# Entropy and Free Energy

Μηχανική

27 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

100 εμφανίσεις

Entropy

Entropy

Entropy

is defined
as a state of
disorder or
randomness.

In general the
universe tends to
move toward
release of energy
and greater entropy.

2

Entropy

The statistical
interpretation of
thermodynamics was
pioneered by James
Clerk Maxwell (1831

1879) and brought to
fruition by the Austrian
physicist Ludwig
Boltzmann (1844

1906).

3

Entropy

Spontaneous chemical
processes often result in a
final state is more
Disordered

or
Random
than the original.

The Spontaneity of a
chemical process is related to
a change in randomness.

Entropy
is a

thermodynamic
property related to the
degree of randomness or
disorder in a system.

Reaction of potassium
metal with water. The
products are more
randomly distributed
than the reactants

4

Entropy and
Thermodynamics

According to the second law or
thermodynamics the entropy of the
universe is always increasing.

This is true because there are many more
possibilities for disorder than for order.

Entropy

Royal
Flush

Nothing
hand

Entropy is Disorder

Disorder
in a system can take many forms.
Each of the following represent an increase in
disorder and therefore in entropy:

1.
Mixing different types of particles. i.e.
dissolving salt in water.

2.
A change is state where the distance between
particles increases. Evaporation of water.

3.
Increased movement of particles. Increase in
temperature.

4.
Increasing numbers of particles. Ex.

2 KClO
3

2 䭃l +″O
2

7

Entropy States

The greatest increase in
entropy
is usually
found when there is an increase of
particles in the gaseous state.

The symbol for the change in disorder or
entropy is given by the symbol,
D
S
.

The
more disordered

a system becomes
the
more positive

the value for
D
S

will be.

Systems that become
more ordered

have
negative
D
S

values.

8

The entropy of a substance depends
on its state:

S (gases) > S (liquids) > S (solids)

Entropy, S

S
o

(J/K
-
1
mol
-
1
)

H
2
O (liquid)

69.95

H
2
O (gas)

188.8

9

Entropy and States of Matter

S˚(Br
2

liquid) < S˚(Br
2

gas)

S˚(H
2
O solid) < S˚(H
2
O liquid)

10

Entropy, Phase & Temperature

S increases
slightly with T

S increases a
large amount
with phase
changes

11

The Entropy of a substance increases with
temperature.

Molecular motions
of heptane, C
7
H
16

Molecular motions of
heptane at different temps.

Entropy and Temperature

12

Entropy
-

Boltzman

Ludwig Boltzman

S = k Ln W

Entropy is proportional
to the number of degrees
of freedom or possible
configurations in a
system.

13

Standard Entropy Values

The standard entropy,
D
S
o
, of a substance
is the
entropy change per mole

that occurs
when heating a substance from
0 K

to the
standard temperature of
298 K.

Unlike enthalpy, absolute entropy changes
can be measured.

Like enthalpy,
entropy is a state function
.
The change in entropy is the difference
between the products and the reactants

D
S
o

=
S

S
o

(products)
-

S

S
o

(reactants)

14

Standard Entropy Values

15

The amount of entropy in a
pure substance depends on
the temperature, pressure,
and the number of molecules
in the substance.

Values for the entropy of
many substances at have
been measured and tabulated.

The standard entropy is also
measured at 298 K.

Some standard enthalpy values

Gibbs Free Energy

16

Spontaneity

A chemical reaction is spontaneous if it
results in the system moving form a less
stable to a more stable state.

Decreases in enthalpy and increases in
entropy move a system to greater stability.

The combination of the enthalpy factor and
the entropy factor can be expressed as the
Gibbs Free Energy
.

17

Gibbs Free Energy

The standard free energy change is defined
by this equation

D
G
o

=
D
H
o

T
D
S
o

Where

D
H
o

= the enthalpy change

D
S
o

= the entropy change

T = Kelvin temperature

A chemical reaction is
spontaneous if it results
in a negative free energy change.

18

Gibbs Free Energy

D
G
o

=
D
H
o

T
D
S
o

D
G

D
H

D
S

D
H
-
T
D
S

Always
Spontaneous

< 0 (
-
)

< 0 (
-
)

> 0 (+)

Always (
-
)

Never
Spontaneous

> 0 (+)

> 0 (+)

< 0 (
-
)

Always (+)

Spontaneous at
High Temperature

< 0 (
-
)

> 0 (+)

> 0 (+)

> 0 (+)

(
-
) if T large

(+) if T small

Spontaneous at
Low Temperature

> 0 (+)

< 0 (
-
)

< 0 (
-
)

< 0 (
-
)

(+) if T large

(
-
) if T small

19

Free Energy Problem 1

A certain chemical reaction is exothermic with a
standard enthalpy of
-

400 kJ mol
-
1
.

The entropy
change for this reaction is +44 J mol
-
1

K
-
1
.
Calculate the free energy change for this reaction
at 25
o
C. Is the reaction spontaneous?

Solution

Convert the entropy value to kJ. 44 J mol
-
1

K
-
1

= 0.044
kJ mol
-
1

K
-
1

D
䜠‽
-

㐰〠
kJ mol
-
1

(298 K)(0.044 kJ
mol
-
1

K
-
1
)

D
G ‽
-

㐰〠
kJ mol
-
1

13.1 kJ
mol
-
1

D
G

-

413⸱
kJ mol
-
1

.
Since
D
G 楳⁮egat楶e the

† ††††††††††††††††††††††
react楯n 楳⁳pontaneous.

Note. Because
D
H <〠慮d
D

at all temperatures.

20

Free Energy Problem 2

A certain chemical reaction is endothermic with a
standard enthalpy of +300 kJ mol
-
1
.

The entropy
change for this reaction is +25 J mol
-
1

K
-
1
.
Calculate the free energy change for this reaction
at 25
o
C. Is the reaction spontaneous?

Solution

Convert the entropy value to kJ. 25 J mol
-
1

K
-
1

= 0.025
kJ mol
-
1

K
-
1

D
䜠‽ +″00
kJ mol
-
1

(298 K)(0.025 kJ
mol
-
1

K
-
1
)

D
G ‽ +″00
kJ mol
-
1

7.45 kJ
mol
-
1

D

=

+ 292⸵5
kJ⁭ol
-
1

.
Since
D
G 楳⁰os楴楶e the

† ††††††††††††††††††††
react楯n 楳⁮on
-
spontaneous.

Note. Because
D
H >〠慮d
D

-
spontaneous at low temperatures. It the temperature were
substantially increased it would become spontaneous.

21