1
Physical Chemistry
Lecture 2
Random walks; microscopic
theory of diffusion
Macroscopic versus microscopic
Fick’s laws describe time
evolution macroscopically
Do not specifically consider
a single molecule (although
we discussed them in that
manner)
Focus on the tendency to
eliminate density gradients
Can be explained by
ad hoc
appeal to kinetic theory
Diffusion can be understood
in terms of a microscopic
process – the random walk
Uses probability concepts
Implies randomness in a
system with many
molecules
Time development occurs
in a “natural” way
Random motion of a single molecule is the
underlying driving force described by diffusion.
Probability of event
Random events
Each event is considered
equally likely unless other
information is known
Can only discuss likelihood
of an event,
p
n
= number of possible
results
Only applies to a “large
sample”
Examples
Coin flips (n=2)
Throws of dice (n=6)
For events that are not
equally likely, one must
know (by some external
means) the probability,
, of
each event
n
p
1
Probability of a sequence
Probability of a sequence,
P
, is product of the
probabilities of the
elementary events that
make up each sequence
When the probabilities of
the elementary events are
the same, this equation
simplifies
Example: tossing a coin
four times or tossing four
coins at the same time
Since
h
=
t
= ½, each
sequence has a
likelihood of happening
= (½)
4
16 possible sequences,
so the probability of any
one sequence is 1/16 (=
(½)
4
)
n
p
p
p
p
p
P
4
3
2
1
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Probability of a configuration
Often concerned only
with the number of
elementary outcomes in
a sequence, not order
Example of tossing a
coin: probability of
getting 3 heads when
tossing a coin four
times
Four different sequences
have three heads
P ‘
= 4(1/6) = 1/4
)
(
'
sequences
all
for
P
P
if
P
n
P
P
i
sequences
e
appropriat
i
sequences
︶
e
appropri at
all
︵
over
Numbers of configurations
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 Fall '10
 Staff
 Physical chemistry, Probability, pH, Brownian Motion, Stochastic process, Random walk

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