Chapter 4
Thermodynamics and Equilibrium
4-1
Refer to the following figures for Exercises 1-6.
Each represents the energies of four molecules at a given instant,
and the dotted lines represent the allowed energies.
Assume constant spacing between levels to determine the
energies of higher energy levels.
0
4
6
8
2
0
4
6
8
2
0
4
6
8
2
0
4
6
8
2
ABC D
Use the letter ‘U’ for the energy unit.
1.
What are the energies of systems A and B?
Which system is at the higher temperature?
E
A
= 4+2+0+2 = 8U
E
B
= 3+2+0+1 = 6U
System A has the greater energy, so it is at the higher temperature.
3.
In how many ways can the energies of systems A and B be distributed?
Which system has the greater entropy?
•
System A has 8U of energy and A molecules have energy levels at 2, 4, 6, and 8U.
The possible combinations
that sum to 8U and the number of each are: one molecule with 8U {4}, One with 6U and one with 2U {12}, two
molecules with 4U each {6}; one molecule with 4U and two with 2U each {12}, all four molecules with 2U each {1}.
The total number of ways = 4 + 12 + 6 + 12 + 1 = 35.
•
System B has 6U of energy and B molecules have energy levels at 1, 2, 3, 4, 5, and 6U.
The possible
combinations that sum to 6U and the number of each are: one molecule with 6U {4}, One with 5U and one with 1U
{12}, one molecule with 4U and one with 2U {12}; one molecule with 4U and two with 1U each {12}, two molecules
with 3U each {6}; one molecule each with 3U, 2U, and 1U {20}; three molecules with 2U each {4}.
The total
number of ways = 4 + 12 + 12 + 12 + 6 + 20 + 4 = 70.
•
There are more ways to distribute the energy in System B, so it has the higher entropy.
Note System A has more
energy, but System B has the higher entropy because the energy levels are closer in System B.
5.
List the systems in order of increasing entropy at a temperature where they all had 12 U of energy.
The entropies of a group of systems at the same temperature increase as the spacing between their energy levels
decreases.
The energy levels are closest in System B, so it would have the highest energy at any given temperature.
7.
State the second law of thermodynamics.
The entropy of the universe must increase during a spontaneous process.
9.
What effect does the enthalpy change of a process have on the entropy of the universe in processes carried out at
constant T and P?
The heat absorbed (or given off) by a system comes from (or enters) the surroundings.
The heat flow causes an
entropy in the surroundings:
∆
S
sur
= -
∆
H/T, which impacts the entropy of the universe:
∆
S
univ
=
∆
S +
∆
S
sur
.
11. Consider the reaction H
2
+ I
2
→
2HI
∆
G
o
= 2.6 kJ at 298 K. Criticize and correct the following statement:
∆
G
o
> 0,
so the reaction is not spontaneous and HI cannot be made from this reaction at 298 K.
`
∆
G
o
indicates the extent of the reaction, not the spontaneity.
∆
G
o
> 0 means that K < 1, so the equilibrium concentration
of HI will be less than at least one of the reactants, but it will not be zero.