Chapter 19 Chemical Thermodynamics

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Oct 27, 2013 (4 years and 12 days ago)

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Chemical

Thermodynamics

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2009, Prentice
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Chapter 19

Chemical
Thermodynamics

Chemistry, The Central Science
, 11th edition

Theodore L. Brown; H. Eugene LeMay, Jr.;

and Bruce E. Bursten

John D. Bookstaver

St. Charles Community College

Cottleville, MO

Chemical

Thermodynamics

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Day 1

First Law of Thermodynamics


You will recall from Chapter 5 that
energy cannot be created nor
destroyed.


Therefore, the total energy of the
universe is a constant.


Energy can, however, be converted
from one form to another or transferred
from a system to the surroundings or
vice versa.

Chemical

Thermodynamics

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Spontaneous Processes


Spontaneous processes
are those that can
proceed without any
outside intervention.


The gas in vessel
B

will
spontaneously effuse into
vessel
A
, but once the
gas is in both vessels, it
will
not

spontaneously
return to vessel
B
.

Chemical

Thermodynamics

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Spontaneous Processes


Processes that are
spontaneous in one
direction are
nonspontaneous in
the reverse
direction.

Chemical

Thermodynamics

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Spontaneous Processes


Processes that are spontaneous at one
temperature may be nonspontaneous at other
temperatures.


Above 0

C it is spontaneous for ice to melt.


Below 0

C the reverse process is spontaneous.

Chemical

Thermodynamics

Identifying Spontaneous Processes

Practice Exercise 19.1
pg

804



Under 1
atm

pressure CO
2(s)

sublimes at
-
78
°
C. Is the
transformation of CO
2(s)

to CO
2(g)

a spontaneous process at



-
100
°
C and 1
atm

pressure?


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Chemical

Thermodynamics

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Reversible Processes


In a reversible
process the system
changes in such a
way that the system
and surroundings
can be put back in
their original states
by exactly reversing
the process.

Chemical

Thermodynamics

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Irreversible Processes


Irreversible processes cannot be undone by
exactly reversing the change to the system.


Spontaneous processes are irreversible.

Chemical

Thermodynamics

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Entropy


Entropy

(
S
) is a term coined by Rudolph
Clausius in the 19th century.


Clausius was convinced of the
significance of the ratio of heat
delivered and the temperature at which
it is delivered, .

q

T

Chemical

Thermodynamics

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Entropy


Entropy can be thought of as a measure
of the randomness of a system.


It is related to the various modes of
motion in molecules.

Chemical

Thermodynamics

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Entropy


Like total energy,
E
, and enthalpy,
H
,
entropy is a state function.


Therefore,


S

=
S
final



S
initial

Chemical

Thermodynamics

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Entropy


For a process occurring at constant
temperature (an isothermal process), the
change in entropy is equal to the heat that
would be transferred if the process were
reversible divided by the temperature:



S

=

q
rev

T

Chemical

Thermodynamics

Calculating
Δ
S for a Phase Change

Practice Exercise 19.2
pg

807



The normal boiling point of ethanol, C
2
H
5
OH is 78.3
°
C and its
molar enthalpy of vaporization is 38.56 kJ/mol. What is the
change in entropy in the system when 68.3 g of C
2
H
5
OH
(g)

at 1
atm

condenses to liquid at the normal boiling point?

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Chemical

Thermodynamics

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Day 2
Second Law of Thermodynamics


The second law of thermodynamics
states that the entropy of the universe
increases for spontaneous processes,
and the entropy of the universe does
not change for reversible processes.

Chemical

Thermodynamics

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Second Law of Thermodynamics

In other words:

For reversible processes:


S
univ

=

S
system

+

S
surroundings

= 0

For irreversible processes:


S
univ

=

S
system

+

S
surroundings

> 0


Chemical

Thermodynamics

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Second Law of Thermodynamics


These last truths mean that as a result
of all spontaneous processes the
entropy of the universe increases.

Chemical

Thermodynamics

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Entropy on the Molecular Scale


Ludwig Boltzmann described the concept of
entropy on the molecular level.


Temperature is a measure of the average
kinetic energy of the molecules in a sample.

Chemical

Thermodynamics

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Entropy on the Molecular Scale


Molecules exhibit several types of motion:


Translational: Movement of the entire molecule from
one place to another.


Vibrational: Periodic motion of atoms within a molecule.


Rotational: Rotation of the molecule on about an axis or
rotation about


bonds.

Chemical

Thermodynamics

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Entropy on the Molecular Scale


Boltzmann envisioned the motions of a sample of
molecules at a particular instant in time.


This would be akin to taking a snapshot of all the
molecules.


He referred to this sampling as a
microstate

of the
thermodynamic system.

Chemical

Thermodynamics

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Entropy on the Molecular Scale


Each thermodynamic state has a specific number of
microstates,
W
, associated with it.


Entropy is

S

=
k

ln
W


where
k

is the Boltzmann constant, 1.38


10

23

J/K.

Chemical

Thermodynamics

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Entropy on the Molecular Scale


The change in entropy for a process,
then, is




S

=
k

ln
W
final



k

ln
W
initial



ln
W
final

ln
W
initial



S

=
k

ln


Entropy increases with the number of
microstates in the system.

Chemical

Thermodynamics

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Entropy on the Molecular Scale


The number of microstates and,
therefore, the entropy tends to increase
with increases in


Temperature.


Volume.


The number of independently moving
molecules.

Chemical

Thermodynamics

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Entropy and Physical States


Entropy increases with
the freedom of motion
of molecules.


Therefore,


S
(
g
)

>
S
(
l
)

>
S
(
s
)

Chemical

Thermodynamics

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Solutions


Generally, when
a solid is
dissolved in a
solvent, entropy
increases.

Chemical

Thermodynamics

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Entropy Changes


In general, entropy
increases when


Gases are formed from
liquids and solids;


Liquids or solutions are
formed from solids;


The number of gas
molecules increases;


The number of moles
increases.

Chemical

Thermodynamics

Predicting the Sign of
Δ
S

Practice Exercise 19.3
pg

814


Indicate whether each of the following processes produces an
increase or decrease in the entropy of the system:

a)
CO
2(s)



CO
2(g)

b)
CaO
(s)

+ CO
2(g)



CaCO
3(s)

c)
HCl
(g)

+ NH
3(g)


NH
4
Cl
(s)

d)
2 SO
2(g)

+ O
2(g)



2 SO
3(g)

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Chemical

Thermodynamics

Predicting Entropy in Samples of
Matter

Practice Exercise 19.4
pg

815


Choose the substance with the greater entropy in each case:


a) 1
mol

H
2(g)

at STP or 1
mol

of H
2(g)

at 100
°
C at 0.5
atm


b) 1
mol

H
2
O
(s)

at 0
°
C or 1
mol

of H
2
O
(l)

at 25
°
C


c) 1
mol

H
2(g)

at STP or 1
mol

SO
2(g)

at STP


d) 1
mol

N
2
O
4(g)

at STP or 2
mol

of NO
2(g)

at STP

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Chemical

Thermodynamics

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Third Law of Thermodynamics

The entropy of a pure crystalline
substance at absolute zero is 0.

Chemical

Thermodynamics

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Standard Entropies


These are molar entropy
values of substances in
their standard states.


Standard entropies tend
to increase with
increasing molar mass.

Chemical

Thermodynamics

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Standard Entropies

Larger and more complex molecules have
greater entropies.

Chemical

Thermodynamics

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Entropy Changes


Entropy changes for a reaction can be
estimated in a manner analogous to that by
which

H

is estimated:



S


=

n

S

(products)




m

S

(reactants)




where
n

and
m

are the coefficients in the
balanced chemical equation.

Chemical

Thermodynamics

Calculating
Δ
S from Tabulated
Entropies

Practice Exercise 19.5
pg

818


Using the standard entropies in Appendix C, calculate the
standard entropy change,
Δ
S
°
for

the following reaction at 298
K.


Al
2
O
3(s)

+ 3 H
2(g)



2 Al
(s)

+ 3 H
2
O
(g)

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Chemical

Thermodynamics

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Entropy Changes in Surroundings


Heat that flows into or out of the
system changes the entropy of the
surroundings.


For an isothermal process:


S
surr

=


q
sys

T


At constant pressure,
q
sys

is simply

H


for the system.

Chemical

Thermodynamics

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Entropy Change in the Universe


The universe is composed of the system
and the surroundings.


Therefore,


S
universe

=

S
system

+

S
surroundings


For spontaneous processes



S
universe
> 0


Chemical

Thermodynamics

From Sample Exercise 19.5

-
Calculate the entropy change of the surroundings,
Δ
S
surr
,

and the universe,
Δ
s
univ

from the following
reaction.


N
2(g)

+ 3 H
2(g)



2 NH
3(g)

Δ
S
°
=
-
198.3 J/K

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Chemical

Thermodynamics

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Day 3
Entropy Change in the Universe


Since

S
surroundings

=


and
q
system

=

H
system


This becomes:




S
universe

=

S
system

+




Multiplying both sides by

T
, we get




T

S
universe

=

H
system



T

S
system




H
system

T


q
system

T

Chemical

Thermodynamics

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Gibbs Free Energy



T

S
universe

is defined as the Gibbs free
energy,

G
.


When

S
universe

is positive,

G

is
negative.


Therefore, when

G

is negative, a
process is spontaneous.

Chemical

Thermodynamics

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Gibbs Free Energy

1.
If

G

is negative, the
forward reaction is
spontaneous.

2.
If

G

is 0, the system
is at equilibrium.

3.
If

G

is positive, the
reaction is
spontaneous in the
reverse direction.

Chemical

Thermodynamics

Calculating Free
-
Energy Change
from
Δ
H
°
, T and
Δ
S
°

Practice Exercise 19.6
pg

821


A particular reaction has
Δ
H
°
= 24.6 kJ and
Δ
S
°
= 132 J/K at
298 K. Calculate
Δ
G
°
. Is the reaction spontaneous under these
conditions?

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Chemical

Thermodynamics

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Standard Free Energy Changes


Analogous to standard enthalpies of
formation are standard free energies of
formation,

G

.

f


G


=

n

G


(products)




m

G


(reactants)

f


f

where
n

and
m

are the stoichiometric
coefficients.

Chemical

Thermodynamics

Calculating Standard Free
-
Energy
Change from Free Energies of
Formation

Practice Exercise 19.7
pg

823


By using data from Appendix C, calculate
Δ
G
°
at 298 K for the
combustion of methane:


CH
4(g)

+ 2 O
2(g)


CO
2(g)

+ 2 H
2
O
(g)

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Chemical

Thermodynamics

Estimating and Calculating
Δ
G
°

Practice Exercise 19.8
pg

824


Consider the combustion of propane to form CO
2(g)

and H
2
O
(g)

at
298 K: C
3
H
8(g)

+ 5 O
2(g)



3 CO
2(g)
+ 4 H
2
O
(g)
. Would you expect
Δ
G
°

to be more negative or less negative than
Δ
H
°
?


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Chemical

Thermodynamics

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Free Energy Changes


At temperatures other than 25
°
C,



G
°

=

H




T

S




How does

G


change with temperature?

Chemical

Thermodynamics

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Free Energy and Temperature


There are two parts to the free energy
equation:



H



the enthalpy term


T

S




the entropy term


The temperature dependence of free
energy, then comes from the entropy
term.

Chemical

Thermodynamics

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Free Energy and Temperature

Chemical

Thermodynamics

Determining the Effect of
Temperature on Spontaneity

Practice Exercise 19.9
pg

826

a)
Using standard enthalpies of formation and standard entropies
in Appendix C, calculate
Δ
H
°
and

Δ
S
°
at 298 K for the
following reaction: 2 SO
2(g)

+ O
2(g)



2 SO
3(g).

b)
Using the values obtained in part (a), estimate
Δ
G
°
at 400 K.

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Chemical

Thermodynamics

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Free Energy and Equilibrium


Under any conditions, standard or
nonstandard, the free energy change
can be found this way:



G

=

G


+
RT
ln
Q


(Under standard conditions, all concentrations are 1
M
,
so
Q

= 1 and ln
Q

= 0; the last term drops out.)

Chemical

Thermodynamics

Relating
Δ
G to a Phase Change at
Equilibrium

Practice Exercise 19.10
pg

828


Use data in Appendix C to estimate the normal boiling point, in
K, for elemental bromine, Br
2(l)
. (The experimental value is given
in Table 11.3)

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Chemical

Thermodynamics

Calculating the Free
-
Energy Change
under Nonstandard Conditions

Practice Exercise 19.11
pg

828


Calculate
Δ
G at 298 K for the reaction of nitrogen and hydrogen
to form ammonia if the reaction mixture consists of 0.50
atm

N
2
,
0.75
atm

H
2
, and 2.0
atm

NH
3
.


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Chemical

Thermodynamics

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Free Energy and Equilibrium


At equilibrium,
Q

=
K
, and

G

= 0.


The equation becomes

0 =

G


+
RT

ln
K


Rearranging, this becomes


G


=

RT

ln
K


or,






K

= e

-

G


RT

Chemical

Thermodynamics

Calculating an Equilibrium Constant
from
Δ
G
°

Practice Exercise 19.12 page 829


Use data from Appendix C to calculate the standard free
-
energy
change,
Δ
G
°
and the equilibrium constant, K, at 298 K for the
reaction: H
2(g)

+ Br
2(l)
(

) 2
HBr
(g)

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