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5/26/2009
121
Gases
Lecture 10 – May 27, 2009 1
Lecture 10
Chapter 5
Effusion and Diffusion (5.7)
Collisions of Gas Particles with the Container Walls
(5.8)
Intermolecular Collisions (5.9)
Real Gases (5.10)
2
Effusion and Diffusion
Effusion:
the passage of a gas through a tiny orifice
into an evacuated chamber
Diffusion:
the migration of (gas) molecules as a result
of random molecular motion
results in the mixing of two or more gases
3
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Effusion
Fig. 5.18
4
Graham’s Law
the rate of effusion of a gas is inversely proportional to
the square root of the mass of its particles
The rates of effusion of two different gases are inversely
proportional to the square roots of their molar masses (M)
rate of effusion for gas 1 M2
=
rate of effusion for gas 2 M1
gases are at the same temperature and pressure
5
Based on Kinetic Theory
expect that rate of effusion of a gas will depend directly
on the average velocity of its particles
effusion rate for gas1 u avg gas1 8RT/πM1 M2
= = =
effusion rate for gas 2 u avg gas 2 8RT/πM 2 M1
Graham’s law
rate of effusion for gas 1 M2
=
rate of effusion for gas 2 M1
the Kinetic model fits the experimental results
6
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Diffusion
rate of diffusion is the rate of mixing of gases
can relate diffusion to the ratio of the distances traveled
by two gases
expect distances traveled to be related to the velocities
of the particles
NH 3(g) + HCl (g) → NH 4 Cl(s)
release a sample of HCl and a sample of NH3 gases
from opposite end of a long tube
distance traveled by NH 3 u avg NH3 M HCl
= =
distance traveled by HCl u avg HCl M NH3
7
Results
progress is slow despite velocities of
450 m/s for HCl
660 m/s for NH3
if we use graham’s law to predict the ration we obtain:
d NH3 M HCl
= = 1.5
d HCl M NH3
the measured value is 1.3
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Experiment
Fig. 5.19
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Collisions with Container Walls
pressure exerted by a gas is due to collisions with the
container walls
rate of collisions (ZA) will depend on
average velocity (uavg) of the particles
size of the area (A)
particle density (particles per unit volume N/V)
N
ZA α u avg x A x
V
units for ZA:
m is meters m particles particles collisions
x m2 x = =
not mass s m3 s s
10
ZA
N 8RT
ZA α A
V πM
proportionality constant = 1/4
1 N 8RT N RT
ZA = A =A
4 V πM V 2πM
11
Intermolecular Collisions – Real Gases
Kinetic molecular theory does not take into account
the collision of gas particles with each other
collisions do occur
consider the collisions of a single particle as it moves
through the container
must take into account the velocity of the particle
and the velocities of the particles moving about it
must consider the diameter of the particles
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Collisions
collision rate Z = volume swept out x (N/V)
particles per unit volume
must consider a relative velocity = 2 µ avg
13
Collisions
N 2 πRT
collision rate, Z = 4 d
V M
where
d is the diameter of the particle
M is molar mass
V is the unit volume
Fig. 5.21
14
Mean Free Path
Z = collisions per second
then
1/Z = seconds between collisions
the mean free path λ
1
λ= x u avg = distance between collisions
Z
1 8RT 1
λ= =
4Nd 2 πRT πM
2(πd 2 )
N
V
V M
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Real Gases
the behaviour of Real Gases approaches that of an
Ideal Gas under conditions of low pressure and/or
high temperatures
Ideal Gas (refer to basic postulates of KMT)
negligible particle volume
no interparticle interactions
PV
A plot of vs P will give a straight line of slope 0
nRT
ie PV/nRT = 1
16
The Kinetic Molecular Theory (KMT)
a simple model used to explain the behaviour of an
ideal gas
Basic Postulates
the volume of individual gas particles is assumed to be
negligible
the pressure of a gas is due to collisions of particles with
the container walls
the particles do not exert any force on each other
the average kinetic energy of the particles is directly
proportional to the temperature of the gas (in Kelvin)
17
Plots of PV/nRT vs P
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N2 at different temperatures
at higher temp, approaches ideal
behaviour 19
Correct for Volume of a Particle
PV
For Real gases plots of vs P deviate significantly
nRT
Add correction terms to PV = nRT to account for this
deviation
Van der Waals: correction for particle volume
nRT where b is an empirical constant, from
P′ =
(V − nb) experiment
n is the number of moles of gas
ie: the actual volume is the container volume minus a
factor for the volume of the molecules
20
Correct for Interactions/Attractions
attractions will cause the observed pressure to be
smaller than if the particles did not interact
nRT
Pobs = (P′− correction factor) = − correction factor
V − nb
number of interactions will depend on the square of the
concentration (particles per unit volume)
2
n
Pobs = P′ − a
v a is a constant
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Van der Waal’s Equation
2
nRT n
Pobs = − a
V − nb V
n
2
Pobs + a ( V − nb ) = nRT
V
corrected volume
corrected pressure
Values for correction factors a and b for some gases are
given in Table 5.3
22
Ideal Behavior in Real Gases
For a gas at low pressure:
there are few particles per unit volume
volume of particle is negligible compared to volume of
the container
interactions are minimized
Real gas behaves more like Ideal gas at low
pressure
For a gas at high temperature
less interaction, particles move further apart, larger
volume,
at low temp, volume decreases, particles closer
together
Real gas behaves more like an Ideal gas at high
temperature
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