Entropy Notes

8/11/2019 Entropy Notes

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Thermodynamics : Entropy

Entropy (S)- A measure of the disorder in a system. Entropy is a state function.

where kis a proportionality constant equal to the ideal gas constant (R) divided by Avogadro's number

(.!"" # $!-"%) and ln& is the natural log of & the number of equivalent ways of describing the state of a

system.

n this reaction the number of ways of describing a system is directly proportional to the entropy of the

system.

Entropy of Reaction ( S)

he difference between the sum of the entropies of the products and the sum of the entropies of

the reactants*

n the above reaction n and m are the coefficients of the products and the reactants in the balanced

equation.

Second Law of Thermodynamics

Natural processes that occur in an isolated system are spontaneouswhen they lead to an increase in

the disorder, or entropy, of the system.

Isolated system- +ystem in which neither heat nor wor, can be transferred between it and its

surroundings. his ma,es it possible to ignore whether a reaction is e#othermicorendothermic.

f Ssys> the system becomes more disorderedthrough the course of the reaction

f Ssys! the system becomes less disordered(or more ordered) through the course of the reaction.

here are a few basic principles that should be remembered to help determine whether a system isincreasing or decreasing in entropy.

iquids are more disordered than solids.

o &/0 - +olids have a more regular structure than liquids.

1ases are more disordered than their respective liquids.

o &/0 - 1ases particles are in a state of constant random motion.
http://library.thinkquest.org/C006669/data/Chem/glossary.html#Statefunctionhttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Statefunctionhttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Spontaneousrxnhttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Exothermichttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Exothermichttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Endothermichttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Endothermichttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Endothermichttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Spontaneousrxnhttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Exothermichttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Endothermichttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Statefunction


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Any process in which the number of particles in the system increases consequently results in an

increase in disorder.

2oes the entropy increase or decrease for the following reactions0

$.".

%.

3.

Answers*

$. IN"RE#SES- he number of particles in the system increases i.e. one particle decomposes into

two. n addition one of the products formed is a gas which is much more disordered than the

original solid.

". $E"RE#SES - he number of particles in the system decreases i.e. there are four moles of gas

reactants and only " moles of gas products.%. IN"RE#SES- he number of particles in the system increases i.e. the single reactantdissociates

into two ion particles. n addition the ions in the ionic solid are organi4ed in a rigid lattice

structure whereas the ions in aqueous solution are free to move randomly through the solvent.3. $E"RE#SES- he reactant changes from a gas to a liquid and gases are more disordered than

their respective liquids.

Third Law of Thermodynamics

The entropy of a perfect crystal is %ero when the temperature of a the crystal is e&ual to a'solute %ero

( ).

At ! 5 there is no thermal motion

and if the crystal is perfect there

will be no disorder

6nce the temperature begins to rise

above ! the particles begin to move

and entropy gradually increases as

the average ,inetic energy of the

particles increases.

&hen temperature reaches the

melting point of the substance (m)

there is an abrupt increase in

entropy as the substance changesfrom a solid to a more disordered

liquid.

Again the entropy increases

gradually as the motion of theparticles increases until the

temperature reaches the boiling

point of the substance (b). At this
http://library.thinkquest.org/C006669/data/Chem/glossary.html#Dissociationhttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Dissociationhttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Solventhttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Dissociationhttp://library.thinkquest.org/C006669/data/Chem/glossary.html#Solvent


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point there is another drasticincrease in entropy as the substance

changes from a confined liquid

particles to radom motion gasparticles.

StandardState Entropy of Reaction ( S )

he entropy of reaction at standard-state conditions.

Standardstate conditions

he partial pressures of any gases involved in the reaction is !.$ 78a.

he concentrations of all aqueous solutions are $ 7.

7easurements are also generally ta,en at a temperature of "9 : (";< 5)

Sample entropy of reaction calculations

*) "alculate the standardstate entropy for the followin+ reaction +ien the followin+ information.

#lso, e-plain the si+n of S for the reaction.

"ompound S (/mol)=a:l(s) >".$%

=a?(aq) 9;.!

:l-(aq) 9.9

n the balanced reaction above one mole of =a:l yields one mole of =a?and one mole of :l-. &e find the

+ by subtracting the entropy of the reactant from the sum of the entropies of the products*

he change in entropy for this reaction is positive. he disorder of the system increases because the numberof particles increases as one solid reactant is converted into two aqueous particles. Also the ions in the

ionic solid are positioned in a rigid lattice structure whereas the ions in solution are free to move around.


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0) "alculate the standardstate entropy for the followin+ reaction +ien the followin+ information.

#lso, e-plain the si+n of S for the reaction.

"ompound S (/mol)

=6"(g) "3!.!

="63(g) %!3.";

n the balanced reaction above two moles of =6"combine to form one mole of ="63. &e find the +

by subtracting the entropy of the reactant from the entropy of the product*

he change in entropy for this reaction is negative. he disorder of the system decreases because the

number of particles decreases as two moles of gas reactant are converted to one mole of gas product.

Thermodynamics : Gibbs Free Energy

1i''s 2ree Ener+y (1)- he energy associated with a chemical reaction that can be used to do wor,. he

free energy of a system is the sum of its enthalpy () plus the product of the temperature (5elvin) and the

entropy (+) of the system*

2ree ener+y of reaction ( 1)

he change in the enthalpy ( ) of the system minus the product of the temperature (5elvin)

and the change in the entropy ( +) of the system*

Standardstate free ener+y of reaction ( 1 )

he free energy of reaction at standard state conditions*

Standardstate conditions


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he partial pressures of any gases involved in the reaction is !.$ 78a.

he concentrations of all aqueous solutions are $ 7.

7easurements are also generally ta,en at a temperature of "9 : (";< 5)

StandardState 2ree Ener+y of 2ormation ( 1f )

he change in free energy that occurs when a compound is formed form its elements in their most

thermodynamically stable states at standard-state conditions. n other words it is the difference

between the free energy of a substance and the free energies of its elements in their most

thermodynamically stable states at standard-state conditions.

he standard-state free energy of reaction can be calculated from the standard-state free energies

of formation as well. t is the sum of the free energies of formation of the products minus the sum

of the free energies of formation of the reactants*

Recall from the enthalpy notesthat reactions can be classified according to the change in enthalpy (heat)*

Endothermic- absorbs heat @ !

E-othermic- releases heat @ !

Reactions can also be classified according to the change in the free energy of the reaction*

Endothermic- =6=-+86=A=E6+ 1 @ !

E-othermic- +86=A=E6+ 1 B !

Summary

Cavorable

:onditions

nfavorable

:onditions

B ! @ !

+ @ ! + @ !

Dne#pected End of Cormulaf a reaction is favorable for both enthalpy ( B ! ) and entropy

( + @ !) then the reaction will be +86=A=E6+ ( 1 B ! ) at any temperature.

f a reaction is unfavorable for both enthalpy ( @ ! ) and entropy ( + B ! ) then the

reaction will be =6=+86=A=E6+ ( 1 @ ! ) at any temperature.

f a reaction is favorable for only one of either entropy or enthalpy the standard-state free energy

equation must be used to determine whether the reaction is spontaneous or not.

Sample free ener+y calculation
http://library.thinkquest.org/C006669/data/Chem/thermodynamics/enthalpy.htmlhttp://library.thinkquest.org/C006669/data/Chem/thermodynamics/enthalpy.html


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"ompound 3f S

=3=6%(s) -%9.9 $9$.!%.$9.


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Temperature and 2ree Ener+y

f a reaction is favorable for enthalpy ( B ! ) but unfavorable for entropy ( + B ! ) then

the reaction becomes E++ +86=A=E6+ as temperature increases.

o &/0 - he standard-state free energy equation states that*

f entropy is unfavorable the + is negative. +ubtracting a negative number is the

same as adding the respective positive number. As the temperature increases the +

factor (which is A22E2 to the enthalpy if the entropy is unfavorable) increases as well.

Eventually the + factor becomes larger than and 1 becomes positivei.e. the reaction is no longer spontaneous.

Sample "alculations

"ompound 3f S

="(g) ! $;$.$

"(g) ! $%!.

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