spontaneity entropy free energy

7/24/2019 Spontaneity Entropy Free Energy

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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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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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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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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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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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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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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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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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8 process is spontaneous if the Suniverse ispositive

9f the Suniverseis 4ero, there is no tendencyfor the reaction to occur


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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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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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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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Signs of Entropy $hanges

Ssys Ssurr Suniv Spontaneous6

' '

* *

' *

* '


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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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%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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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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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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;) "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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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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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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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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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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Entropy is a state function entropy does not depend on the pathway

ta0en Sr2n> nSoproducts* nSoreactant


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$alculate Soat )=o$ for );iS"s# ' D ()"g# **+ ) S()"g# ' ) ;i("s#

Substance So"1.mol#S() )H

;i( DH

() )5=;iS =D


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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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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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$alculate Ao for the reaction at )=o$)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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$alculate Aofor the reaction $dia **+ $grusing the following data7

$dia' ()**+ $()"g# Ao> *DGI 0$gr' ()**+ $()"g# Ao > *DG 0


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$alculate Aofor the reaction)$%D(% ' D ()**+ ) $()' %)(

Substance Aof"0mol#$%D(% *


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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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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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$alculate A at )=o$ 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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?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 ?

spontaneity entropy free energy

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