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Spontaneity, Entropy & Free Energy
First Law of Thermodynamics Basically the law of conservation of energy
energy can be neither created nor destroyed
i.e., the energy of the universe is constant the total energy is constant
energy can be interchanged
! e.g. potential energy "stored in chemical bonds# can beconverted to thermal energy in a chemical reaction
! $%&' ()**+ $()' %)( ' energy
oesn-t tell us why a reaction proceeds in aparticular direction
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Spontaneity, Entropy & Free Energy
Spontaneous rocesses and Entropy
Spontaneous processes occurs without
outside intervention Spontaneous processes can be fast or slow
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Thermodynamics
lets us predict whether a process will occur
tells us the direction a reaction will go only considers the initial and final states
does not re/uire 0nowledge of the pathway
ta0en for a reaction
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1inetics
depends on the pathway ta0en
tells us the speed of the process depends on
activation energy
temperature concentration
catalysts
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Spontaneity, Entropy & Free Energy
Spontaneous rocesses a ball rolls downhill, but the ball never
spontaneously rolls uphill
steel rusts, but the rust never spontaneously
forms iron and o2ygen a gas fills its container, but a gas will never
spontaneously collect in one corner of thecontainer.
3ater spontaneously free4es at temperaturesbelow 5o$
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Spontaneity, Entropy & Free Energy
3hat thermodynamic principle e2plains whythese processes occur in one direction6
The driving force for a spontaneous reactionis an increase in the entropy of the universe
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Spontaneity, Entropy & Free Energy
Entropy Symbol7 S
8 measure of randomness or disorder The natural progression is from order to disorder
9t is natural for disorder to increase
Entropy is a thermodynamic function
escribes the number of arrangements that areavailable to a system in a given state
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Entropy
The greater the number of possiblearrangements, the greater the entropy of asystem, i.e., there is a large positionalprobability.
The positional probability or the entropy
increases as a solid changes from a li/uid oras a li/uid changes to a gas
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Spontaneity, Entropy & Free Energy
Ssolid: Sli/uid: Sgas $hoose the substance with the higher
positional entropy7 $()"s# or $()"g#6
;)"g# at < atm and )=o$ or ;)"g# at .5
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Spontaneity, Entropy & Free Energy
redict the sign of the entropy change
solid sugar is added to water
iodine vapor condenses onto a cold surfaceforming crystals
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Spontaneity, Entropy & Free Energy
Second Law of Thermodynamics
The entropy of the universe is increasing
The universe is made up of the system andthe surroundings
Suniverse> Ssystem' Ssurroundings
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Spontaneity, Entropy & Free Energy
8 process is spontaneous if the Suniverse ispositive
9f the Suniverseis 4ero, there is no tendencyfor the reaction to occur
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Spontaneity, Entropy & Free Energy
The effect of temperature on spontaneity
%)("l# **+ %)("g#
water is the system, everything else is thesurroundings
Ssystemincreases, i.e. Ssystemis positive, becausethere are more positions for the water moleculesin the gas state than in the li/uid state
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Spontaneity, Entropy & Free Energy
3hat happens to the surrounding6 %eat leaves the surroundings, entering the system
to cause the li/uid molecules to vapori4e
3hen heat leaves the surroundings, the motion ofthe molecules of the surroundings decrease, whichresults in a decrease in the entropy of thesurroundings
Ssurroundingsis negative
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Spontaneity, Entropy & Free Energy
Sign of S depends on the heat flow E2othermic ?2n7 Ssurr+5
Endothermic ?2n7
Ssurr: 5 @agnitude of S is determined by the temperature
Ssurr> * %
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Spontaneity, Entropy & Free Energy
Signs of Entropy $hanges
Ssys Ssurr Suniv Spontaneous6
' '
* *
' *
* '
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Spontaneity, Entropy & Free Energy
Free Energy a0a Aibbs Free Energy
A another thermodynamic function
related to spontaneity
A > % * TS
for a process that occurs at constanttemperature "i.e. for the system#7
A > % * TS
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Spontaneity, Entropy & Free Energy
%ow does the free energy related to spontaneity6A > % * TS
A > * % ' S "remember, * % > Ssurr#
T T TA > Ssurr' Ssys "remember, Ssurr' Ssys> Suniv#
T
*A > Suniv
T
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Spontaneity, Entropy & Free Energy
Suniv+ 5 for a spontaneous reaction A : 5 for a spontaneous reaction
A + 5 for a nonspontaneous reaction seful to loo0 at A because many chemical
reactions ta0e place under constant pressureand temperature
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%)("s# **+ %)("l# %o> C.5D 2 )).< 1.mole $alculate A, Ssurr, and Sunivat *
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8t what temperatures is Br)"l# **+ Br)"g#spontaneous6
3hat is the normal boiling point of Br)6%o= 31.0 0mol So> GD.5 1.mol
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Spontaneity, Entropy & Free Energy
Entropy $hanges in $hemical ?eactions
ust li0e physical changes, entropy changes
in the surroundings are determined by heatflow
Entropy changes in the system aredetermined by positional entropy "the
change in the number of possiblearrangements#
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Spontaneity, Entropy & Free Energy
;) "g# ' D %)"g# **+ ) ;%D"g# The entropy of the this system decreases
because four reactant molecules form two product
molecules
there are less independent units in the system
less positional disorder, i.e. fewer possibleconfigurations
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Spontaneity, Entropy & Free Energy
3hen a reaction involves gaseousmolecules7
the change in positional entropy isdetermined by the relative numbers ofmolecules of gaseous reactants andproducts
9.e., if you have more product moleculesthan reactant molecules, S will be positive
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Spontaneity, Entropy & Free Energy
9n thermodynamics, the change in afunction is usually what is important
usually we can-t assign an absolute value toa function li0e enthalpy or free energy
we can usually determine the change inenthalpy and free energy
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Spontaneity, Entropy & Free Energy
3e can assign absolute entropy values,i.e., we can find S
8 perfect crystal at 5 1, whileunattainable, represents a standard all molecular motion stops
all particles are in their place the entropy of a perfect crystal at 0 Kis zero> third law of thermodynamics
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Spontaneity, Entropy & Free Energy
9ncrease the temperature of ourperfect crystal
molecular motion increases disorder increases
entropy varies with temperature
See thermodynamic tables for Sovalues "at)GH 1 and < atm#
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Spontaneity, Entropy & Free Energy
Entropy is a state function entropy does not depend on the pathway
ta0en Sr2n> nSoproducts* nSoreactant
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Spontaneity, Entropy & Free Energy
$alculate Soat )=o$ for );iS"s# ' D ()"g# **+ ) S()"g# ' ) ;i("s#
Substance So"1.mol#S() )H
;i( DH
() )5=;iS =D
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Spontaneity, Entropy & Free Energy
3hat did you e2pect the So to be6 3hy is it large and positive6
%)( is nonlinear and triatomic %)( has many rotational and vibrational motions
%)is linear and diatomic %
)has less rotational and vibrational motions
The more comple2 the molecule, thehigher the So
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Spontaneity, Entropy & Free Energy
Free Energy and $hemical ?eactions
Standard Free Energy $hange
Ao
the change in the free energy that occurs if thereactants in their standard states are changed toproducts in their standard states
can-t be measured directly
calculate from other values
allows us to predict the tendency for a reaction to go
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Spontaneity, Entropy & Free Energy
$alculate Ao for the reaction at )=o$)S()"g# ' ()"g# **+ ) S(D"g#
Substance %of"0mol# So"1.mol#S()"g# *)GI )H
S(D *DGC )=I
() 5 )5=
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Spontaneity, Entropy & Free Energy
$alculate Aofor the reaction $dia **+ $grusing the following data7
$dia' ()**+ $()"g# Ao> *DGI 0$gr' ()**+ $()"g# Ao > *DG 0
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Spontaneity, Entropy & Free Energy
$alculate Aofor the reaction)$%D(% ' D ()**+ ) $()' %)(
Substance Aof"0mol#$%D(% *
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Spontaneity, Entropy & Free Energy
The dependence of free energy on pressure %ow does pressure affect enthalpy and entropy6
ressure does not affect enthalpy
ressure does affect entropy because pressuredepends on the volume
< mole of a gas at
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Spontaneity, Entropy & Free Energy
Aiven that A > Ao' ?Tln"# where A is the free energy at some "not necessarily < atm#
where Aois the free energy at < atm
E27 ;)"g# ' D %)"g# **+ ) ;%D"g#"lots of e/uationsJlots of e/uationsJ#
A > Ao' ?T ln K K is the reaction /uotient "from the law of mass action#
T is the temperature in 1 ? is the gas constant, H.D
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Spontaneity, Entropy & Free Energy
$alculate A at )=o$ for the reaction$("g# ' ) %)"g# **+ $%D(% where carbon
mono2ide is =.5 atm and hydrogen gasat D.5 atm are converted to li/uidmethanol.
3hat does the answer tell us about thisreaction under these conditions6
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Spontaneity, Entropy & Free Energy
?elationship between Aoand 1e/ Ao 1e/
> 5 < : 5 +>>>+ )Fe)(D $alculate thee/uilibrium constant using the following
information7Substance %of"0mol# So"1.mol#Fe)(D *H)C G5
Fe 5 )I
() 5 )5=
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1e/and temperature
3e used Le $hatelier-s rinciple to determine
how 1e/would change when temperaturechanges
se A to determine the new 1e/at a newtemperature
Ao> *?T ln 1 > %o* TSo
ln 1 > * %o. < ' So
? T ?