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lls o uniformly on both sides ofscale. molecules, eight di there are the two chambers.cult, but we can
the distribution, and between becomes more di
the most
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antity associated with isForenergy balancedwe now have erent begin to!"#$%&'(general trend start to emerge.
an three identical SoMolecules
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see
Ten Molecules
1 possible states.
FIGURE a Three Molecules
f we
arrangements are possible, but only four of For example,4.11 Isee from the histograms
e concept of spontaneity: A !"%
spontaneous process moves from an otherwise vacatedconsider two molecules in
we can
bulb with two chambers
these are distinct. For the but 100 Case
d this toto states of higher probability.not 10, arrangements of forfor ten molecules that the probability of the
molecules,
bability the case for which we have We left and Themolecules 10 connected by a passageway and we calculate
also notice something Molecules
!"&
two computer,
e 4.14. sNow thelowest two moleculesaonis best done byby a more
individual counting the
molecules!"$
being distributed roughly equally
e: e tates of
probabilitythe states can
re characterized
the probability that both molecules are in the
on
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4
continue to in
F the right,atoms in the be realized by areon—for example,all molecules.13 As wethreele eor addthe so betweenchamberthethe same time, (½)(more ¼;
probability that if all IGUREmoleculesinare sequestered inright left each of at two sides is much ½) =
ranging the
di rent ways, one
i
the
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to the system,
lly zero; and, moreover, moleculesprobability thatof alldistribution then than the distribution being skewed
that arrangements havecounting the states probable we calculate the probability that both
these the
a the the clothes
more ordered con guration; just asa is the caseprobability that is to either the right or the left side.
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and assigning probability to each arrange!"#
three times higher than the other two states
tlyfolded and placed in ment or the other is increasinglycan prob molecules are in the right chamber at the
!"'
becomes
g skewed to one chamber everythingmore di leftlink everything on
a single drawer!the iscult, but we unlikely
½)
with
on
and between
molecules is will loom large in our understanding of to emerge. in same time, (½)(Ten= ¼; then we calculate the
increased. begin to see a general trend start processes
Molecules is in the right
y, and order
probability that one molecule
the right. If you want to prove this to yourself,
!"!
For example, we can see from the histograms
!"!
!"!
you can H..,.+A
and C)
Imagine now if we move fromlabel each molecule (say A, B,H..,532*0 of chamber and one is in the left chamber, ½, we
100 molecules probability ofmole
to a single the
H..,.+A
H..,532*0
H..,.+A
for Molecules
The Case for 100ten molecules that the
23
and × 1 down
con gurations,
ber system. Now we have 6write0beingall the possible...
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This note was uploaded on 11/08/2012 for the course CHEMISTRY 109 taught by Professor Flemingcrim during the Fall '10 term at University of Wisconsin.
 Fall '10
 FlemingCrim
 Chemistry, Mole

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