CHEM 255 LECTURE NOTES-Condensed Matter.pptx

CHEM 255:
STATES OF MATTER II AND
CHEMICAL KINETICS II
Dr. Michael Baah Mensah
Department of Chemistry
KNUST, Kumasi
1

The Kinetic Molecular Theory of the States of
Matter
• Kinetic molecular theory explains the behavior of gases in terms of
the constant, random motion of gas molecules
2

Matter
• Because of the empty spaces in gases—they can be readily compressed
and have very low densities under normal conditions
• Lack of strong forces between gas molecules allows them to expand to fill
the volume of their container.
• The major difference between the condensed states of matter (liquids and
solids) and the gaseous state is the distance between molecules.
• Liquid molecules are so close together that there is very little empty space.
Thus, liquids are much more difficult to compress than gases, and they are
also much denser under normal conditions. Molecules in a liquid are held
together by one or more types of attractive forces
• Liquid also has a definite volume, because molecules in a liquid do not
break away easily from attractive forces. The molecules can, however,
move past one another freely, and so a liquid can flow, can be poured, and
assumes the shape of its container.
3

Matter
• Solid molecules are held rigidly in position with virtually no freedom
of motion. Solid molecules are arranged in regular configurations in
three dimensions.
• There is less empty space in a solid than in a liquid. Thus, solids are
almost incompressible and possess definite shapes and volumes.
• The density of the solid form of a substance is higher than that of the
liquid form, however, with very few exceptions.
• Questions (Assignment 1):
• Explain why ice (solid water) floats on liquid water
• Draw a table showing the differences between gas, liquid, and solid
4

Intermolecular Forces
• Intermolecular forces are attractive forces between molecules.
• They are responsible for the nonideal behavior of gases. They are
more pronounced in liquids and solids.
• As the temperature of a gas drops, the average kinetic energy of its
molecules decreases. Eventually, at a sufficient temperature, the
molecules no longer have enough energy to break away from the
attraction of neighboring molecules. At this point, the molecules
aggregate to form small drops of liquid.
• This transition from the gaseous to the liquid phase is known as
condensation.
5

Intermolecular and Intramolecular Forces
• In contrast, intramolecular forces hold atoms together in a molecule, and
intermolecular forces stabilize individual molecules.
• Intermolecular forces are primarily responsible for the bulk properties of matter
(for example, melting point and boiling point).
• Generally, intermolecular forces are much weaker than intramolecular forces. It
usually requires much less energy to evaporate a liquid than to break the bonds
in the molecules of the liquid. For example, it takes about 41 kJ of energy to
vaporize 1 mole of water at its boiling point; but about 930 kJ of energy are
necessary to break the two O-H bonds in 1 mole of water molecules
6

Intermolecular forces and bulk properties
• The boiling points of substances often reflect the strength of the
intermolecular forces operating among the molecules. At the boiling
point, enough energy must be supplied to overcome the attractive
forces among molecules before they can enter the vapor phase.
• If it takes more energy to separate molecules of substance A than of
substance B because A molecules are held together by stronger
intermolecular forces, then the boiling point of A is higher than that
of B.
• The same principle applies also to the melting points of the
substances. In general, the melting points of substances increase with
the strength of the intermolecular forces.
7

Types of intermolecular forces
Ion-dipole forces
NB: Not van der Waals
forces
van der Waals
forces
Dipole-dipole
forces
Hydrogen
bonding
Dipole-induced
dipole forces
Dispersion
forces
Named after Dutch
physicist Johannes
van der Waals
8

Ion-dipole forces
• Ion-dipole forces: an ion (a cation or an anion)
and a polar molecule attract each other.
• The strength of this interaction depends on the
charge and size of the ion and on the magnitude
of the dipole moment and size of the molecule.
• The charges on cations are generally more
concentrated because cations are usually
smaller than anions. Therefore, a cation
interacts more strongly with dipoles than does
with an anion having a charge of the same
magnitude
• Hydration is one example of ion-dipole
interaction
9

Dipole-dipole forces
• Dipole-dipole forces are attractive forces between
polar molecules, that is, between molecules that
possess permanent dipole moments
• They are electrostatic, and they can be understood in
terms of Coulomb’s law.
• The larger the dipole moment, the greater the
attractive force.
• In liquids, polar molecules are not held as rigidly as in a
solid, but they tend to align in a way that, on average,
maximizes the attractive interaction.
Molecules that have a
permanent dipole moment
tend to align with opposite
polarities in the solid phase
for maximum attractive
interaction
10

Dipole – dipole attraction
• It requires the presence of polar
bonds and an unsymmetrical
molecule
• These molecules have a permanent
separation of positive and negative
charge
• In the illustration the H end of HCl is
permanently slightly positive charge
• The Cl end of HCl has a permanent
slight negative charge
• The H atom in one molecule is attracted
to the Cl in a neighbour
Weak attractions between polar HCl molecules
11

Induced dipole
• If an ion or a polar molecule is placed near a nonpolar molecule (or an atom), the
electron distribution of the nonpolar molecule (or atom) is distorted due to the
force exerted by the ion or polar molecule, resulting in the formation of a kind of
dipole.
• The formed dipole in the nonpolar molecule (or atom) is said to be an induced
dipole because the separation of positive and negative charges in the nonpolar
molecule (or atom) is due to the proximity of an ion or a polar molecule.
• The attractive interaction between an ion and the induced dipole is called ion-
induced dipole interaction
• The attractive interaction between a polar molecule and the induced dipole is
called dipole-induced dipole interaction.
• The likelihood of an induced dipole depends on:
• Charge on ion
• Strength of dipole
• Polarizability of atom or molecule 12

Dipole-induced dipole forces
13

London dispersion forces
• London dispersion force is a temporary attractive
force that results when the electrons in two
adjacent atoms occupy positions that make the
atoms form temporary dipoles (a short-lived
charge imbalance).
• This force is an induced dipole-induced dipole
force or attraction.
• London forces are the attractive forces that cause
nonpolar substances to condense to liquids and
freeze into solids when the temperature is
lowered sufficiently.
• Because of the constant motion of the electrons,
an atom or molecule can develop a temporary
(instantaneous) dipole when its electrons are
distributed unsymmetrically about the nucleus
14

• Dispersion forces are also called London dispersion forces
• A quantum mechanical interpretation of temporary (instantaneous)
dipoles was provided by Fritz London in 1930.
• London showed that the magnitude of this attractive interaction is
directly proportional to the polarizability of the atom or molecule.
15

• A second atom or molecule, in turn, can be distorted by the appearance of
the dipole in the first atom or molecule (because electrons repel one
another) which leads to an electrostatic attraction between the two atoms
or molecules
• Dispersion forces are present between any two molecules (even polar
molecules) when they are almost touching.
• Dispersion forces are present between all molecules, whether they are
polar or nonpolar
16

London dispersion forces and molecular size
• Larger and heavier atoms and molecules exhibit stronger dispersion
forces than smaller and lighter ones
• In a larger atom or molecule, the valence electrons are, on average,
farther from the nuclei than in a smaller atom or molecule. They are
less tightly held and can more easily form temporary dipoles
• The ease with which the electron distribution around an atom or
molecule can be distorted is called polarizability
• London dispersion forces tend to be:
ostronger between molecules that are easily polarized
oweaker between molecules that are not easily polarized
• Assignment: Explain why neopentane (C5H12) is a gas whereas n-
pentane (C5H12) is a liquid, both at room temperature.
17

Hydrogen bonding
• Hydrogen bond, which is a special type of dipole-dipole interaction
between the hydrogen atom in a polar bond, such as N–H, O–H, or
F–H, and an electronegative O, N, or F atom.
• Note that the O, N, and F atoms all possess at least one lone pair that
can interact with the hydrogen atom in hydrogen bonding
18

Hydrogen bonding
• The average strength of a hydrogen bond is quite large for a dipole-
dipole interaction (up to 40 kJ/mol). Thus, hydrogen bonds have a
powerful effect on the structures and properties of many compounds.
• The strength of a hydrogen bond is determined by the coulombic
interaction between the lone-pair electrons of the electronegative
atom and the hydrogen nucleus.
• Assignment: Explain why the boiling point of HF is lower than that of
water
19

Effect of hydrogen bonding
Boiling points of the hydrogen
compounds of Groups 4A, 5A, 6A,
and 7A elements. Although
normally we expect the boiling
point to increase as we move
down a group, we see that
three compounds (NH3, H2O,
and HF) behave differently.
The anomaly can be explained in
terms of intermolecular hydrogen
bonding.
21

Effect of hydrogen bonding
• Hydrogen bonding is responsible for
the expansion of water when it
freezes.
• The water molecules in the solid state
have tetrahedral arrangement for the
two lone pairs and two single bonds
radiating out from the oxygen.
• The lone pairs on the “O” atom can
be attracted to nearby water
molecules through hydrogen bonds
and a cage like structure results. Hydrogen bonding in ice
22

Properties of Liquids: Vapour pressure
• When a liquid is placed in an open vessel, it
evaporates. The molecules in the liquid are
moving with different kinetic energies. The
molecules that possess above-average kinetic
energies can overcome the intermolecular
forces that hold them in the liquid. These
energetic molecules escape from the liquid
surface as vapour.
• The process by which molecules of a liquid go
into the gaseous state (vapours) is called
Vaporization or Evaporation. The reverse
process whereby gas molecules become liquid
molecules is called Condensation.
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Heating
24

Vapour pressure
• If the liquid is placed in a closed vessel, the
molecules with high kinetic energies escape into
space above the liquid.
• As the number of molecules in the gas phase
increases, some of them strike the liquid surface
and are recaptured (condensation).
• A stage comes when the number of molecules
escaping from the liquid is equal to the number of
molecules returning to the liquid. In other words,
the rate of evaporation exactly equals the rate of
condensation.
• Thus a dynamic equilibrium is established
between the liquid and the vapour at the given
temperature.
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Heating
25

Vapour pressure
• Now the concentration of the vapour in the space above the liquid will
remain unchanged with lapse of time. Hence the vapour will exert a
definite pressure at the equilibrium.
• The vapour pressure of a liquid is defined as : the pressure exerted by the
vapour in equilibrium with the liquid at a fixed temperature.
• The vapour pressures of various liquids differ considerably, depending upon
the identity of the liquid with its particular intermolecular forces.
• Thus ethanol having weaker hydrogen bonding than water, evaporates
faster than water. Hence we expect that ethanol (350 torr at 60 oC) will
have higher vapour pressure than water (150 torr) at the given
temperature.
26

Effect of temperature on vapour pressure
• If the temperature of the liquid is increased, the
vapour pressure will increase.
• This is so because at higher temperature more
molecules in the liquid will have larger kinetic energy
and will break away from the liquid surface.
Therefore the concentration of vapour molecules
will increase before the equilibrium is re-established.
Also, at higher temperature, the average kinetic
energy of the vapour molecules will increase.
• Both vapour concentration and kinetic energy are
proportional to temperature. Therefore, any
increase of temperature will result in the increase of
vapour pressure.
• From the experimental curves shown (on your right),
it is clear that for both ethyl alcohol and water, the
vapour pressure rises with increase of temperature.
Vapour pressure increases with
temperature for ethanol and water
27

Determination of vapour pressure
• The vapour pressure of a given liquid can be measured by either
Static method or Dynamic method
• Static method
Determination of vapour pressure by Static method
A sufficient amount of the liquid whose vapour pressure is to
be determined is placed in the bulb connected to a mercury
manometer and a vacuum pump. All the air from the bulb is
removed by working the vacuum pump and the stopcock
closed. A part of the liquid evaporates. The system is then
maintained at a fixed temperature for enough time so that
the equilibrium is established. The difference in the levels of
mercury in the manometer is equal to the vapour pressure
of the liquid. By adjusting the thermostat at a different
temperature, the vapour pressure of the liquid at another
temperature can be determined. This method is used for
liquids having vapour pressures up to one atmosphere
28

Determination of vapour pressure
• Dynamic Method
Determination of vapour pressure by Dynamic method
An inert gas is passed through the given liquid
at a constant temperature (T). The gas
saturated with the vapour of the liquid leaves
the flask at the exit tube. If V be the volume
of the gas passed and m the loss in weight of
the liquid, the vapour pressure is given by
𝑽𝒂𝒑𝒐𝒖𝒓 𝒑𝒓𝒆𝒔𝒔𝒖𝒓𝒆 =
𝒎
𝑴𝑽
× 𝑹𝑻
where M = molecular weight of the liquid and
R = gas constant. This method is particularly
suited for liquids of very low vapour pressure
29

Effect of vapour pressure on boiling point
|||||||||||
Heating
• A liquid boils when the pressure of the vapour within the bubble equals
the atmospheric pressure exerted on the bubble at the liquid surface.
• When a liquid is heated, tiny bubbles are formed in
it. These rise to the liquid surface and burst. The
temperature at which it happens is the boiling point
of the liquid.
• Consider an individual bubble: the liquid vaporizes
into it and the vapour pressure in the bubble keeps it
in form. However, the pressure of the atmosphere
exerted on the liquid top tends to collapse the
bubble. As the bubble goes to the surface, the
vapour pressure in the bubble equals the
atmospheric pressure. Thus the bubble collapses.
• The boiling point of the liquid may, therefore, be
defined as the temperature at which the vapour
pressure of the liquid is equal to the atmospheric
pressure.
30

Effect of vapour pressure on boiling point
• Because the atmospheric pressure varies with altitude and other
conditions, the boiling points are reported at 760 torr (1 atm).
• Therefore the normal boiling point of a liquid is the temperature
at which the vapour pressure of the liquid is 760 torr or 1 atm.
• The boiling point of ethanol is 78 oC and that of water is 100 oC.
Explain.
• The boiling point of a liquid can be lowered by reducing the
external pressure by using a vacuum pump. Then the vapour
pressure of the liquid is equal to the external pressure at a lower
temperature.
• The boiling point of a liquid can be increased by raising the
external pressure. Thus the vapour pressure of the liquid is equal
to the external pressure at a higher temperature.
Explain the principle of a
domestic pressure cooker
31

Surface tension
Surface tension is caused by the net
inward pull on the surface molecules
• Surface tension arises from the intermolecular
forces of attraction in liquids
• A molecule in the interior of a liquid is attracted
equally in all directions by the molecules around it.
• A molecule in the surface of a liquid is attracted
only sideways and toward the interior.
• The forces on the sides being counterbalanced the
surface molecule is pulled only inward the liquid.
• Thus there is a tendency on the part of the surface
molecules to go into the bulk of the liquid.
32

Surface tension
• The liquid surface is, therefore,
under tension and tends to
contract to the smallest possible
area in order to have the
minimum number of molecules at
the surface.
• It is for this reason that in air,
drops of a liquid assume spherical
shapes because for a given
volume a sphere has the
minimum surface area
The surface tension (γ) of a liquid is defined as
the force in dynes acting at right angles to the
surface along 1 cm length of the surface
The inward forces on the surface
molecules minimize the surface
area and form a drop
33

Units of surface tension
• In CGS system, the unit of surface tension is dyne per centimeter
(dyne cm–1)
• In SI system, the unit of surface tension is Newton per meter (Nm–1)
• Note that:
1 dyne cm–1 = 1 m Nm–1
34

Effect of temperature on surface tension
• A change in temperature causes a change in surface tension of a liquid.
• When temperature increases, there is an increase in kinetic energy of liquid
molecules (KE ∝ T), thereby decreasing intermolecular forces.
• It results in a decrease in the inward pull acting on the surface of the
liquid. In other words, surface tension decreases with an increase in
temperature.
• Relationship between surface tension and temperature (by W. Ramsay and
J. Shields, 1893)
𝜸
𝑴
𝝆
𝟐/𝟑
= 𝒌 𝒕𝒄 − 𝒕 − 𝟔
• where k is a constant (temperature coefficient), tc is the critical
temperature and t is any other temperature, (𝑴
𝝆)𝟐/𝟑
represents molar
surface energy of the liquid.
35

Effect of temperature on surface tension
36

Determination of surface tension
• Capillary-rise Method • A capillary tube of radius r is vertically
inserted into a liquid. The liquid rises to
a height h and forms a concave
meniscus.
• The surface tension (γ) acting along the
inner circumference of the tube exactly
supports the weight of the liquid in the
column.
• By definition, surface tension is force
per 1 cm acting at a tangent to the
meniscus surface. If the angle between
the tangent and the tube wall is θ, the
vertical component of surface tension
is 𝛾Cos𝜃
(a) Rise of liquid in a capillary tube; (b ) Surface tension (𝛾) acts
along tangent to meniscus and its vertical component is 𝛾Cos𝜃 ;
(c) Upward force 2𝜋r𝛾Cos𝜃 counterbalances the downward
force due to weight of liquid column, 𝜋r2hgd. 37

• The total surface tension along the circular contact line of meniscus is 2πr times.
Therefore,
𝑼𝒑𝒘𝒂𝒓𝒅 𝒇𝒐𝒓𝒄𝒆 = 𝟐𝝅𝒓𝜸𝑪𝒐𝒔𝜽
• where r is the radius of the capillary. For most liquids, θ is essentially zero, and
cos θ = 1. Then the
𝑼𝒑𝒘𝒂𝒓𝒅 𝒇𝒐𝒓𝒄𝒆 = 𝟐𝝅𝒓𝜸
• The downward force on the liquid column is due to its weight which is mass ×
gravity (g). Thus,
𝑫𝒐𝒘𝒏𝒘𝒂𝒓𝒅 𝒇𝒐𝒓𝒄𝒆 = 𝒉𝝅𝒓𝟐𝝆𝒈
• Where 𝜌 is the density of the liquid
• But Upward force = Downward force, thus
2𝜋𝑟𝛾 = ℎ𝜋𝑟2
𝜌𝑔
𝜸 =
𝒉𝒓𝝆𝒈
𝟐
𝒅𝒚𝒏𝒆𝒔/𝒄𝒎
• In order to know the value of γ, the value of h is found with the help of a
travelling microscope (in mm) and density with a pyknometer 38

• Drop Formation Method
Stalagmometer A drop forming from a tube of radius r
A drop of liquid is allowed to form at the lower end
of a capillary tube. The drop is supported by the
upward force of surface tension acting at the outer
circumference of the tube. The weight of the drop
(mg) pulls it downward. When the two forces are
balanced, the drop breaks. Thus at the point of
breaking,
𝒎𝒈 = 𝟐𝝅𝒓𝜸
Where
m = mass of the drop
g = acceleration due to gravity
r = outer radius
The apparatus employed in the drop formation
method is called Stalagmometer or Drop pipette
41

• The stalagmometer is cleaned, dried and filled with the experimental liquid, up to
mark A. Then the surface tension is determined by one of the two methods given
below:
a) Drop-weight Method: About 20 drops of the given liquid are received from the
stalagmometer or drop-pipette in a weighing bottle and weighed. Thus weight
of one drop is found. The drop-pipette is again cleaned and dried. It is filled
with a second reference liquid (say water) and weight of one drop determined
as before.
𝑚1𝑔 = 2𝜋𝑟𝛾1 …………………..(1)
𝑚2𝑔 = 2𝜋𝑟𝛾2 ………………….(2)
Dividing eqn. (1) by (2), we obtain
𝜸𝟏
𝜸𝟐
=
𝒎𝟏
𝒎𝟐
• Knowing the surface tension of the reference liquid from Tables, that of the
liquid under study can be found.
42

b) Drop-number Method: The drop-pipette is filled up to the mark A with the
experimental liquid. The number of drops is counted as the meniscus travels from A
to B. Similarly, the pipette is filled with the reference liquid as the meniscus passes
from A to B. Let n1 and n2 be the number of drops produced by the same volume V
of the two liquids.
Thus
𝑇ℎ𝑒 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑜𝑛𝑒 𝑑𝑟𝑜𝑝 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑 1 = 𝑉 𝑛1
𝑇ℎ𝑒 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑑𝑟𝑜𝑝 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑 1 = (𝑉 𝑛1) × 𝜌1
𝑆𝑖𝑚𝑖𝑙𝑎𝑟𝑙𝑦, 𝑡ℎ𝑒 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑑𝑟𝑜𝑝 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑 2 = (𝑉 𝑛2) × 𝜌2
Thus, we can write that
𝜸𝟏
𝜸𝟐
=
𝑽
𝒏𝟏
𝝆𝟏
𝑽
𝒏𝟐
𝝆𝟐
=
𝒏𝟐𝝆𝟏
𝒏𝟏𝝆𝟐
• The value of 𝝆𝟏 is determined with a pycnometer or density bottle. Knowing 𝝆𝟐
and 𝜸𝟐 from reference tables, 𝜸𝟏 can be calculated.
43

• Ring-detachment Method
du Nouy ring with
a suspending hook
du Nouy Tensiometer
45

• In this method the force required
to detach a platinum ring (du
Nouy ring) from the liquid surface
is measured.
• This force (F) is exactly equal to
the downward pull due to
surface tension γ acting along
the circumference of the ring.
• Twice the length of the
circumference (2 × 2πr) is taken
since the liquid is in contact with
both the inside and the outside of
ring. Thus,
𝐹 = 4𝜋𝑟𝛾 𝑜𝑟 𝜸 =
𝑭
𝟒𝝅𝒓
• Where r is the radius of the ring
• The apparatus employed is called
the du Nouy Tensiometer
• One end of the torsion wire is fixed while the
other is attached to a knob carrying a pointer.
• The pointer moves on a fixed scale. The scale
is previously calibrated by taking different
weights on the beam and noting the scale
reading when it is lifted from the horizontal
position.
• The liquid whose surface tension is to be
determined is placed in a watch glass so that
the Pt ring just touches its surface. The knob
of the torsion wire is then slowly turned till
the ring is just detached from the surface.
• The reading shown by the pointer on the scale
gives the force F. The surface tension is then
calculated from the equation.
46

• Maximum Bubble Pressure Method
A simple apparatus for maximum bubble pressure method
• In this method air-pressure is
applied slowly through a capillary
tube dipping in the experimental
liquid.
• A bubble is formed at the end of the
capillary.
• Slowly the bubble grows and
becomes hemispherical. Then it
breaks away when the pressure
recorded by the manometer is
noted. This is the maximum
pressure required to make a bubble
at the end of the capillary.
47

• At the moment of breaking, the forces due to
maximum pressure P equals that of the opposing
hydrostatic pressure Ph and the surface tension γ
at the circumference of the capillary. Thus,
• 𝑃𝜋𝑟2 = 𝑃ℎ𝜋𝑟2 + 2𝜋𝑟𝛾
• 𝑃 = 𝑃ℎ +
2𝛾
𝑟
𝑷 = 𝒉𝝆𝒈 +
𝟐𝜸
𝒓
• where r = radius of capillary; 𝜌 = density of the
liquid; h = depth of liquid.
• Knowing the value of P, h, 𝜌 and r, γ can be found
Applied pressure on bubble is
opposed by hydrostatic
pressure and surface tension
48

Viscosity
• A liquid may be considered to be consisting of molecular layers arranged one over
the other.
• When a shearing force is applied to a liquid, it flows. However, the forces of
friction between the layers offer resistance to this flow.
• Viscosity of a liquid is a measure of its frictional resistance
Flow of a liquid on a glass surface
49

Viscosity
• Considering a liquid flowing on a glass surface
(shown on previous slide). The molecular layer in
contact with the stationary surface has zero
velocity. The successive layers above it move
with increasingly higher velocities in the
direction of the flow.
• Consider two adjacent moving layers of a liquid.
Let these be separated by a distance dx and have
a velocity difference dv.
• The force of friction (F) resisting the relative
motion of the two layers is directly proportional
to the area A and the velocity difference dv,
while it is inversely proportional to the distance
between the layers.
Two parallel layers moving in a liquid
𝐹 ∝ 𝐴
𝑑𝑣
𝑑𝑥
= 𝜂𝐴
𝑑𝑣
𝑑𝑥
𝜂 =
𝐹
𝐴
×
𝑑𝑥
𝑑𝑣
𝜂 is the proportionality constant
or Coefficient of Viscosity or
simply viscosity of a liquid
50

Viscosity
• η has a specific value for a given liquid at the same temperature.
• Viscosity of a liquid may be defined as the force of resistance per
unit area which will maintain unit velocity difference between two
layers of a liquid at a unit distance from each other.
• The reciprocal of viscosity is called Fluidity and is denoted by φ
𝝓 =
𝟏
𝜼
51

Units of Viscosity
• The dimensions of the coefficient of viscosity (η) may be derived from the
equation:
• 𝜂 =
𝐹
𝐴
×
𝑑𝑥
𝑑𝑣
=
𝐹𝑜𝑟𝑐𝑒
𝐴𝑟𝑒𝑎
×
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
=
𝑚𝑎𝑠𝑠×𝑙𝑒𝑛𝑔𝑡ℎ×𝑡𝑖𝑚𝑒−2
𝑙𝑒𝑛𝑔𝑡ℎ2 ×
𝑙𝑒𝑛𝑔𝑡ℎ
𝑙𝑒𝑛𝑔𝑡ℎ/𝑡𝑖𝑚𝑒
• 𝜂 = 𝑚𝑎𝑠𝑠 × 𝑙𝑒𝑛𝑔𝑡ℎ−1
× 𝑡𝑖𝑚𝑒−1
• Thus in CGS system the unit of η is expressed as g cm–1 s–1. It is called poise
(P).
• In practice smaller units centipoise (10–2 poise) and millipoise (10–3 poise)
are used.
• The SI unit is kg m–1 s–1
• 1 P = 1 g cm–1 s–1 = 0.1 kg m–1 s–1
52

Measurement of Viscosity - The Ostwald
Method
• Viscosity of a liquid can be determined with the help of Pioseulle’s
equation. The expression governs the flow of a liquid through a
capillary.
𝜼 =
𝝅𝑷𝒓𝟒
𝒕
𝟖𝑽𝒍
• where V is the volume of the liquid flowing through the capillary in
time t, P the pressure-head, r the radius of the tube and l is the
length.
• The experimental measurement of P, r, l and V offers considerable
difficulty. Therefore, it is not possible to find the absolute coefficient
of viscosity (η) straight away from Poiseulle’s equation.
54

Measurement of Viscosity - The Ostwald
Method
• Ordinarily, the viscosity of a liquid is determined with respect to that of
water. This is called Relative Viscosity.
• Let t1 and t2 be the times of flow of a fixed volume (V) of the two liquids
through the same capillary. The expression for relative viscosity (η1/η2) can
be derived from the Poiseulle’s equation.
• 𝜂1 =
𝜋𝑃1𝑟4𝑡1
8𝑉𝑙
…….(1) 𝜂2 =
𝜋𝑃2𝑟4𝑡2
8𝑉𝑙
……….(2)
•
𝜂1
𝜂2
=
𝜋𝑃1𝑟4𝑡1
8𝑉𝑙
×
8𝑉𝑙
𝜋𝑃2𝑟4𝑡2
=
𝑃1𝑡1
𝑃2𝑡2
• Since the pressure-head is proportional to density (𝜌) of the liquid, thus;
𝜼𝟏
𝜼𝟐
=
𝝆𝟏𝒕𝟏
𝝆𝟐𝒕𝟐
• Substituting the value of the viscosity coefficient of water (η2), we can find
the absolute viscosity of the given liquid (η1).
55

Ostwald Viscometer
Ostwald Viscometer
• The apparatus commonly used for the determination of relative
viscosity of a liquid is known as Ostwald viscosimeter or viscometer.
• Viscometer: The left-hand limb is essentially a pipette with two
calibration marks A and B. A length of capillary tube joins the pipette to
a bulb C in the right-hand limb. A definite volume of liquid (say 25 ml) is
poured into the bulb C with a pipette. The liquid is sucked up near to the
top of the left-limb with the help of a rubber tubing attached to it. The
liquid is then released to flow back into the bulb C. The time (t1) from A
to B is noted with a stopwatch. Then the apparatus is cleaned and the
experiment repeated with water, taking about the same volume. The
time of flow of water (t2) from A to B is recorded. The density of the
liquid (𝜌) and water (𝜌𝑤) are determined with the help of a pycnometer
or density bottle. Using the equation below, the absolute viscosity of the
liquid can be found at the temperature of the experiment.
𝜼
𝜼𝒘
=
𝝆𝒕𝟏
𝝆𝒘𝒕𝟐
56

Effect of temperature on viscosity of a liquid
• In general, the viscosity decreases with increase in
temperature. The variation of viscosity (η) with
temperature can be expressed by the following relationship
• 𝜂 = 𝐴𝑒−𝐸/𝑅𝑇
• Where A and E are constant (preexponential factor) and
Arrhenius activation energy, respectively
• Taking logarithms on both sides
• ln 𝜂 = ln 𝐴 +
𝐸
𝑅𝑇
• 𝐥𝐧 𝜼 =
𝑬
𝑹
𝟏
𝑻
+ 𝐥𝐧 𝑨
• A plot of log η versus 1/T should be a straight line
• It has also been found that there is 2% decrease in viscosity
for every increase in one degree of temperature of any
liquid
Plot of log η versus I/T
58

Refractive Index
The refractive index (n) of a substance is defined as the ratio of the
velocity of light in vacuum or air, to that in the substance
𝑛 =
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑙𝑖𝑔𝑛𝑡 𝑖𝑛 𝑎𝑖𝑟
Refraction of light through a denser liquid medium
59

Refractive Index
• When a ray of light passes from air into a liquid, its direction is changed.
This change of direction is called refraction.
• The refractive index of a liquid with respect to air is given by Snelle’s Law:
𝒏 =
𝑺𝒊𝒏 𝒊
𝑺𝒊𝒏 𝒓
• where i is the angle of incidence and r the angle of refraction
• The refractive index of a liquid can be easily determined to a high degree of
accuracy.
• It is a characteristic property of a liquid. It varies with temperature and
wavelength of light used.
60

Refractive Index
• The wavelength of D-line of the sodium spectrum (589 nm) is
generally used for the purpose.
• If the refractive index of a liquid is measured at 20 oC and using D-line
of sodium, it is represented by the following symbol.
• Because refractive index is a ratio, it has no units.
61

Specific Refraction
• Lorenz and Lorenz (1880) purely from theoretical considerations
derived the following relation for the refractive power of substance
𝑹𝒔 =
𝒏𝟐 − 𝟏
𝒏𝟐 + 𝟐
×
𝟏
𝝆
• where Rs is the Specific Refraction, 𝜌 the density and n the refractive
index.
• The value of Rs was constant at all temperatures
62

Molar Refraction
• Molar refraction is defined as the product of specific refraction and
molecular mass.
• Thus molar refraction of a liquid (RM) is obtained by multiplying equation Rs
equation by molecular mass (M).
𝑹𝑴 =
𝒏𝟐
− 𝟏
𝒏𝟐 + 𝟐
×
𝑴
𝝆
• The value of molar refraction is characteristic of a substance and is
temperature-independent.
• Since it depends on the wavelength of light, the values of molar refraction
are generally reported for D-line of sodium.
• Since the value of refractive index (n) is dimensionless, from the above
equation it is evident that RM has the units of the molar volume i.e., cm3
mol–1.
63

Determination of Refractive Index
• The refractive index of a liquid can be determined with the help of an
instrument called Abbe Refractometer
The Abbe refractometer
• A thin film of the liquid is placed between the two
prisms. Light from a sodium lamp is made to fall on
lower side of the lower prism with the help of a
mirror. The hypotenuse surface of the lower prism is
ground and, therefore, light enters the liquid at all
angles of incidence.
• However, no ray can enter the upper prism with
greater angle of refraction than the grazing incidence
(i.e., at an angle) slightly less than 90 oC. Thus the
view in the telescope appears to be divided into two
bands, one bright and one dark.
• The prism assembly is rotated with the help of a side
knob till the cross wire of the telescope coincides with
the edge of the bright band. A pointer attached to the
prism assembly indicates the refractive index on the
scale calibrated to read refractive indices directly
65

Molar Refraction and Chemical Constitution
• The molar refraction (RM) is an additive property i.e. molar refraction of a
molecule is the sum of the molar refraction of its constituent atoms. It is helpful
in determining the constitution of a compound.
• The molar refraction values are calculated for various possible structures and the
formula which is in accordance with the calculated molar refraction is the correct
formula (or structure) of that compound.
• The molar refraction values for some atoms and bonds are given in the Table
below
66

Optical activity
• A beam of ordinary light consists of
electromagnetic waves oscillating in many
planes.
• When passed through a polarizer (e.g., a
Polaroid lens), only waves oscillating in a single
plane pass through.
• The emerging beam of light having oscillations
in a single plane is said to be plane polarized.
• When plane-polarized light is passed through
certain organic compounds, the plane of
polarized light is rotated.
• A compound that can rotate the plane of
polarized light is called optically active. This
property of a compound is called optical activity
Plane-polarized light
68

Optical activity
• A compound which rotates the plane-polarized light to the left
(anticlockwise), is said to be levorotatory.
• A compound that rotates the plane-polarized light to the right (clockwise),
is said to be dextrorotatory.
• By convention, rotation to the left is given a minus sign (–) and rotation to
the right is given a plus sign (+). For example, (–)-lactic acid is levorotatory
and (+)-lactic acid is dextrorotatory
Optical Activity illustrated 69

Specific rotation
• The rotation of plane-polarized light is an intrinsic property of optically active molecules.
• When a polarized beam of light is passed through the solution of an optically active
compound, its plane is rotated through an angle α (angle of rotation).
• This rotation depends on the number of optically active molecules encountered. Therefore, α
is proportional to both the concentration and the length of the sample solution.
• The specific rotation which is characteristic of an optically active substance, is expressed as
𝜶 =
𝜶
𝒍 × 𝒄
• Where 𝜶 is specific rotation, 𝛼 is observed angle of rotation in degrees, 𝑙 is length of the
sample solution in decimeter (dm; 10 cm) and c is the concentration of the sample solution in
g/ml
• Thus from the equation above, the specific rotation can be defined as the observed angle of
rotation at a concentration of 1 g/ml and path length of 1 dm. Conventionally, a specific
rotation is reported as [𝜶]𝑫
𝒕
, where t stands for temperature and D for D-line of sodium used
for determination.
70

Measurement of Optical Activity
Schematic diagram of a polarimeter
polarimeter
• Optical activity is measured with the help of an instrument known as polarimeter.
• This is basically a system of polarizers with a sample tube placed in between.
71

Measurement of Optical Activity
• First, an optically inactive medium (air or solvent) fills the sample
tubes and polarized sodium light emerging from the polarizer passes
through it. The analyzer is then turned to establish a dark field. This
gives a zero reading on the circular scale around the analyzer.
• Then the solution of the given optically active compound is placed in
the sample tube. The plane of polarized light passing through it is
rotated. The analyzer is turned to re-establish the dark field. The
angle of rotation (α) is then noted in degrees on the circular scale.
• The specific rotation is calculated using the expression stated in
previous slide.
72

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