Chem 2 - Gibbs Free Energy and Spontaneous Reactions VI

1. Gibbs Free Energy and
Spontaneous Reactions
(Pt 6)
By Shawn P. Shields, Ph.D.
This work is licensed by Shawn P. Shields-Maxwell under a Creative Commons
Attribution-NonCommercial-ShareAlike 4.0 International License.

2. Recall: Suniv and Spontaneous
Processes
The total entropy change of the
universe (Suniv) for any
spontaneous process is positive.
+ Suniv
Suniv = Ssys + Ssurr

3. Suniv and Gibbs Free Energy (G)
Calculating Suniv is not convenient.
Suniv = Ssys + Ssurr
Gibbs proposed a new thermodynamic
state function that is derived from three
other state functions for the system.
Enthalpy, Entropy, and Temperature.

4. Gibbs Free Energy (G)
G = H  TS
The Gibbs Free Energy change for
a given process is
G = H  TS
(at constant T and P)

5. Suniv and Gibbs Free Energy (G)
Entropy S is maximized at
equilibrium
Free energy G is minimized at
equilibrium.

6. Gibbs Free Energy G
Without derivation:
TSuniv = Hsys  T Ssys
TSuniv = G
G
When G for a given process is negative,
the process is spontaneous in the forward
direction (as written).

7. Predicting Spontaneity and G
Negative G means the process is
spontaneous (as written; in the forward
direction).
Positive G means the process is
nonspontaneous (as written). However, it
is spontaneous in the reverse direction!
If G = 0, the reaction is at equilibrium.

8. Gibbs Free Energy (G) and Predicting
Spontaneous Processes
The sign of the Gibbs Free Energy for a
given process will depend on the signs of
H and S.
G = H  T S
We can predict whether a given process
will b spontaneous by analyzing the signs
of H and S.

9. H, S, and the Sign of G
Sign of H Sign of S Sign of G Type of
Process
negative positive negative
spontaneous at all
temperatures
positive negative positive
nonspontaneous at
all temperatures
positive positive () or (+)
Spontaneous if the
temperature is high
enough
negative negative (+) or ()
Spontaneous if the
temperature is low
enough
G = H  T S

10. Case 1: H and S Agree (Spontaneous)
When H is negative and S is positive, G is
always negative. The reaction is spontaneous in
the forward direction (any T).
G = H  T S
G = ()  T (+)
G = ()  (+)(+)
G = a negative number (any T)
T in K, so always
a positive number!
Negative term

11. Case 2: H and S Agree (Nonspontaneous)
H is positive and S is negative, so G is always
positive. The reaction is nonspontaneous in the
forward direction (any T). Spontaneous in reverse
direction.
G = H  T S
G = (+)  T ()
G = (+)  (+)()
G = a positive number (any T)
T in K, so always
a positive number!
Positive term

12. Case 3: H and S Disagree (G “Decides”)
H is positive and S is positive, so G is negative
or positive depending on the temperature. The
reaction is spontaneous in the forward direction if
T is high enough.
G = H  T S
G = (+)  T (+)
G = (+)  (+)(+)
T in K, so always
a positive number!
Positive term

13. Case 3: H and S Disagree (G “Decides”)
The reaction is spontaneous in the forward
direction if T is high enough.
G = H  T S
G = (+)  T (+)
G = (+)  (+)(+)
G = a positive number (at low T)
G = a negative number (at high T)
Subtract a large
positive term
If T is high, subtract a
larger number than H

14. Case 4: H and S Disagree (G “Decides”)
H is negative and S is negative, so G is
negative or positive depending on the
temperature. The reaction is spontaneous in the
forward direction if T is low enough.
G = H  T S
G = ()  T ()
G = ()  (+)()
T in K, so always
a positive number!
negative term

15. Case 4: H and S Disagree (G “Decides”)
The reaction is spontaneous in the forward
direction if T is low enough.
G = H  T S
G = ()  T ()
G = ()  (+)()
G = a negative number (at low T)
G = a positive number (at high T)
a positive term
overall
If T is low, add a smaller
number than H

16. Summary: Gibbs Free Energy (G)
G = H  T S
When H is () and S is (+) , G is
always (). Spontaneous in the forward
direction (any T).
H is (+) and S is (), so G is always
(+). Nonspontaneous in the forward
direction (any T).

17. Summary: Gibbs Free Energy (G)
G = H  T S
H is (+) and S is (+), so G is ()
or (+) depending on the
temperature.
Spontaneous in the forward
direction if T is high enough.

18. Summary: Gibbs Free Energy (G)
G = H  T S
H is () and S is (), so G is (+)
or () depending on the
temperature.
Spontaneous in the forward
direction if T is low enough.

19. Next up…
Free Energies of Formation and
Calculating Free Energy of
Reaction (G) (Pt 7)