Chapter 17: Free Energy & Thermodynamics

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35

Chapter 17: Free Energy & Thermodynamics


I) Thermodynamics: A Brief Review



1.
First Law of Thermodynamics




-

Energy of universe is constant. (Law of Conservation of Energy/Matter)



2. First law can function as a method of energy bookkeeping, but it
d
oes not



answer the question





Why does a process occur in a given direction?


II) Spontaneous Processes & Entropy



1. Spontaneous processes occur
without

outside intervention.



2. Spontaneous does
not

mean fast as it did in the kinetics chapter.



3.

Thermodynamics can tell us the direction in which a process will occur but can

say nothing about the speed of the process.



4. Thermodynamics considers the initial & final states; not the path taken (recall

this is the definition of a state function).



5. Review the following terms that were first introduced in Chapter
6




-

system


-

surroundings



-

universe



-

energy


-

enthalpy



-

heat



-

exothermic


-

endothermic



-

standard states



6. Need thermodynamics & kinetics to describe chemical rea
ctions fully.



7. What thermodynamic principle will provide an explanation as to why a process

occurs in one direction (under a given set of conditions) and never in the reverse ?




A)
Entropy (S)





-

Entropy is a measure of randomness or disorder.


-

Driving force for a spontaneous process is an increase in entropy of
the universe. This statement is often termed the
Second Law of
Thermodynamics


36


-

Entropy is a thermodynamic function that describes the number of
arrangements (microstates) that are avai
lable to a system existing in a
given state.


-

Solids have lowest entropy (most ordered), while gases have the
highest entropy (least ordered). Liquids fall in between the two
extremes.








S
solid

< S
liquid

<< S
gas



III) Entropy & Second Law of Th
ermodynamics



1.
Second Law of Thermodynamics



A) In any spontaneous process there is
always

an increase in the entropy of the
universe.
Entropy of universe is increasing.



2.

S
universe

=

S
system

+

S
surroundings




3. Predicting Spontaneity







S
universe


(+)

spontaneous process





S
universe

(
-

)

not spontaneous





S
universe

(0 )

equilibrium



IV) Effect of Temperature on Spontaneity



1. Entropy change in system is relatively straightforward to predict. Nature

spontaneously proceeds toward

the states that have the highest probabilities of

existing.



2. Entropy change in surroundings is more difficult to figure out.




A)
Key:

Examine direction of heat flow.


B) Exothermicity is an important driving force for spontaneity. Must know T (in
K
elvin) @ which process occurs.






S
surroundings

=
-


H
system

/ T






Exothermic



S
surroundings

= +





Endothermic



S
surroundings

=
-


37



3.
Review Figure 17.9


V) Free Energy



1. The thermodynamic quantity Free Energy (G) is useful in dea
ling with


temperature dependence on spontaneity.






G =

H
-

T

S


( no subscript denotes system)



2. How are

G and

S
universe

related ?






G =

H
-

T

S


(divide both sides by
-

T)





-


G / T =
-


H / T
-

T

S /
T






-


G / T =

S
surrounding
s

+

S
system

=

S
universe






-


G / T =


universe



@ constant T & P



3. Predicting Spontaneity

(Relating G, H, & S)


[Review Table 17.2]






G =

H
-

T

S






Case





Result






S +

H
-



Spontaneous @ all T





S +

H +



Spontaneous @ hi
gh T





S
-


H
-



Spontaneous @ low T





S
-


H +



Not Spontaneous @ any T


VI)
Third Law of Thermodynamics



1. Entropy of a perfect crystal @ 0 K is zero.

(Unattainable ideal case)



2. Typically refer to state where P = 1 atm & T = 298 K

(standa
rd state)



3. Standard state conditions are denoted by a superscript zero

(
0

)



4. Some Useful Mathematical Relationships for state functions S, H, & G






S
0

rxn

=


n
p

S
0

produtcts

-



n
r

S
0

reactants




38





H
0

rxn

=


n
p

H
0

produtcts

-



n
r

H
0

react
ants







G
0

rxn

=


n
p

G
0

produtcts

-



n
r

G
0

reactants



VII) Dependence of Free Energy on Pressure



1. The equilibrium position represents the lowest free energy value available to a

particular reaction system.



2. How does pressure affect G, H, &
S ?


-

For an ideal gas, enthalpy (H) is not affected by pressure, while entropy (S)
and free energy (G) are affected by pressure changes.


-

The relationship expressed mathematically is shown below.



G =

G
o

+ RTln(Q)


3. A chemical system will seek the lowe
st possible free energy, which is the equilibrium
position.


4. The relationship between

G and K


Since @ equilibrium

G = 0 & Q = K



G = 0 =

G
o

+ RTln(Q)



G
o

=
-

RTln (K)


Review Table 17.4