Thermodynamics
Spontaneity
• What does it mean when we say a process
is spontaneous?
• A spontaneous process is one which
occurs naturally with no external
influence.
• The reverse process will not occur
naturally under the same conditions!
Spontaneity, Cont.
• Spontaneous processes may occur slowly
or quickly, spontaneous does not mean
that it is an instantaneous process.
• What are some examples of spontaneous
processes?
Spontaneity, Cont.
• So, how can you tell whether a chemical
rxn or physical process will occur
spontaneously (naturally with no external
influence)?
• Also, why is a rxn spontaneous and under
what conditions (temperature, etc.)?
Spontaneity, Cont.
• To answer this, we need to talk about the
two factors of spontaneity:
– enthalpy (a measure of the heat energy
change in a system) and
– entropy (a measure of the randomness or
disorder of a system)
Entropy
• Entropy, S, is a measure of the molecular
disorder or randomness.
• Like enthalpy, entropy is a state function,
so it is independent of path.
 S is the change in entropy of a system,
S = Sf – Si, and this value is also
independent of path.
Entropy
• You can see from the above equation,
that if the entropy of a system increases,
then S is positive, while it will be
negative if the entropy decreases.
• It is true that chemical systems tend to
move spontaneously in the direction
which will increase the randomness or
entropy of the system.
Entropy
• So one indicator of spontaneity is the
entropy change of a system: it is likely to
be spontaneous if S is +.
• How can you predict whether S is
increasing or decreasing?
• Well first of all, use your common sense
and knowledge: which state is the most
disordered: solid, liquid, or gas?
Entropy
• So you can eyeball many processes or
rxns and see whether more or less gas
molecules are being formed: the side with
the most disorder is favored.
• Also, mixing processes tend to increase
the disorder of a system (although these
are 2 or more steps, and not all of the
steps have favorable entropy changes).
Entropy
• Changing the temperature increases
molecular motion and velocity, which
increases entropy.
• This is because of the Third Law of
Thermodynamics which states that the
entropy of a perfectly ordered crystal is 0
at 0K.
Entropy
• Changing the volume of a gas (at
constant T) changes the entropy:
increasing the volume gives the gas more
space in which to move, so entropy
increases.
Entropy
• Likewise, changing the pressure of a gas
(at constant T) changes the entropy: here
increasing the pressure, by decreasing
the volume, forces the molecules closer
together into a more ordered state.
Entropy
• Problem: Predict the sign of S for the
following processes.
• Which are likely to be spontaneous?
Entropy
• In reality, entropy is really a function of
statistics and probability: the most likely,
most statistically probable state is a
disordered state!
Entropy
• Mathematically, there is an equation:
S = k lnW or S = k ln, where k is
Boltzmann’s constant and W or  is the
number of ways the system can be
arranged.
• So the more ways a system can be
arranged, the higher the entropy.
Entropy
• This also means that the more molecules
or particles in the system, the more ways
a system can be arranged. So the more
particles in the system, the higher the
entropy.
Entropy and the Second Law of
Thermodynamics
• The Second Law of Thermodynamics
states that for any process to be
spontaneous, the overall entropy of the
Universe MUST increase.
• Now we have to think beyond the entropy
of the system itself to the entropy of the
surroundings and the overall entropy of
the universe.
Entropy and the Second Law
• What this means is this:
Suniverse = Ssys + Ssurr
• For a process to be spontaneous, Suniverse
must be +.
• How do we find Suniverse?
Entropy and the Second Law
• Finding Ssys is easy:
Ssys = Srxn = Sproducts – Sreactants
• As standard molar entropies, S°, at
25°C are easy to find in Tables, we
calculate S°rxn
Entropy and the Second Law
• Ex: Find Ssys for the following rxn at
25°C:
Entropy and the Second Law
• OK, it’s easy to find Ssys, but how do
you find Ssurr?
Back to Enthalpy!
• Enthalpy Change, H, measures whether
heat is absorbed or released by a process.
• Just like Ssys , we find Hrxn :
Back to Enthalpy!
• If H is -, then heat energy is released by
the system to the surroundings
• If H is +, then heat energy is absorbed
from the surroundings by the system
• Which is likely to be spontaneous, a – or
+ H?
Back to Enthalpy!
• Think about what happens to the entropy
of the surroundings when the
temperature changes!
• Mathematically, Hrxn affects the entropy
of the surroundings:
Back to Enthalpy!
• If Hrxn is -, an exothermic rxn, then
Ssurr is +, which indicates that the rxn
(or process) is likely to be spontaneous
• So there is a balance between the two
factors H and S to determine whether
a rxn is spontaneous.
Back to Enthalpy!
• Also, spontaneity depends on
temperature as shown in the following:
Gibbs Free Energy
• Chemists have named a thermodynamic
function of energy, Gibbs Free Energy, G
or G, which predicts spontaneity.
• Gibbs Free Energy is a measure of the
energy which is available in a system; it is
also the maximum work which a system
can perform.
Free Energy
• It is defined as:
Free Energy
• If G is -, it IS spontaneous in that
direction;
• If G is +, it is spontaneous in the
REVERSE direction;
• If G = 0, then the system is at
equilibrium.
Free Energy
• Here is a table which shows the balance
and importance of T in determining G
and spontaneity:
Free Energy
• Let’s look at a cold pack.
• This is a dissolving process and a
hydration process!
• Will this rxn be spontaneous at room
temperature and why?
Free Energy
• Now anyone who’s used a cold pack
knows that it is spontaneous, but the
question is why and for what
temperatures?
Free Energy
• So at temperatures higher/lower (circle
the correct one) than ________, this will
not be a spontaneous process, instead the
reverse process is!
• So the rxn is spontaneous for
temperatures higher/lower (circle the
correct one) than ________.
Review:
• You learned how to calculate G from
the enthalpy and the entropy
• You learned how to predict the
spontaneity of a process from G
• You learned the temperature dependence
of S and G
Free Energy
• Take-Home Problem: For what
temperatures will the following rxn be
spontaneous (greater than, lower than
what)?
Calculating G°
• You can calculate G° from the
equation: G° = H° - TS°
• But you can also calculate it from table
values of G°f just as you do for H.
G° and Rxn Composition
 G° tells you which direction the given
rxn is spontaneous at standard state
conditions.
• But how often are you at standard state
conditions?
• How do you calculate just plain G at
non-standard state conditions?
G° and Rxn Composition
• There is a mathematical relationship
between G and G° based on the
reaction quotient, Q
• Note we adjust G° to the temperature
we are actually at.
G° and Rxn Composition
• What is true if we are at standard state?
The Meaning of G and G°
• What else does G° tell us?
• All rxns come to “equilibrium”, or an end
point.
• So G° also tells us which direction a
rxn must shift from standard state
conditions in order to reach the end or
“equilibrium”.
The Meaning of G and G°
• The magnitude of G° tells us how far
away it is from “equilibrium”.
– If it is very positive, then the rxn must shift
far to the left.
– If it is very negative, then it must shift far to
the right.
The Meaning of G and G°
• Lastly, G° tells us what is favored at
equilibrium, reactants or products.
– At standard state, Q = 1.
– So if G° is negative, then the rxn proceeds
to the right making products, so Q is now >
1.
– So if G° is positive, then the rxn proceeds
to the left making reactants, so Q is now < 1.
The Meaning of G and G°
 G tells us what direction the rxn is
proceeding right now, under the current
conditions!
• Unlike G°, which is fixed for a given
temperature, G changes as the rxn
progresses toward equilibrium or
completion.
The Meaning of G and G°
• How does G change as the rxn
progresses and what is the value of G at
equilibrium?
• What is the value of Q at equilibrium?
The Meaning of G and G°
• This gives us a relationship between
G° and K: