# CHAPTER 18: THERMODYNAMICS

Mechanics

Oct 27, 2013 (4 years and 8 months ago)

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1

CHAPTER 18: THERMODYNAMICS

-
Permaul

Valencia College

CHM 1046

Thermodynamics

Thermodynamics: The study of interconversion of
heat and other forms of energy.

Internal energy (U): the sum of the kinetic and
potential energies of the particles making up a
system.

State Function: a property of a system that depends
only on its present state which is determined by
variables such as temperature and pressure.

2

3

Heat (q): energy that moves into or out of the system
because of a temperature difference between the system and
it’s surroundings

Work (w): energy exchange that results when a force
(F)moves an object through distance (d) w = F x d

1
st

Law of Thermodynamics:

D
U = q + w

The change in internal energy of a system is equal to heat
plus work.

if heat evolves from system (
-
)

if heat is absorbed by the system (+)

work done by the system (
-
)

work done on a system (+)

Thermodynamics

Thermodynamics

Spontaneous process: Process that proceeds on its
own without external influence

Non
-
spontaneous: Needs continuous external
influence to take place

4

Thermodynamics

Entropy (S): a thermodynamic quantity that is a measure
of how dispersed the energy of a system is among the
different possible ways that system can contain energy.

2
nd

Law of Thermodynamics:

D
S = q

T

For a spontaneous process at a given temperature, the
change in entropy of a system is greater than the heat
divided by the absolute temperature.

The total entropy of a system and its surroundings always
increases for a spontaneous process

5

Entropy and temperature

3
rd

Law of Thermodynamics

a) The entropy of a perfectly ordered crystalline

substance at 0 K is zero

b) As the temperature increases, the KE

increases, Molecular motion increases,

entropy increases

6

Thermodynamics

Entropy (S):

Disorder, molecular randomness

D
S = S
final

-

S
initial

When disorder increases +
D
S

When disorder decreases
-
D
S

Enthalpy (H):

Heat flow

In to the system
+
D
H

Out of the system
-
D
H

Enthalpy change:

D
H = T
D
S

7

Thermodynamics

The Entropy of a system usually increases in the
following situations:

1.
A reaction in which a molecule is broken down
into 2 or more smaller molecules

2.
A reaction in which there is an increase in moles
of gas

3.
A process on which a solid changes to liquid or
gas or a liquid changes to a gas

8

Example 1:

Predict the sign of
D
S in the system for each of the
following

a)

H
2
O
(g)

H
2
O
(l)

b)

I
2(g)

2I
-
(g)

c)

CaCO
3(s)

CaO
(s)

+ CO
2(g)

d)

Ag
+
(aq)

+ Br
-
(aq)

AgBr
(s)

9

Example 2:

Which of the following reactions has an increase
in entropy?

1.
H
2
O
(g)

H
2
O
(l)

2.
H
2
O
(l)

H
2
O
(g)

3.
H
2
O
(g)

H
2
O
(s)

10

Standard Molar Entropies and Standard Entropies of Reaction

Standard Molar Entropy, S

The entropy of one mole of the pure substance at 1
atm pressure and a specific temperature usually 25

C

Standard Entropy of Reaction,
D
S

Entropy change for a chemical reaction

D
S

=

S

products

-

S

reactants

Based on 1 mole of substance so you have to multiply S

by the
number of moles present

11

Standard Entropy of Reaction,
D
S

aA + bB

cC + dD

D
S

= [c S

(C) + d S

(D)]

[a S

(A) + b S

(B)]

Units: coefficients are moles

S

= J/K mol

D
S

=

J/K

12

Example 3:

Calculate the standard entropy of reaction at 25

C
for the decomposition of calcium carbonate

CaCO
3(s)

CaO
(s)

+ CO
2(g)

Substance

S

(J/K mol)

CaCO
3(s)

92.9

CaO
(s)

39.7

CO
2(g)

213.6

13

Entropy and the Second Law of Thermodynamics

1
st

Law of Thermodynamics

In any process, spontaneous or nonspontaneous,
the total energy of a system and its surroundings
is constant

2
nd

Law of Thermodynamics

In any spontaneous process, the total entropy of
a system and its surroundings always increases

14

Entropy and the Second Law of Thermodynamics

D
S
total

=
D
S
system

+
D
S
surroundings

if
D
S > 0 spontaneous

if
D
S< 0 non spontaneous

if
D
S = 0 equilibrium

D
S
surr

=
-
D
H / T

15

Entropy and the Second Law of Thermodynamics

a)

Exothermic reaction:
D
H<0, because the surroundings

gain heat (entropy increases), heat is lost from the system

b)

Endothermic reaction:
D
H>0, surroundings lose heat

(entropy decreases), and system gains the heat

16

Example 4:

Which of the following reactions is endothermic?

1.
N
2
O
4(g)

2 NO
2(g)

D
H = +57.1 kJ

2.
2 NO
2(g)

N
2
O
4(g)

D
H =
-
57.1 kJ

17

Free
-
Energy

Free energy (G): A thermodynamic quantity defined
by the equation:

G = H

TS

D
G =
D
H
-

T
D
S

if
D
G < 0 spontaneous

if
D
G > 0 nonspontaneous

if
D
G = 0 equilibrium

18

Example 5:

Consider the decomposition of gaseous N
2
O
4

N
2
O
4(g)

2 NO
2(g)

D
H = +57.1 kJ

D
S = +175.8 J/K

a)
Is this reaction spontaneous under standard
-
state conditions at 25

C?

b)
Estimate the temperature at which the reaction
becomes spontaneous

19

Standard Free
-
Energy Changes for Reactions

1.
Standard State Conditions
: Solids, liquids, and
gases in pure form at 1 atm pressure, Solutes at
1M concentration, specified temperature, usually
25 celsius

2.
Standard Free Energy Change,
D
G

: The change
in free energy that occurs when reactants in their
Std. States are converted to products in their Std.
States.

3.
D
G =
D
H
-

T
D
S
D
G

=
D
H

-

T
D
S

20

Example 6:

Consider the thermal decomposition of calcium
carbonate

CaCO
3(s)

CaO
(s)

+ CO
2(g)

D
H

= 178.3 kJ

D
S

= 160.4 J/K

a)

Calculate the standard free energy change for this

reaction at 25

C

b)

Will a mixture of solid CaCO
3
,
CaO
, and gaseous CO
2

at 1

atm

pressure react spontaneously at 25

C?

c)

Assuming that
D
H

and
D
S

are independent of

temperature, estimate the temperature at which the

reaction becomes spontaneous

21

Standard Free Energies of Formation

1.
Standard Free Energy of Formation,
D
G

f

The free energy change for formation of one mole of the
substance in its standard state from the most stable form of
its constituent elements in their standard states

2.
D
G

f

measures the substances thermodynamic stability with
respect to its constituent elements

3.
-
D
G

f

are stable and do not decompose to their constituent
elements under standard state conditions

22

Standard Free Energies of Formation

4.

+
D
G

f

are thermodynamically unstable with respect to their
constituents elements

a) There is no point in trying to synthesize a substance that
has a +
D
G

f

because it would degrade into it’s constituents

b) You would need to synthesize it at different temperatures
that has a reaction with a
-
D
G

f

5.
D
G

=
D
G

f
(products)
-

D
G

f
(reactants)

6.

General reaction: aA +bB

cC + dD

D
G

= [c
D
G

f
(C) + d
D
G

f
(D)]

[a
D
G

f
(A) + b
D
G

f
(B)]

23

Standard Free Energies of Formation

To judge the spontaneity of a reaction:

1.
When
D
G
o

is a large negative number (more than
-
10kJ), the
reaction is spontaneous as written and reactants transform
almost entirely to products when equilibrium is reached.

2.
When
D
G
o

is a large positive number (more than 10kJ), the
reaction is nonspontaneous as written and reactants do not
give significant amounts of products at equilibrium.

3.
When
D
G
o

has a small negative or positive value, the
reaction gives an equilibrium mixture with significant
amounts of both reactants and products.

24

Example 7:

Calculate the standard free energy change for the
reaction of calcium carbide with water. Might this
reaction be used for the synthesis of acetylene (C
2
H
2
)?

CaC
2(s)

+ 2 H
2
O
(l)

C
2
H
2(g)

+ Ca(OH)
2(s)

D
G

f

(CaC
2
) =
-
64.8 kJ/mol

D
G

f

(H
2
O
(l)
) =
-
237.2 kJ/mol

D
G

f

(C
2
H
2
) = 209.2 kJ/mol

D
G

f

(Ca(OH)
2
) =
-
898.6 kJ/mol

25

Free Energy Changes and Composition of the Reaction Mixture

Standard state conditions are unrealistic, the
reaction itself will change the temperature and
pressure, so what can we use to calculate the
free energy change under non
-
standard state
conditions?

D
G =
D
G

+ RT
ln

Q

R = gas constant

T = temperature in
Kelvins

Q =

reaction quotient (Q
c

or
Q
p
)

26

Free Energy Changes and Composition of the Reaction Mixture

Thermodynamic Equilibrium Constant (K):

the equilibrium constant in which gases are
expressed in partial pressures (atm) whereas the
concentrations of solutes in liquid solutions are
expressed in molarities.

27

Example 8:

Calculate the Free energy change for the formation of
ethylene (C
2
H
4
) from carbon and hydrogen at 25

C
when the partial pressures are 100 atm H
2

and 0.10
atm C
2
H
4

2 C
(s)

+ 2 H
2(g)

C
2
H
4(g)

D
G

= 68.1 kJ/mol

Is the reaction spontaneous in the forward or reverse
direction
?

28

Free Energy and Chemical Equilibrium

1. When the Reaction Mixture is mostly reactants

Q<<1 RT lnQ <<0
D
G<0

2. When the Reaction Mixture is mostly products

Q>>1 RT lnQ >>0
D
G>0

3.
D
G

=
-
RT ln K

K = equilibrium

constant K
c

or K
p

29

Example 9:

Calculate the K
p

at 25

C for the reaction

CaCO
3(s)

CaO
(s)

+ CO
2(g)

D
G

= 130.5 kJ/mol

30

Example 10:

Which of the following can
always

predict the
spontaneity of a reaction?

1.
D
H

2.
D
S

3.
D
G

31

32

Spontaneity and Temperature Change

Effect of Temperature on the Spontaneity of Reactions