Chapter 18 Thermodynamics: Entropy and Free Energy
Section 18.2 Spontaneous Change and Equilibrium. We must now address why
reactions occur, and what controls the equilibrium position of a reaction. To do this, we must
introduce the idea of a spontaneous process.
“spontaneous” means occurs by itself ∴ a spontaneous reaction or change occurs by itself
(until it reaches equilibrium), whereas a “nonspontaneous” reaction is in a direction away from
equilibrium and can thus occur only if we force it to happen by inputting energy.
** Let’s consider reactions that lie ~100% to one side or the other to help get the points across,
and then we will be more general later.**
Examples. 1) Sodium metal, Na(s), will spontaneously react with Cl gas2to give NaCl, but
NaCl will not spontaneously give Na metal and Cl 2as unless we input energy.
2) Iron metal will spontaneously rust when exposed to water and oxygen gas, but rust will not
spontaneously give Fe metal.
These examples are obvious, but what about:
+ ? 2+
Pb (s) + 2 Ag (aq) Pb + Ag (s)
Which is the spontaneous direction in which the reaction will go by itself, and which is the
direction we must force it to go???
Similarly, consider something falling, e.g. a ball or chalkboard eraser
Note: “spontaneousness” (or “spontaneity”) does not tell us anything about rates of reaction,
only about whether it will occur by itself.
What factors determine which direction of a reaction is spontaneous? We shall see
in Chapter 18, and involves the 2 Law of Thermodynamics. First, let’s refresh our memories
of the 1 Law.
First Law of Thermodynamics = Conservation of Energy
ΔE = q + w E = internal energy of system
(sum of potential and kinetic energies)
q = heat
w = work
1 As chemists, our “system” is usually a reaction in a beaker or flask everything else is
∴ EuniverseEsystem E surroundings
The universe consists of everything ∴ its energy is constant (ΔEuniv0)
∴ ΔE univE + sys= 0 surr
i.e., ΔEsysnd ΔE surrel each other out ∴ energy (E) cannot be created or destroyed. This is
the First Law of Thermodynamics
NOTE: First Law does not by itself help us to understand and predict the spontaneous
How is E, the internal energy of the system, related to H, the enthalpy we learned about in
H = E + PV (P = pressure, V = volume)
ΔH = ΔE + PΔV (at constant pressure)
For most reactions (in solution), ΔV is insignificant
∴ ΔH ≈ ΔE
ΔH = enthalpy change = the heat gained or lost at constant pressure.
Can we predict spontaneity from the sign of ΔH?
i.e., are all exothermic rxns ΔH 0) nonspontaneous?
19 century scientists used to think so for a long time, but the answer is NO.
CH 4g) + 2 O 2(g) → CO 2g) + 2 H O2(g) ΔH° rxn802 kJ
Na (s) + ½ Cl 2(g) → NaCl (s) ΔH° rxn411 kJ
These are spontaneous as written (left to right), and their ΔH 0 (endothermic) that are
**spontaneous reactions are usually exothermic, but not always!**
e.g., melting of ice: H 2 (s) → H O 2l) ΔH° rxn6.02 kJ
evaporation of H O2 H O (2) → H O (g2 ΔH° rxn44.0 kT
2 ΔH > 0 for both, yet both occur spontaneously.
∴ ΔH by itself does not determine spontaneity ! We must keep looking to find the law that
Sections 18.3/4. Entropy, and the 2 Law of Thermodynamics
Spontaneity is determined by a thermodynamic function called ENTROPY (symbol S,
units Joules/Kelvin (J/K). This is the basis of the 2 law of Thermodynamics and allows us to
predict when a process is spontaneous.
First, let’s think about entropy.
What is an increase in entropy? Increasing the dispersal of energy or matter over more
energy states corresponds to an increase in entropy
e.g. dispersing (spreading) energy over more atoms represents an increase in entropy (think of a
hot metal in contact with a cold one the heat will be spread out spontaneously).
e.g. dispersing (spreading) matter over a bigger volume represents an increase in entropy (think
of a gas in one container distributing between it and an empty container when connected).
Entropy is often related to the idea of DISORDER. Increasing disorder (i.e. decreasing order)
is increasing entropy. Spreading (dispersing) heat energy over a bigger amount of metal, or
spreading (dispersing) the gas molecules over a greater volume are both examples of going to a
situation with greater disorder (smaller order)
new deck of cards shuffled deck
protein amino acids
house pile of bricks
Nature has an inherent tendency towards greater dispersal (spreading out) of energy and
matter i.e. to greater disorder.
e.g., gas vs crystal. A gas is much more disordered than a crystal
3 A measure of dispersal (or disorder) in a system is ENTROPY (S). Increasing entropy (S) =
increasing dispersal (disorder)
i.e. disordered systeordered system
e.g. S(gas) >> S(crystal)
S is a state function, like enthalpy H or energy E — it depends on the present state of the
system, not how it got there.
The Boltzmann Equation for Entropy
Entropy S is related to disorder (number of equivalent ways of distributing energy). In 1877,
Boltzmann defined S
S = k ln(W) W = No. of ways system can be arranged.
k = kB = Boltzmann’s Constant
Interesting, but rarely useful in practice because on a molecular level we rarely know or can
Thus, entropy (S) measures the extent of disorder resulting from dispersal of energy and matter.
We can now state the rule for a spontaneous process.
Section 18.4 Second Law of Thermodynamics
**2 Law of Thermodynamics: in a spontaneous process, the change in the
entropy of the universe is positive, i.e. ΔS universe> 0 **
i.e. spontaneous processes occur in the direction that increases the entropy of the universe.
True but doesn’t help yet with figuring out which is the spontaneous direction of a
reaction we’ll get to that later.
Now, ΔS universeΔS system ΔS surroundings
∴ ** ΔS sysS surr> 0 for a spontaneous process **
Note: ΔS sys or may not be > 0 (positive)
ΔS surror may not be > 0 (positive)
but ΔS universeWAYS > 0 for a spontaneous process
First, let’s look at ΔS (or ΔS ) in detail we’ll return to ΔS later
sys rxn surr
4 Standard Molar Entropies (S°)
Remember from Chapter 6 that enthalpy (H) cannot be determined absolutely, only changes
However, absolute entropies can be determined because of:
The 3 Law of Thermodynamics .
= A perfect crystal has zero entropy at absolute zero.
i.e., Ssys at 0 K.
As with ΔH, we normally quote S at standard conditions for molar amounts, i.e., S° =
standard molar entropy (J/mol.K or J.mol K )
Standard conditions = 1 atm pressure for gases, 1 M molarities for solutions.
Predicting Relative S° Values
See Appendix 3 for tables of standard molar entropies (S°) at 298 K (25 ºC).
See also the table
Let’s use ideas of dispersal/disorder and W (ways of distributing energy).
(1) As temperature increases, S° increases (i.e. ΔS > 0).
(2)When more ordered phase → more disordered phase, ΔS > 0
e.g., Na (s) → Na (g) ΔS° = 102.2 J.mol K 1 1
S° = 51.4 S° = 153.6 Figure 18.6
1 1 1 1
J.mol K J.mol K