# Thermodynamics

Thermodynamics

Brown,
LeMay

Ch 19

AP Chemistry

Monta Vista High School

Review

2

1
st

Law of Thermodynamics

In any process energy is neither created nor destroyed.

When a system changes from one state to another (
D
E =
q + w), it

1.
Gains heat (+ q) or loses heat (
-

q) and/or

2.
Does work (
-

w) or has work done on it (+ w)

T and internal energy, E, are state functions (depend only
on initial and final states of system and not path taken
between them).

q and w are not state functions.

But
why

does a reaction occur in a particular direction?

19.1: Spontaneous Processes

3

Reversible reaction:
can proceed forward and
backward along same path (equilibrium is possible)

Ex: H
2
O freezing & melting at 0ºC

Irreversible reaction:
cannot proceed forward and
backward along same path

Ex: ice melting at room temperature

Spontaneous reaction:
an irreversible reaction that occurs
without outside intervention

Ex: Gases expand to fill a container, ice melts at room
temperature (even though endothermic), salts dissolve in water

19.2: Molecules & Probability

4

Spontaneity of a reaction is related to the number of
possible
states

a system can have.

Ex: 2 gas molecules are placed in a two
-
chambered container, yielding
4 possible states:

There is a ½ probability that one molecule will be in
each chamber, and a ¼, or (1/2)
2
, probability that both
will be in the right
-
side chamber.

5

With 3 molecules:

There is a ¾ probability that one molecule will be in one
chamber and two in the other, and only a 1/8, or (1/2)
3
,
probability that all 3 molecules will be in the right
-
side
chamber.

All on left Evenly distributed All on right

Frequency

6

All on left Evenly distributed All on right

Frequency

As the number of molecules increases to 100, a bell
-
shaped distribution of probable states, called a
Gaussian

distribution, is observed.

# molecules = 100

Carl Gauss

(1777
-
1855)

7

All on left Evenly distributed All on right

Frequency

# molecules = 10
23

Expanding this to 1 mole of molecules, there is only a (1/2)
10^23
probability that every molecule will be in the right
-
side
chamber.

T
he Gaussian distribution is so narrow that we often forget
that it is a distribution at all,

thinking of the most probable
state as a necessity.

This demonstrates that:

The most probable
arrangements are those in
which the molecules are
evenly distributed.

Processes in which the
disorder

of the system
increases tend to occur
spontaneously.

8

spontaneous

non
-
spontaneous

These probability
distributions apply to the
motion and energy of
molecules, and thus can
predict the
most probable

flow of heat.

We call a process
spontaneous

if it
produces a more probable
outcome, and
non
-
spontaneous
if it
produces a less likely one.

9

spontaneous

non
-
spontaneous

high K.E.

low K.E.

evenly distributed K.E.

Entropy

10

Entropy (S):
a measure of molecular randomness or disorder

S is a state function:
D
S = S
final
-

S
initial

+
D
S

= more randomness

-

D
S

= less randomness

For a reversible process that occurs at constant
T:

Units: J/mol.K

2
nd

Law of Thermodynamics

11

The entropy of the universe increases in a
spontaneous process and remains unchanged in a
reversible (equilibrium) process.

S is not conserved; it is either increasing or constant

Reversible reaction:

D
S
UNIVERSE
= S
SYS
+ S
SURR
= 0

or

S
SYS
=
-

S
SURR

Irreversible reaction:

D
S
UNIV
= S
SYS
+ S
SURR
> 0

Examples of spontaneous reactions:

12

Gases expand to fill a container:

Ice melts at room temperature:

Salts dissolve in water:

Particles are more evenly distributed

Particles are no longer in an ordered crystal lattice

Ions are not locked in crystal lattice

19.3: 3
rd

Law of Thermodynamics

13

The entropy of a crystalline solid at 0 K is 0.

How to predict
D
S
:

S
gas

> S
liquid
> S
solid

S
more gas molecules
> S
fewer gas molecules

S
high T

> S
low T

Ex: Predict the sign of
D
S for the following:

1.
CaCO
3
(s)

CaO (s) + CO
2
(g)

2.
N
2
(g) + 3 H
2
(g)

2 NH
3
(g)

3.
N
2
(g) + O
2
(g)

2 NO (g)

+, solid to gas

-
, fewer moles produced

?

19.4: Standard Molar Entropy, Sº

14

Standard state (º): 298 K and 1 atm

Units = J/mol∙K

D

f

of all elements = 0 J/mol

However, S
°

of all elements ≠ 0 J/mol·K

See Appendix C for list of values.

Where n and m are coefficients in the balanced chemical equation.

19.5: Gibbs free energy, G

15

Represents combination of two

forces that drive a reaction:

D
H (enthalpy) and
D
S (disorder)

Units: kJ/mol

D
G =
D

-

T
D
S

D
G
°

=
D
H
°

-

T
D
S
°

(absolute T)

Josiah Willard Gibbs

(1839
-
1903)

Determining Spontaneity of a Reaction

16

If
D
Gi猠:
ion)

Positive

Forward reaction is non
-
spontaneous; the reverse
reaction is spontaneous

Zero

The system is at equilibrium

19.6: Free Energy & Temperature

17

D
G depends on enthalpy, entropy, and temperature:

D
G =
D
H
-

T
D
S

D
H

D
S

D
Gandreactionoutcome

-

+

Always (
-

2 O
3

(g)

3 O
2

(g)

+

-

Always +; non
-
spontaneous at all T

3 O
2

(g)

2 O
3

(g)

-

-

Spontaneous at low T; non
-
spontaneous at high T

H
2
O (l)

H
2
O (s)

+

+

Spontaneous only at high T ; non
-
spontaneous at

low T

H
2
O (s)

H
2
O (l)

19.7: Free Energy &
Equilibria

18

Nernst Equation
The value of
D
G determines where the
system stands with respect to equilibrium.

D
G =
D
G
°

+ RT ln Q
(Nernst Equation)

where R = 8.314 J/K

mol

-
Used for calculating
D
G
under experimental conditions from
standard conditions
D
G
°
.

-
How do you calculate
D
G
°

?

-
Nernst Equation when the system is at equilibrium:
Note that
D
G
becomes zero at equilibrium and not
D
G
°

19.7: Free Energy & Equilibria

19

D
G

Reaction outcome

Negative

Spontaneous forward rxn, K > 1

Positive

Non
-
spontaneous forward rxn, K < 1

Zero

System is at equilibrium, K = 1