# Chapter 19 Thermodynamics and Equilibrium

Mechanics

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

145 views

Chapter 19

Thermodynamics and Equilibrium

Thermodynamics

is the study of heat and other forms of energy
involved in chemical or physical processes.

First Law of Thermodynamics

The first law of thermodynamics is essentially the law of conservation
of energy applied to a thermodynamic system.

Recall that the
internal energy,
U
,

is the sum of the kinetic and
potential energies of the particles making up the system:

D
U =
U
f

U
i

Exchanges of energy between the
system and its surroundings are of
two types: heat,
q
, and work,
w
.

Putting this in an equation gives us
the first law of thermodynamics.

D
U

=
q
+

w

Sign Convention for
q

When heat is
evolved

by the system,
q

is negative. This decreases the
internal energy of the system.

When heat is
absorbed

by the system,
q

is positive. This increases the
internal energy of the system.

Sign Convention for
w

Recall that
w

=

P
D
V.

When the system expands,
D
V
is positive, so
w

is negative. The system
does work on the surroundings, which decreases the internal energy of
the system.

When the system contracts,
D
V
is negative, so
w

is positive. The
surroundings do work on the system, which increases the internal
energy of the system.

Here the system expands and evolves heat from A to B.

Zn
2+
(
aq
) + 2Cl
-
(
aq
) + H
2
(
g
)

D
V

is positive, so work is negative.

At constant pressure:
q
P

=
D
H

The first law of thermodynamics can now be expressed as follows:

D
U

=
D
H

P
D
V

To understand why a chemical reaction goes in a particular direction,
we need to study spontaneous processes.

A
spontaneous process

is a physical or chemical change that occurs
by itself. It does not require any outside force, and it continues until
equilibrium is reached.

A ball will roll downhill
spontaneously. It will eventually
reach equilibrium at the bottom.

A ball will not roll uphill
spontaneously. It requires
work.

The first law of thermodynamics cannot help us to determine
whether a reaction is spontaneous as written.

We need a new quantity

entropy.

Entropy,
S,

is 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.

Examining some spontaneous processes will clarify this definition.

First, heat energy from a cup of hot coffee spontaneously flows to
its surroundings

the table top, the air around the cup, or your
hand holding the cup. The entropy of the system (the cup of hot
coffee) and its surroundings has increased.

The rock rolling down the hill is a bit more complicated. As it
rolls down, the rock’s potential energy is converted to kinetic
energy. As it collides with other rocks on the way down, it
transfers energy to them. The entropy of the system (the rock)
and its surroundings has increased.

Now consider a gas in a flask connected to an equal
-
that is evacuated. When the stopcock is open, the gas will flow
the entropy of the system has increased.

In each of the preceding examples, energy has been dispersed

Entropy is a state function. It depends on variables, such as
temperature and pressure, that determine the state of the substance.

Entropy is an extensive property. It depends on the amount of
substance present.

Entropy is measured in units of J/K.

Entropy change is calculated as follows:

D
S

=
S
f

S
i

The iodine has spread out, so its entropy has increased.

Second Law of Thermodynamics

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

Note:

Entropy is a measure of energy dispersal, not a measure of
energy itself.

For a spontaneous process at a constant temperature, we can
state the second law of thermodynamics in terms of only the
system:

D
S

= entropy created +

For a spontaneous process:

D
S

>

A pendulum is put in motion, with all of its molecules moving in the
same direction, as shown in Figures A and B.

As it moves, the pendulum collides with air molecules.

When it comes to rest in Figure C, the pendulum has dispersed its
energy. This is a spontaneous process.

Now consider the reverse process, which is not spontaneous. While this
process does not violate the first law of thermodynamics, it does violate
the second law because the dispersed energy becomes more concentrated
as the molecules move together.

Entropy and Molecular Disorder

Entropy is essentially related to energy dispersal. The entropy of a
molecular system may be concentrated in a few energy states and
later dispersed among many more energy states. The energy of such
a system increases.

In the case of the cup of hot coffee, as heat moves from the hot
coffee, molecular motion becomes more disordered. In becoming
more disordered, the energy is more dispersed.

Likewise, when the gas moves from one container into the evacuated
container, molecules become more disordered because they are
dispersed over a larger volume. The energy of the system is dispersed
over a larger volume.

When ice melts, the molecules become more disordered, again
dispersing energy more widely.

When one molecule decomposes to give two, as in

N
2
O
4
(
g
)

2NO
2
(
g
)

more disorder is created because the two molecules produced can
move independently of each other. Energy is more dispersed.

In each of these cases, molecular disorder increases, as does
entropy.

Note:

This understanding of entropy as disorder applies only to
molecular situations in which increasing disorder increases the
dispersion of energy. It cannot be applied to situations that are
not molecular

such as a desk.

Entropy Change for a Phase Transition

In a phase transition process that occurs very close to equilibrium,
heat is very slowly absorbed or evolved. Under these conditions,
no significant new entropy is created.

D
S

=

This concept can be applied to melting using
D
H
fus

for
q

and to
vaporization using
D
H
vap

for
q
.

Acetone, CH
3
COCH
3
, is a volatile liquid solvent; it is used in
nail polish, for example. The standard enthalpy of formation,
D
H
f
°
, of the liquid at 25
°
C is

247.6 kJ/mol; the same quantity
for the vapor is

216.6 kJ/mol.

What is the entropy change when 1.00 mol liquid acetone
vaporizes at 25
°
C?

CH
3
COCH
3
(
l
)

CH
3
COCH
3
(
g
)

D
H
f
°

247.6 kJ/mol

216.6 kJ/mol

n

1 mol

1 mol

n
D
H
f
°

247.6 kJ

216.6 kJ

Third Law of Thermodynamics

A substance that is perfectly crystalline at zero Kelvin (0 K) has an
entropy of zero.

The standard entropy of a substance

its absolute entropy,
S
°

is
the entropy value for the standard state of the species. The standard
state is indicated with the superscript degree sign.

For a pure substance, its standard state is 1
atm

pressure. For a
substance in solution, its standard state is a 1
M

solution.

Standard Entropy of Bromine, Br
2
, at Various Temperatures

Entropy Change for a Reaction

Entropy usually increases in three situations:

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

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

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

The equation below describes the endothermic reaction of solid
barium hydroxide
octahydrate

and solid ammonium nitrate:

Ba(OH)
2

8H
2
O(
s
) + 2NH
4
NO
3
(
s
)

2NH
3
(
g
) + 10H
2
O(
l
) + Ba(NO
3
)
2
(
aq
)

Predict the sign of
D
S
°

for this reaction.

3 moles of reactants produces 13 moles of products
.

Solid reactants produce gaseous, liquid, and aqueous products.

D
S
°

is
_________.

To compute
D
S
°

where n = moles:

When wine is exposed to air in the presence of certain bacteria, the
ethyl alcohol is oxidized to acetic acid, giving vinegar. Calculate the
entropy change at 25
°
C for the following similar reaction:

CH
3
CH
2
OH
(
l
) + O
2
(
g
)

CH
3
COOH(
l
) + H
2
O(
l
)

The standard entropies,
S
°
,

of the substances in J/(K

mol) at
25
°
C are CH
3
CH
2
OH(
l
),161; O
2
(
g
), 205; CH
3
COOH
(l
)
,

160; H
2
O(
l
), 69.9.

CH
3
CH
2
OH
(
l
) + O
2
(
g
)

CH
3
COOH(
l
) + H
2
O(
l
)

S
°

J/(mol

K)

161

205

160

69.9

n

mol

1

1

1

1

n
S
°

J/K

161

205

160

69.9

Free Energy and Spontaneity

Physicist J. Willard Gibbs introduced the concept of
free energy,
G.

Free energy is a thermodynamic quantity defined as follows:

G = H

TS

As a reaction proceeds,
G

changes:

D
G =
D
H

T
D
S

Standard free energy change:

D
G
°

=
D
H
°

T
D
S
°

Using standard enthalpies of formation,
D
H
f
°

and the value of
D
S
°

from the previous problem, calculate
D
G
°

for the oxidation
of ethyl alcohol to acetic acid.

CH
3
CH
2
OH
(
l
) + O
2
(
g
)

CH
3
COOH(
l
) + H
2
O(
l
)

D
H
f
°

kJ/mol

277.6

0

487.0

285.8

n

mol

1

1

1

1

n
D
H
f
°

kJ

277.6

0

487.0

285.8

Standard Free Energies of Formation,
D
G
f
°

The standard free energy of formation is the free
-
energy change
that occurs when 1 mol of substance is formed from its elements in
their standard states at 1
atm

and at a specified temperature, usually
25
°
C.

The corresponding reaction for the standard free energy of
formation is the same as that for standard enthalpy of formation,
D
H
f
°
.

To find the standard free energy change for a reaction where

n = moles:

Calculate the free
-
energy change,
D
G
°
,

for the oxidation of
ethyl alcohol to acetic acid using standard free energies of
formation.

CH
3
CH
2
OH
(
l
) + O
2
(
g
)

CH
3
COOH(
l
) + H
2
O(
l
)

CH
3
CH
2
OH
(
l
) + O
2
(
g
)

CH
3
COOH(
l
) + H
2
O(
l
)

D
G
f
°
, kJ/mol

174.8

0

392.5

237.2

n
, mol

1

1

1

1

n
D
G
f
°
, kJ

174.8

0

392.5

237.2

D
G
°

as a Criterion for Spontaneity

The spontaneity of a reaction can now be determined by the
sign of
D
G
°
.

D
G
°

<

10 kJ: spontaneous

D
G
°

> +10 kJ:
nonspontaneous

D
G
°

= very small or zero (< +10 kJ and >

10 kJ): at
equilibrium

For the reaction as written,
D
G
°

= 173.20 kJ.

For 1 mol NO(
g
),
D
G
f
°

= 86.60 kJ/mol.

The reaction is
nonspontaneous
.

;
D
G
°

= 173.2 kJ