of liquid
B increases due to presence of liquid A.
• The increase in force of molecular attraction will result in
decrease in escaping tendency of liquid molecules to vapour
phase resulting in decrease in vapour pressure.
• As a result, the v.p. of each liquid component will be less than
that of expected or ideal v.p.
• The dotted line in the figure represent ideal v.p.
• eg. Pyridine +formic cid ; HCl+ HNO3 ; CHCl3 + acetone:
HClO4+ water
Vapour
pressure
Vapour
pressure
Mole fraction
B
XB= 1
XA = 0
A
XA= 1
XB = 0
Po
B
Po
A
Vapour
pressure
Vapour
pressure
Mole fraction
B
XB= 1
XA = 0
A
XA= 1
XB = 0
Po
B
Po
A

12. Distillation of Ideal Solution
Distillation curve of Ideal Solution
• Consider a solution mixture prepare by mixing liquid A and Liquid B together.
• TA is the b.p. of pure liquid A while TB is .the b.p. of pure liquid B.
• Since TA > TB , it indicate liquid A is high boiling and hence less volatile than liquid B.
• In the diagram curve L gives b.p. of the solution while curve V gives composition of
vapour formed at the b.p. of the solution.
• Consider the solution of composition Y (80%A & 20%B) which boils at temperature T1 (as
given by curve L).
• At b.p. T1 the composition of vapours formed will X (40% A & 60% B) which is obtained by
curve V.
• The vapours when condensed will give distillate of same composition X (40% A & 60% B) .
• The distillate of Composition X will now have greater composition of liquid B (60%) and less
composition of liquid A (40%) .
• The distillate of composition X will now boil at low temperature T2 (as given by curve L).
• At b.p. T2 the composition of vapours formed will Z (10% A & 90% B) which is given by
curve V.
• The vapours when condensed will give distillate of same composition Z (10% A & 90% B) .
• The distillate of Composition Z will now have still greater composition of liquid B (90%) and
less composition of liquid A (10%) .
• The distillate of composition Z will now boil at still lower temperature T3 (as given by curve
L).
• At b.p. T3 the composition of vapours formed will be 0% A & 100% B which is given by
curve V.
• Thus after every distillation, the distillate will have higher concentration of B and low
concentration of A.
T2
T1
Temperature
Composition
100% A
0% B
0% A
100% B
Y X Z
TA
TB
V
L
T3
80
20
40
60
10
90

13. Distillation of non- ideal solution
Distillation curve of solution showing
+ive deviation from Roult’s Law
• If the solution mixture is non-ideal showing +ive deviation from Roult’s Law, the b.p. curve shows minimum.
• The b.p. of solution is less than the b.p. of individual liquid component TA & TB..
• Consider a solution mixture prepare by mixing liquid A and Liquid B together.
• TA is the b.p. of pure liquid A while TB is .the b.p. of pure liquid B.
• In the diagram curve L gives b.p. of the solution while curve V gives composition of vapour formed at the
b.p. of the solution.
• Consider the solution of composition M (90%A & 10%B) which boils at temperature T1 (as given by curve L).
• At b.p. T1 the composition of vapours formed will N (50% A & 50% B) which is given by curve V.
• The vapours at temperature T1 will condensed to give distillate of same composition N (50% A & 50% B) .
• The distillate of composition N on redistillation will now boil at low temperature T2 (as given by curve L).
• At b.p. T2 the composition of vapours formed will O (40% A & 60% B) which is given by curve V.
• The vapours at temperature T2 will condensed to give distillate of same composition O (40% A & 60% B) .
• The distillate of composition O will now have still higher composition of liquid B (60%) and less composition of
liquid A (40%) .
• The distillate of composition O will now boil at still lower temperature T3 (as given by curve L).
• Thus after every distillation, the distillate will have higher concentration of B and low concentration of A.
• The process of distillation is continued till distillate with composition Z (35% A and 65% B) is obtained .
• The distillate of composition Z will boil at temperature T3 , forms vapour of same composition Z and will again
give distillate of same composition Z.
• The solution of composition Z is called azeotropic mixture which will boil at constant temperature T3, hence it
is also called constant boiling mixture.
• Beyond composition Z, separation of liquid A from liquid B is not possible, because solution mixture will get
distilled out completely with out change in composition.
• Eg. Water + alcohol will form constant boiling azeotropic mixture at 78.15oC and the composition of azeotropic
mixture will be 4.40 % water & 95.60 % alcohol.
50
50
40
60
T2
T1
Temperature
Composition
100% A
0% B
0% A
100% B
M N O
TA
TB
V
L
T3
90
10
Z
35
65

14. Distillation of non- ideal solution
Distillation curve of solution showing - ive deviation from
Roult’s Law
• If the solution mixture is non-ideal showing -ive deviation from Roult’s Law, the b.p.
curve shows maximum.
• The b.p. of solution is greater than the b.p. of individual liquid component TA & TB.
• Consider a solution mixture prepare by mixing liquid A and Liquid B together.
• TA is the b.p. of pure liquid A while TB is .the b.p. of pure liquid B.
• In the diagram curve L gives b.p. of the solution while curve V gives composition of
vapour formed at the b.p. of the solution.
• Consider the solution of composition M (90%A & 10%B) which boils at temperature T1
(as given by curve L).
• At b.p. T1 the composition of vapours formed will N (70% A & 30% B) which is given
by curve V.
• The vapours at temperature T1 will condensed to give distillate of same composition N
(70% A & 30% B) .
• The distillate of Composition N on redistillation will now boil at higher temperature T2
(as given by curve L).
• At b.p. T2 the composition of vapours formed will O (60% A & 40% B) which is given
by curve V.
• The vapours at temperature T2 will condensed to give distillate of same composition
O (60% A & 40% B) .
• The distillate of Composition O will now have still higher composition of liquid B
(40%) and less composition of liquid A (60%) .
• The distillate of composition O will boil at temperature T2 , forms vapour of same
composition O and will again give distillate of same composition O.
• The solution of composition O is called azeotropic mixture which will boil at constant
temperature T2, hence it is also called constant boiling mixture.
• Beyond composition O, separation of liquid A from liquid B is not possible, because
solution mixture will get distilled out completely with out change in composition.
• Eg. Water + HF will form constant boiling azeotropic mixture at 114oC and the
composition of azeotropic mixture will be 64.50 % water & 35.50 % HF.
60
40
70
30
T2
T1
Temperature
Composition
100% A
0% B
0% A
100% B
M N O
TA
TB
V
L
90
10

15. Partially Miscible Liquid System
• There are certain liquid pairs which are normally immiscible with each other, but will become miscible only in a
limited range of concentration.
• Such liquid pairs are called partially miscible liquid pairs.
• If a small quantity of organic liquid is added to water at room temperature, the two layers
One layer of Water saturated with organic liquid
Second layer of Organic liquid saturated with water
will formed.
• Such solution layers of different compositions co-existing with one another are called conjugated solutions.
• The two layers which are separated from each other forming sharp and distinct boundary will become miscible
with each other on changing the temperature.
• Sometimes by increasing the temperature above room temperature the two immiscible liquid layers may become
completely miscible forming the homogeneous solution (i.e. the boundary separating the two layers will
disappear).
• Such temperature is called Upper consulate temperature or Upper critical solution temperature (upper CST).
• Sometimes by decreasing the temperature below room temperature the two immiscible liquid layers may
become completely miscible forming the homogeneous solution (i.e. the boundary separating the two layers will
disappear).
• Such temperature is called lower consulate temperature or lower critical solution temperature (lower CST).
• In addition to above there are certain partially miscible liquid pairs which are having both upper CST as well as
lower CST.

16. Depending upon CST, there are 3 types of partially miscible liquid
pair systems
1. Liquid pairs whose miscibility increases with rise in
temperature above room temperature hence having Upper
CST. eg. Phenol-water system.
2. Liquid pairs whose miscibility increases with decrease in
temperature below room temperature hence having Lower
CST. eg. triethylamine-water system.
3. Liquid pairs which are completely miscible with each other by
increasing or decreasing the temperature than room
temperature hence having both Upper & Lower CST eg.
Nicotine-water system.

17. Phenol –Water System
• When phenol is added to water, it will form homogeneous solution till
conc. Of phenol in water reach 8%.
• Further addition of phenol in water will result in the formation of two
immiscible layers.
• The upper layer will be a water layer saturated with phenol and lower
layer will be the phenol layer saturated with water.
• This two layers which are in equilibrium with each other are called
conjugated solutions.
• If this conjugated solution is heated, it is observed that the mutual
solubility of phenol in water layer and water in phenol layer will increase
as shown in the figure.
• In the figure, curve PQ indicate % solubility of phenol in water at
different temperatures.
• Similarly curve PQ indicate % solubility of water in phenol at different
temperatures.
• Point Q represent the temperature of 68.0oC at which two liquid layers
become completely miscible in each other forming homogeneous
solution having composition 36% phenol & 64%water.
• Hence 68.0oC represent Upper CST for Phenol-water system.
• Below point Q (68.0oC), the system will be partially miscible
(heterogeneous) forming two different layers of phenol and water.
• Further addition of phenol to water or water to phenol above point Q
(68.0oC) the system will become completely miscible (homogeneous).
R
P
68oC
36%
Water 100% 0%
100% Phenol
0%
64%
Q
% Concentration
Temperature
Homogeneous system
(completely miscible)
System with 2 layers
(partially miscible)

18. Triethyl amine (TEA) –Water System
• When TEA is added to water or water to TEA at room temperature, it
is observed that there will be formation of 2 immiscible liquid layers.
• One layer will be layer of TEA saturated with water and second layer
will the layer of water saturated with TEA.
• Such system will be heterogeneous.
• However, if the system is cooled below room temperature, the mutual
miscibility of TEA in water and water in TEA will increase.
• When the temperature of the system reaches 18.5oC, the 2 layers will
become completely miscible with each other forming a homogeneous
solution.
• In the figure, curve AB indicate % solubility of TEA in water at different
temperatures.
• Similarly curve BC indicate % solubility of water in TEA at different
temperatures.
• The 2 curves meet at point B when the temperature is 18.5oC and
composition is 30% TEA and 70 % water.
• Above point B the system will be partially miscible (heterogeneous)
forming 2 layers while below point B (18.5oC) the system will be
completely miscible forming homogeneous solution.
• Further addition of water to TEA or TEA to water below 18.5oC the
system will remain homogeneous.
• The temperature 18.5oC is the lower critical solution temperature of
TEA-water system.
C
A
18.5oC
30%
Water 100% 0%
100% TEA
0%
70%
B
Concentration
Temperature
System with
2 layers
(partially
miscible)
Homogeneous system
(completely miscible)

19. Nicotine-Water System
• In case of Nicotine-water system, the mutual miscibility of
nicotine in water & water in nicotine increases by
increasing the temperature and at 208oC the system will
convert from heterogeneous (partially miscible) to
homogeneous (completely miscible).
• Thus 208oC is the upper CST of nicotine-water system.
• Also the mutual miscibility of nicotine in water & water in
nicotine increases by decreasing the temperature and at
60.8oC the system will convert from heterogeneous
(partially miscible) to homogeneous (completely
miscible).
• Thus 60.8oC is the lower CST of nicotine-water system.
• Above 208oC (upper CST) & below 60.8oC (lower CST) the
Nicotine-water system will be completely miscible
forming homogeneous solution.
• Between 60.8oC (lower CST ) & 208oC (upper CST) the
system will be partially miscible (heterogeneous) forming
2 layers. One layer will be the layer of nicotine saturated
with water and second layer will be the layer of water
saturated with nicotine.
• At upper & lower CST the composition of the system will
be 32% nicotine and 68% water.
60.8oC
32%
Water 100% 0%
100% Nicotine
0%
68%
208oC
System with 2 layers
(partially miscible)
Homogeneous system (completely miscible)
Homogeneous system (completely miscible)
Concentration
Temperature