Thyroid Physiology_Dr.E. Muralinath_ Associate Professor
Kinetic theory of gases
1. Kinetic Theory of Gases
Dr.S.Radha
Assistant Professor of
Chemistry
SaivaBhanuKshatriya College
Aruppukottai
2. Postulates of Kinetic Theory Of
Gases
Gases are mostly empty space
Gases contain molecules which have random
motion
The molecules have kinetic energy
The molecules act independently of each other –
there are no forces between them
Molecules strike the walls of the container – the
collisions are perfectly elastic
Exchange energy with the container
The energy of the molecules depends upon the
temperature
3. Large collections are very
predictable
Fluctuations in behaviour of a small group of
particles are quite noticeable
Fluctuations in behaviour of a large group (a mole)
of particles are negligible
Large populations are statistically very reliable
4. Pressure and momentum
Pressure = force/unit area
Force = mass x acceleration
Acceleration = rate of change of velocity
Force = rate of change of momentum
Collisions cause momentum change
Momentum is conserved
5. Elastic collision of a particle with the wall
Momentum lost by particle = -2mv
Momentum gained by wall = 2mv
Overall momentum change = -2mv + 2 mv = 0
Momentum change per unit time = 2mv/Δt
momentum change no collisions 1
collision time area
P x x=
6. Factors affecting collision
rate
1. Particle velocity – the faster the particles the more
hits per second
2. Number – the more particles – the more collisions
3. Volume – the smaller the container, the more
collisions per unit area
2
2
2 o ovN mv N
P mv
V V
= • =
7. Making refinements
We only considered one wall – but there are six
walls in a container
Multiply by 1/6
Replace v2
by the mean square speed of the
ensemble (to account for fluctuations in velocity)
2
1
3
om v N
P
V
=
2 2
21
6 3
o omv N mv N
P x
V V
= =
8. Boyle’s Law
Rearranging the previous equation:
Substituting the average kinetic energy
Compare ideal gas law PV = nRT:
The average kinetic energy of one mole of
molecules can be shown to be 3RT/2
2
2 2
3 2 3
o o k
m v
PV N N E
÷= =
÷
3
2
kE nRT=
9. Root mean square speed
Total kinetic energy of one mole
But molar mass M = Nom
Since the energy depends only on T, vRMS decreases
as M increases
21 3
2 2
k oE N m v RT= =
M
RT
mN
RT
v
o
RMS
33
==
10. Speed and temperature
Not all molecules move at the same speed or in the
same direction
Root mean square speed is useful but far from
complete description of motion
Description of distribution of speeds must meet two
criteria:
Particles travel with an average value speed
All directions are equally probable
11. Maxwell meet Boltzmann
The Maxwell-Boltzmann
distribution describes the
velocities of particles at a
given temperature
Area under curve = 1
Curve reaches 0 at v = 0
and ∞
2
/ 22
3/ 2
( )
4
2
Bmv k T
B
F v Kv e
m
K
k T
π
π
−
=
= ÷
12. M-B and temperature
As T increases vRMS
increases
Curve moves to right
Peak lowers in height
to preserve area
13. Boltzmann factor: transcends
chemistry
Average energy of a particle
From the M-B distribution
The Boltzmann factor – significant for any and all
kinds of atomic or molecular energy
Describes the probability that a particle will adopt a
specific energy given the prevailing thermal energy
1
exp
expB
B
k T
k T
ε
ε
− = ÷
÷
2
2
mv
ε =
( ) exp
B
P
k T
ε
ε
µ − ÷
14. Applying the Boltzmann
factor
Population of a state at a level ε above the ground
state depends on the relative value of ε and kBT
When ε << kBT, P(ε) = 1
When ε >> kBT, P(ε) = 0
Thermodynamics, kinetics, quantum mechanics
( ) exp
B
P
k T
ε
ε
µ − ÷
15. Collisions and mean free path
Collisions between
molecules impede
progress
Diffusion and effusion
are the result of
molecular collisions
16. Diffusion
The process by which gas molecules become
assimilated into the population is diffusio n
Diffusion mixes gases completely
Gases disperse: the concentration decreases with
distance from the source
17. Effusion and Diffusion
The high velocity of molecules leads to rapid mixing
of gases and escape from punctured containers
Diffusion is the mixing of gases by motion
Effusion is the escape of a gas from a container
18. Graham’s Law
The rate of effusion of a gas is inversely proportional
to the square root of its mass
Comparing two gases
m
Rate
1
∝
1
2
1
2
2
1
m
m
m
m
Rate
Rate
==
19. Living in the real world
For many gases under most conditions, the ideal
gas equation works well
Two differences between the ideal and the real
Real gases occupy nonzero volume
Molecules do interact with each other – collisions are
non-elastic
20. Consequences for the ideal gas
equation
1. Nonzero volume means actual pressure is larg e r
than predicted by ideal gas equation
Positive deviation
1. Attractive forces between molecules mean
pressure exerted is lower than predicted – or
volume occupied is less than predicted
Negative deviation
Note that the two effects actually offset each other
21. Van der Waals equation:
tinkering with the ideal gas equation
Deviation from ideal is more apparent at high P, as
V decreases
Adjustments to the ideal gas equation are made to
make quantitative account for these effects
( ) nRTnbV
V
an
P =−
+ 2
2
Correction for
intermolecular
interactions
Correction for
molecular
volume
22. Real v ideal
At a fixed temperature
(300 K):
PVobs < PVideal at low P
PVobs > PVideal at highP
23. Effects of temperature on deviations
For a given gas the
deviations from ideal
vary with T
As T increases the
negative deviations
from ideal vanish
Explain in terms of van
der Waals equation
( ) nRTnbV
V
an
P =−
+ 2
2
24. Interpreting real gas
behaviorsFirst term is correction for
volume of molecules
Tends to increase Preal
Second term is correction
for molecular interactions
Tends to decrease Preal
At higher temperatures,
molecular interactions are
less significant
First term increases relative to
second term
( )
2
2
2
2
V
an
nbV
nRT
P
nRTnbV
V
an
P
−
−
=
=−
+