Entropy and Gibbs Free Energy
Objectives
1. Define entropy
2. List two factors that affect entropy (state of matter and number of particles)
3. Predict spontaneity based on entropy
4. Predict spontaneity based on enthalpy and entropy using Gibbs Free Energy
5. Perform Gibbs Free Energy calculations
Objective 1:
Entropy – amount of disorder, randomness
Symbol: S
Units: J/Kmol
Example:
If you put a cube of sugar in a cup of tea, the sugar will dissolve and never come back
to form the cube – the sugar molecules become more disordered
If you spray perfume, the perfume will diffuse throughout the air - the molecules become
more disordered.
There is tendency in the universe for greater disorder
How is it measured?
 It’s a probability calculation
What is it good for?
 Explaining spontaneous endothermic reactions
History:
Entropy was introduced in 1865 by Rudolf J. E. Clausius, a German physicist. Clausius said
he derived the term from the Greek words en trope, which means “in the transformation”
He used it to describe the dissipation or apparent loss of energy available to do work as
energy is transformed in a system.
Objective 2:
Factors that affect entropy
1. State of matter
a. Gas (most) particle motion is more random in a gas
b. Liquid (middle) particle motion is less random than a gas but more
than a solid
c. Sold (least) particle motion is restricted. Possible positions for
molecules are restricted
d. Examples
i. (changing state) H2O(l)  H2O(g)
ii. (changing state) H2O(s)  H2O(l)
2. Temperature
a. Comparing two gasses, one at 20 C and one at 80 C
b. Molecules in the 80 C gas have more kinetic energy, they are moving
more and colliding more
3. The number of molecules
a. More molecules means more possible positions relative to the other
molecules
i. (more moles and change of state) Li2CO3(s)  Li2O(s) + CO2(g)
ii. (more moles) MgSO48H2O  Mg2+(aq) + SO42-(aq) + 8H2O(l)
4. More complex molecules have higher entropy values
Is entropy an extensive or intensive property?
 Extensive because it depends upon the amount of mass
Objective 3:
Predictions
1. Ag+1 + Cl-1  AgCl(s)
2. 2 Fe(s) + O2(g)  2 FeO (s)
3. NaCl  Na+1 + Cl-1
Objective 4:
Which is more important enthalpy or entropy?
Gibbs Free Energy
Josiah Willard Gibbs (1839-1903) was little known during his lifetime of work at Yale
University in Connecticut.
Gibbs Free Energy is the available, useful energy from a process
Spontaneous: a process that is likely to occur without the continuous input of energy
If G > 0, not spontaneous
If G < 0, spontaneous
The following equation can be used to predict spontaneity:
G = H - TS
 Notice that entropy is affected by temperature
H
S
G
Spontaneous
Negative
Positive
Negative
YES
Positive
Negative
Positive
NO
Depends
on H
Negative Negative
Depends
compared to S
Positive
Positive
Depends
YES at high
Temperatures
Gibbs Free Energy Calculations
Objective 5:
Example calculation:
Given that the changes in enthalpy and entropy are -139 kJ and 277 J/K respectively for
the reaction given below, calculate the change in Gibbs energy. Then state whether the
reaction is spontaneous at 25 C
C6H12O6(aq)  2C2H5OH(aq) + 2CO2(g)
(this reaction is used in baking)
H = -139 kJ  139000 J
S = 277 J/K
T = 25 C  25 + 273.15 = 298.15 K
G = ?
Plug into the equation:
 G = 139000 J
– (298.15 K)( 277 J/K) = -222000 J = -222 kJ
Determine Spontaneity
 Is G < 0 ? Yes,
than the reaction is spontaneous
Summary of Thermodynamics
Three laws of Thermodynamics
0th Thermal Equilibrium
1st Law of Conservation of Energy
2nd Increasing entropy