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Chapter
6
Chapter
Properties of Liquids
6.1 Surface Tension
The term surface is customarily used when referring to either a gas–solid or
gas–liquid interface, whereas interface is commonly used to refer to a boundary
between two liquids. Since every particle of matter possess an interface at the
boundary of its surroundings the topic becomes very important in pharmacy
and medicine. Interfacial phenomenon is a significant factor that affects the
absorbance of drugs onto solid adjunct in dosage form, crossing of biomembranes
by drug molecules, in emulsion and suspension, their stability, etc.
The properties of molecules in the bulk are often different from molecules
forming surface/interface because the molecules in bulk are surrounded
uniformly in all directions by other molecules, i.e. they are attracted equally from
all directions by the molecules around it causing a net force of zero where as
molecules which form the surface are subjected to unequal attraction, i.e. they
are pulled/attracted sideways and downwards only as there are less number of
molecules per unit volume in the phase above the surface of liquid. Therefore, the
molecules at the surface experience an inward pull perpendicular to the surface.
As a result, the liquid surface under tension tends to contract to smallest possible
area in order to have the minimum number of molecules at surface. So the shape
of a free drop is always spherical. This property of a liquid is known as surface
tension.
Liquids will bead up as the surface tension is pulling it into a spherical shape,
which has less surface area compared with other shapes. Figure 6.1 shows how
surface tension pulls a water drop into a round or a spherical shape. The red
arrows show how the water molecules are pulled in toward the middle of the
water drop.
Another way to view the surface tension is that a molecule in contact with
the neighbouring molecules is in a lower state of energy than if it wasn’t in
contact with a neighbour. All the interior molecules have as many neighbours
as they can possibly have. But molecules in the boundary have fewer neighbours
than interior molecules and are therefore in a higher state of energy. For the
168
Practical Pharmaceutical Analytical Chemistry
liquid to minimize its energy state, it must minimize its number of boundary
molecules and must therefore minimize its surface area. As a result of surface area
minimization, a surface will assume the smoothest shape it can (mathematical
proof that smooth shapes minimize surface area relies on the use of the Euler–
Lagrange equation). Since any curvature in the surface shape results in a greater
area, a higher energy will also result. Consequently, the surface will push back
against any curvature in much the same way as a ball pushed uphill will push
back to minimize its gravitational potential energy.
Tension exists on the surface of a liquid due to the attraction of surface
molecules by the molecules in the bulk of the liquid. It is like the tension
produced in a string when it is pulled to any side at right angles to itself. A
steady force of tension exists in the surface of a liquid when the liquid is in
contact and in equilibrium with its vapour or air saturated with its vapour. This
force is the same for all directions in the surface acts along and in the direction
of the surface. It is measured for each liquid in terms of its surface tension. It is
the surface tension force which compels a freely falling drop of a liquid to take
up a spherical shape.
The surface tension is denoted by g and is defined as the force in dynes acting
along the surface of liquid at right angle to any line 1 cm in length. That is, in
order to increase the surface area, force must be exerted to overcome the surface
tension. In other words, work will have to be done to increase the surface area.
Fig. 6.1
Surface tension pulls water
into a spherical shape
h
q
q
Fig. 6.1
Surface tension
measurement
169
Properties of Liquids
Therefore, surface tension is work (energy) required to expand the surface of
liquid by unit area. Mathematically
Surface tension (g) work done/change in area Jm
2
Since Jm
2
(Nm)m
2
Nm
1
. So, surface tension can also be expressed as
Nm
1
, i.e. force necessary to rupture its surface along unit length. In CGS system
unit of surface tension is dyne cm
1
, dyne 10
10
N and cm 10
2
m. Therefore,
dyne cm
1
10
5
N/10
2
m 10
3
Nm
1
. For example, surface tension of water
at 293 k 72.8 dyne cm
1
or 72.8 u 10
3
Nm
1
.
Surface Energy
The effect of surface tension is to reduce the surface area to a minimum. So in
order to increase the area of the surface of the liquid, work is required against
the force of surface tension. The work that is required to be done in order to
extend the area of surface of a liquid by 1 cm
2
is called surface energy of the liquid.
Surface energy is expressed in ergs per cm
2
. The dimensions of surface energy
may also be expressed as (dynes u cm) cm
2
, i.e. dynes cm
1
which is also the unit
of surface tension. Thus, surface tension is equal to surface energy numerically as
well as dimensionally. In SI unit, surface energy is expressed in joules per square
metre ( Jm
2
).
Surface Tension and Temperature
Surface tension varies linearly with temperature as suggested by the following
expression, derived by Eotvos,
g(M/r)
2/3
a kt (1)
where M is the molecular weight, r is the density, g is the surface tension of
liquid at temperature t, a and k are constants.
At critical temperature (i.e. when t t
c
) the surface tension is zero, then
Equation (1) becomes
0 a kt
c
a kt
c
(2)
Substituting the value of a, Eotvos equation can be written as
Ȗ(M/r)
2/3
k(t
c
t) (3)
This equation has been said to be satisfactory in giving variation of
surface tension with temperature for number of liquids over a wide range of
temperatures.
170
Practical Pharmaceutical Analytical Chemistry
This is also known as Eotvos law. V
m
stands for molar volume (molar mass /
density) of the liquid. The factor (V
m
)
2/3
is generally known as molar surface energy.
Ȗ (M/d)
2/3
K(t
c
t 6) (4)
where g is the surface tension, M is the molar mass, d is the density of the
liquid, t
c
is the critical temperature (Kelvin scale) and t is the temperature of the
experiment (Kelvin scale) and K is the Eotvos constant.
Now applying Equation (4) to two experimental temperatures T
1
and T
2
, we
get:
Ȗ
1
(M/d
1
)
2/3
K (t
c
t
1
6) (5)
Ȗ
2
(M/d
2
)
2/3
K (t
c
t
2
6) (6)
Ȗ
1
(M/d
1
)
2/3
Ȗ
2
(M/d
2
)
2/3
K (t
2
t
1
) (7)
{Ȗ
1
(M/d
1
)
2/3
Ȗ
2
(M/d
2
)
2/3
}/{t
2
t
1
} K (8)
where d
1
and d
2
are densities of the liquid at temperatures t
1
and t
2
, respectively.
The value of constant K for nonassociated liquids is approximately 2.12, when g
is measured in CGS units. Thus, for different nonassociated liquids, the expression
may be written as
{Ȗ
1
(M/d
1
)
2/3
Ȗ
2
(M/d
2
)
2/3
}/{t
2
t
1
} 2.12 (9)
In this way it has been found that in the case of a number of liquids, especially
those having hydroxyl groups such as alcohols, carboxylic acids, oxides, etc., the
value of the constant is less than 2.12. Now, in order to obtain this value it is
necessary to multiply the normal molecular masses of a substance by a factor x,
greater than unity. The factor x is known as the association factor. On multiplying
M by x the equation becomes
{Ȗ
1
(xM/d
1
)
2/3
Ȗ
2
(xM/d
2
)
2/3
}/{t
2
t
1
} 2.12 (10)
x (2.12/K)
2/3
(11)
Parachor
Molecular volume is not a satisfactory criterion of chemical constitution. Surface
tension of liquid decreases with increase in temperature and vanishes completely
at critical temperature. Van der Waal’s equation describes the variation of surface
tension as
171
Properties of Liquids
Ȗ Ȗ
o
(1 t/t
c
)
n
(12)
where
Ȗ
o
is a constant, t
c
is the critical temperature and n is the constant,
1, 2, 3.
So, in order to have satisfactory results related to molecular structure of
compounds, Sugden introduced a term parachor (P)
P M/D d Ȗ
1/4
(13)
where M is the molecular weight of liquid,
Ȗ is the surface tension in dyne cm
1
,
D is the density of liquid and d is the density of vapour in g cm
3
at temperature
of experiment.
Since d is very small compared to D, the expression becomes
P M/D Ȗ
1/4
, i.e. molecular volume u Ȗ
1/4
(14)
Thus, parachor (P ) is molecular volume multiplied by the fourth root of
surface tension. If two liquids having the same surface tension are examined
under such conditions their parachor will be proportional to their molecular
volume. Hence, comparison of the parachor of different liquids is the same thing
as comparison of their molecular volumes at temperature at which liquids have
the same surface tension. For calculation of parachor value of surface tension,
density of liquid and its molecular weight is required.
Parachor is an additive as well as constitutive property, i.e. its value is
determined by the number of atoms present in the molecule and the mode
of linkage. By measuring the surface tension of a series of compounds,
it is possible to calculate the atomic and structural contribution towards
parachor. For example, surface tension of benzene is 28.9 dyne cm
1
, density
is 0.88 g cm
3
.
The parachor is
Molecular weight of benzene (C
6
H
6
): (M) 78
Ȗ 28.9 dyne cm
1
, d 0.88 g cm
1
P M/D Ȗ
1/4
206
The average increment for CH
2
calculated from large number of consecutive
series has been found to be 39. The value of atomic and structure parachors as
determined by Syden and revised by Vogel (1948) on more accurate measurement
basis are given in Table 6.1.
172
Practical Pharmaceutical Analytical Chemistry
Table 6.1ȳAtomic and structural parachor
Atom Parachor Group Parachor Linkage Parachor
C 8.6
!C O
44.4
!C C
19.9
H 15.7 –OH 30.2
–C∫C–
40.8
O 19.8 –COOH 73.7 3-membered ring 12.3
Cl 55.2 –NO
2
73.8 4-membered ring 10.0
Br 68.8 O
2
in esters 60.0 5-membered ring 4.6
I 90.3 6-membered ring 1.4
P 37.7 Naphthalene ring 12.2
S 48.2
Parachor of benzene
6 C atoms
6 u 8.6 51.6
6 H atoms
6 u 15.7 94.2
2C C 3 u 19.9 59.7
One six-membered ring
1.4
Total value calculated
206.9
Observed value
206.2
6.1.1 Determination of Surface Tension
Generally the surface tension of a liquid is determined by the following methods:
1. Static method
a. Stalagmometer
i. Drop weight method
ii. Drop number method
b. Capillary rise method (single and double capillaries)
c. Maximum bubble pressure method
2. Dynamic method
a. Torsion balance method
The selection of a method depends upon the accuracy required, practical
convenience, quantity of the liquid and the speed of working. Surface tension
is highly susceptible to contamination by minute traces of grease and other
impurities. While measuring surface tension additional cleanliness is required.
173
Properties of Liquids
Generally dynamic methods are preferred over static methods as in the former
type the surface of the liquid is constantly renewed. The laborious absolute
determination of surface tension in physical chemistry are rarely used, however
calibration of the apparatus with a liquid of known surface tension is good
enough to produce accurate results of interest.
The stalagmometer or the drop weight method is the one of the most often
used method in chemical laboratories and is shown in Figure 6.3.
Drop Weight Method
This method is based on the principle that the weight (w) of a drop of a liquid
falling from capillary tube held vertically is approximately proportional to
its surface tension. The size of the drop falling off from the end of capillary
tube depends on the surface tension of the liquid and the size of the capillary
end. Thus, when a liquid is allowed to flow through a capillary tube, a drop
will increase in size up to a certain point (equal to the weight it can hold)
and then fall off. The total surface tension force supporting the drop is 2Sr
g,
where r is the radius of the outer circumference of the drop at the end of the
capillary tube. It is along this line that the liquid, glass and air meet and the
force of surface tension operates. The drop will fall when its weight force, w,
or mg, just exceeds the surface tension force acting along the circumference,
hence
w mg 2prg (15)
where w is the weight of the drop, m is the mass of the drop and 2Sr is the
external circumference of contact of the drop with the capillary tip.
From the above expression it is clear that the surface tension of a liquid may
be determined if the mass of a single drop and the external circumference of
the drop at the place of hanging from the tip of the dropping tube are known.
Mar A
Mar
Fig. 6.3
Stalagmometer
174
Practical Pharmaceutical Analytical Chemistry
When the liquid completely wets the bottom surface of the capillary, drop
circumference can be taken to be the same as that of the tip of the capillary. If
we have two liquids such that
w
1
m
1
g 2prg
1
(16)
and w
2
m
2
g 2prg
2
(17)
then,
w
w
m
m
1
2
1
2
(18)
Thus, the drop weight method can be employed for comparing the surface
tensions of two different liquids. If
g
1
for any one of the liquid is known, g
2
for
the other liquid can be found without requiring a measurement of r, the radius
of the dropping end of the capillary tube or the circumference of the surface of
contact between the drop and the glass surface.
Drop Number Method
Instead of finding the masses of single drops, it is easier to count the number of
drops formed by equal volumes of two liquids. With two different liquids, masses
of equal volumes are proportional to their densities. If n
1
and n
2
are the number
of drops produced from the same volume v of two liquids, then
Volume of a single drop of liquid (l ) v/n
1
(19)
Mass of its single drop, m
1
(v u d
1
)/n
1
(20)
2Sr g
1
(v u d
1
u g)/n
1
(21)
And for the second liquid 2Sr g
2
(v u d
2
u g)/n
2
(22)
Dividing Equation (21) by Equation (22), we get
g
1
/g
2
n
2
d
1
/n
1
d
2
(23)
where
g
1
and g
2
are the surface tensions of two liquids and d
1
and d
2
are the densities
of the respective liquids. One of the liquids is usually water as its surface tension
data at different temperatures is easily available. Hence, it is concluded that for the
determination of surface tension of a liquid by this method, one should know the
number of drops produced from equal volumes of two liquids and the densities
g
1
g
2
175
Properties of Liquids
Table 6.2 Surface tensions of different liquids at different temperatures
Liquid Temperature (˚C)
0 20 25 40 50 60 80 100
Water 75.64 72.75 71.97 69.56 67.91 66.28 62.28 58.85
Methanol – 22.6 – 20.9 – – – –
Ethanol – 22.27 – 20.60 – 19.01 – –
Acetone – 23.7 – 21.2 – 18.6 16.2 –
Benzene – 28.9 – 26.3 - 23.7 21.3 –
Table 6.3 Surface tensions of some other liquids
Liquid Temperature (°C) Surface tension (g)
Acetic acid 20 27.6
Acetic acid (40.1%) water
30 40.68
Acetic acid (10.0%) water
30 54.56
Diethyl ether 20 17.0
Ethanol (40%) water
25 29.63
Ethanol (11.1%) water
25 46.03
Glycerol 20 63
n-Hexane 20 18.4
Isopropanol 20 21.7
n-Octane 20 21.8
Sodium chloride 6.0 M aqueous solution 20 82.55
Sucrose (55%) water
20 76.45
of the two liquids. In addition to this, surface tension of water (any one liquid)
should also be known. The experiment should be performed in a thermostat as
the surface tension of a liquid is greatly reduced by an increase in temperature
(Tables 6.2 and 6.3).
176
Practical Pharmaceutical Analytical Chemistry
Description of Stalagmometer
The apparatus employed to determine the surface tension using
the drop weight or the drop number method is known as Traube’s
stalagmometer which is a drop measurer. This is especially useful in
comparing surface tensions. It consists of a capillary tube with
a thick wall and a ground glass flattened end with sharp edges.
This helps in giving large well-formed drops. The function of
the capillary tube is only to slow down the rate of flow of the
liquid. On the stem of the tube two marks A and B are etched,
one above and the other below the bulb. The surface tension may
thus be determined by counting the number of drops formed
by the liquid volume flowing from the upper to the lower mark.
To increase the sensitivity of the instrument, the tube above and
below the bulb is marked with a scale. With the help of this scale,
fractions of a drop may be estimated to an accuracy of 0.05 of
a drop. This is done by determining how many scale divisions
correspond to one drop. The rate of flow should not exceed 15
drops per minute. If it is more than this, it should be decreased.
This can be done by attaching a rubber tube with a screw pinch
cock to the open end of the tube for regulating the air inflow.
This adjustment can be altered to readjust the rate of flow of the
liquid at any time and will be required to different extents for
different liquids.
A
Experiment 1 Determine the surface tension of alcohol by drop number
method at room temperature.
Requirements
Traube’s stalagmometer, a wide mouth weighing b ottle, rubber stopper, a small
piece of rubber tube, a screw pinch cock.
Procedure
Clean a stalagmometer by chromic acid solution to remove grease, etc., then wash
it with distilled water and finally with acetone. Dry it by passing air or in an oven.
Now tightly fit a rubber stopper having two holes to the wide mouth weighing
bottle. Insert the stalagmometer in one of the holes and through the other pass
a glass tube (this tube serves as an air leak). Attach small rubber tubing having a
screw pinch cock to the upper end of the stalagmometer to regulate the flow rate
of the liquid. A small glass tube may be fixed at the free end of rubber tube as a
mouth piece for convenience of suction.