Chemistry 142 Chapter 17: Free Energy and Thermodynamics

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Chemistry 142

Chapter 17: Free Energy and Thermodynamics

Outline

I.
First Law of Thermodynamics

II.
Entropy

III.
Second Law of Thermodynamics

IV.
Third Law of
Thermodynamics

V.
Gibbs Free Energy


What is chemical spontaneity?

Tro, Chemistry: A Molecular
Approach

4

Thermodynamics vs. Kinetics

4 Gas Molecules

Relative Probability

4 Gas Molecules

Relative Probability 1:4:6:4:1

How does entropy change?

Chapter 17


Thermodynamics

Example


Entropy

17
.
1

Predict

the

sign

of

the

entropy

change

for

each

of

the

following

processes
:



a
.

Solid

sugar

is

added

to

water

to

make



a

solution
.



b
.

Iodine

vapor

condenses

on

a

cold



surface

to

form

crystals
.

Tro, Chemistry: A Molecular
Approach

10

How does a change in state change the entropy?

Tro, Chemistry: A Molecular
Approach

11

Entropy Change and State Change

How does a temperature change effect entropy?

What effects the relative standard entropy?

Tro, Chemistry: A Molecular Approach

13

Substance

S
°
,

(J/
mol∙K
)

H
2
O (
l
)

70.0

H
2
O (
g
)

188.8

Tro, Chemistry: A Molecular Approach

14

Substance

Molar

Mass

S
°
,

(J/mol∙K)

Ar (
g
)

39.948

154.8

NO (
g
)

30.006

210.8

Substance

S
°
,

(J/mol∙K)

KClO
3
(
s
)

143.1

KClO
3
(
aq
)

265.7

What effects the relative standard entropy?

Chapter 17


Thermodynamics

Example


Entropy

17
.
2

Calculate

Δ
S
˚

at

25
˚C

for

the

reaction
:

2
NiS

(s)

+ 3 O
2 (g)



2 SO
2 (g)

+ 2
NiO

(s)



Given

the

following

values
:




Substance

S
˚

(J/mol K)

SO
2 (g)

248

NiO

(s)

38

O
2 (g)

205

NiS

(s)

53

Chapter 17


Thermodynamics

Example


Entropy

17
.
3

Calculate

Δ
S
˚

for

the

reduction

of


aluminum

oxide

by

hydrogen

gas
:

Al
2
O
3 (g)

+ 3 H
2 (g)



2 Al
(s)

+ 3 H
2
O

(g)




Given

the

following

values
:




Substance

S
˚

(J/mol K)

Al
2
O
3 (g)


51

H
2 (g)

131

Al
(s)

28

H
2
O

(g)

189

Tro, Chemistry: A Molecular
Approach

17

How are
D
G
,
D
H
, and
D
S
related?

Chapter 17


Thermodynamics

Example


Free Energy

17
.
4

At

what

temperature

is

the

following


process

spontaneous

at

1

atm
?

What

is


the

normal

boiling

point

of

liquid

bromine?

Br
2 (l)



Br
2 (g)

Δ
H
˚

= 31.0 kJ/mol








Δ
S
˚

=

93
.
0

J/K

mol


Chapter 17


Thermodynamics

Example


Standard Free Energy

17
.
5

Use

the

following

data

at

25

˚C

to

calculate



Δ


for

the

reaction
:

C
diamond

(s)



C
graphite

(s)



Δ
G˚ = ?



Given
:

C
diamond

(s)

+ O
2 (g)



CO
2 (g)




Δ
G˚ =
-
397 kJ


C
graphite

(s)

+ O
2 (g)



CO
2 (g)




Δ
G˚ =
-
394 kJ



Chapter 17


Thermodynamics

Example


Standard Free Energy

17
.
6

A

chemical

engineer

wants

to

determine

the


feasibility

of

making

ethanol

(C
2
H
5
OH)

by

reacting


ethylene

(C
2
H
4
)

and

water

according

to

the

reaction
:

C
2
H
4 (g)

+ H
2
O
(l)



C
2
H
5
OH

(l)




Is

the

reaction

spontaneous?

Given
:

Substance

Δ
G
f
˚

(kJ/mol)

C
2
H
5
OH

(l)

-
175

C
2
H
4 (g)

-
237

H
2
O
(l)

68

Chapter 17


Thermodynamics

Example


Standard Free Energy

17
.
7

One

method

for

synthesizing

methanol

(CH
3
OH)

involves


reacting

carbon

monoxide

and

hydrogen

gases
:

CO

(g)

+ 2 H
2 (g)



CH
3
OH

(l)




Calculate

Δ
G

at

25

˚C

for

the

reaction,

if

carbon

monoxide


is

at

5
.
0

atm

and

hydrogen

gas

is

at

3
.
0

atm
.


Substance

Δ
G
f
˚

(kJ/mol)

CH
3
OH

(l)

-
166

CO

(g)

-
137

H
2 (g)

0

Tro, Chemistry: A Molecular
Approach

22

How are K
and
D
G related?

K < 1

K > 1

K = 1

Tro, Chemistry: A Molecular
Approach

24

Chapter 17


Thermodynamics

Example


Free Energy and Equilibrium

17
.
8

The

overall

reaction

for

the

corrosion

of

iron

by

oxygen


gas

is
:

4 Fe

(s)

+ 3 O
2 (g)



2 Fe
2
O
3 (s)




Using

the

following

data

at

25

˚C

calculate

the


equilibrium

constant,

K
.


Substance

Δ
H
f
˚

(kJ/mol)

S
˚

(J/mol K)


Fe

(s)

0

27

Fe
2
O
3 (s)

-
826

90

O
2 (g)

0

205

Chapter 17


Thermodynamics

Example


Free Energy and Equilibrium

17
.
9

Calculate


H
°
rxn

and


S
°
rxn

for

the

decomposition

of


carbon

dioxide

into

carbon

monoxide

and

oxygen

gases
.


2 CO

2 (g)



2 CO

(g)

+ O
2 (g)





Using

the

following

data
:


T(K)

K
c

1500

5.5E
-
09

2500

4E
-
01

3000

40.3

Chapter 17


Thermodynamics

Example


Free Energy and Equilibrium

17
.
9

Calculate


H
°
rxn

and


S
°
rxn

for

the

decomposition

of


carbon

dioxide

into

carbon

monoxide

and

oxygen

gases
.


2 CO

2 (g)



2 CO

(g)

+ O
2 (g)





Using

the

following

data
:


l n
(K)
=
-
68070 K/T
+ 26.353

R² = 1

-25.00
-20.00
-15.00
-10.00
-5.00
0.00
5.00
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
ln(K)

1/T (1/K)

Van’t

Hoff Plot

ln
(K
) versus
Reciprical

Kelvin Temperature

T(K)

K
c


1/T (1/K)

ln
(
K
c
)

1500

5.5E
-
09

0.0006667

-
19.02

2500

4.0E
-
01

0.0004000

-
0.92

3000

40.3

0.0003333

3.696

Chapter 17


Thermodynamics

Example


Free Energy and Equilibrium

17
.
10

Automobiles

and

trucks

pollute

the

air

with

nitrogen


monoxide
.

At

2000

°
C,

K
c

for

the

reaction

N
2(g)

+ O
2 (g)



2 NO
(g)




is

4
.
10

x

10
-
4
,

and

Δ
H
˚

=

180
.
6

kJ
.

What

is

the

value

of

K
c


at

25

°
C?


Tro, Chemistry: A Molecular
Approach

29

What is the energy tax?


you can’t break even!


to recharge a battery with 100 kJ of
useful energy will require more than
100 kJ


every energy transition results in a
“loss” of energy


conversion of energy to heat which is
“lost” by heating up the surroundings

Tro, Chemistry: A Molecular
Approach

30

What is the heat tax?

fewer steps
generally results
in a lower total
heat tax

What happens in real reactions?

Tro, Chemistry: A Molecular Approach

31