The document discusses Gibbs free energy and its relationship to chemical equilibrium. It defines Gibbs free energy and how it can be used to predict the spontaneity of reactions. The Gibbs free energy change, ΔG, is related to the standard Gibbs free energy change, ΔG°, and the reaction quotient, Q, by the equation ΔG = ΔG° + RTlnQ. At equilibrium when ΔG = 0, Q equals the equilibrium constant, K. Expressions are provided for calculating K for different types of reactions, such as gas phase, liquid phase, and liquid-solid reactions. The key points are that a reaction will only proceed spontaneously if ΔG is negative and that a reaction will reach equilibrium when ΔG equals

1. CHEMICAL THERMODYNAMICS.
FREE ENERGY,
FREE ENERGY AND EQUILIBRIUM
Lecture 4
17 March 2023 PHYSICAL CHEMISTRY 1

2. PLAN
- Gibbs free energy function
- Gibbs Free Energy of Reaction System
- Chemical equilibrium
- Relationship between Gibbs Free Energy and
chemical equilibrium
17 March 2023 PHYSICAL CHEMISTRY 2

3. Gibbs Free Energy
• Predicts the direction of a spontaneous reaction.
• Uses properties of the system to calculate.
• For a constant pressure-temperature process.
17 March 2023 : PHYSICAL CHEMISTRY 3
DG = DHsys -TDSsys
DG < 0 The reaction is spontaneous in the
forward direction.
DG > 0 The reaction is non spontaneous as written.
The reaction is spontaneous in the reverse
direction.
DG = 0 The reaction is at equilibrium.

4. 17 March 2023 PHYSICAL CHEMISTRY 4
Standard Free-Energy Changes
The standard free-energy of reaction (DG0 )
is the free-energy change for a reaction when it occurs under
standard-state conditions.
Rxn
Standard free energy of formation
(DG0)f is the free-energy change
that occurs when 1 mole of the
compound is formed from its
elements in their standard states.
f
DG0
rxn nDG0 (products)
f
= S mDG0 (reactants)
f
S
-

5. 5
Gibbs Free Energy of Reaction System
• Gibbs free energy (also called Gibbs function) definition
G = U + PV -TS = H - TS DG= DH - TDS at constant T,P
• Gibbs free energy calculation
Standard Gibbs free energy, G°298
Similar to S° and H°, the standard Gibbs free energy of formation of a substance, G°, is
defined at reference state of T=298 K and P=1 atm
(G°298 values of common substances are available in most chemistry / chem. engg
handbooks.)
• Gibbs free energy change in a reaction at T, P
reaction: vAA + vBB D vCC + vDD
or, DGT° can be determined directly from
Chemical Reaction
- 0
0
0
T
T
T S
T
H
G D
D

D
-
inwhich 0
0
0
0
0
0
T
,
i
T
,
i
T
,
i
reac
T
,
i
i
prod
T
,
i
i
T S
T
H
G
)
G
v
(
)
G
v
(
G D
D

D


D 

value of each individual
substance
value from overall reaction

6. 6
Gibbs Free Energy of Reaction System (2)
• DG° is one of the most important thermodyn. properties for a chemical reaction system.
– It determines the direction of reaction to proceed
• DG°< 0 is the pre-condition which MUST be met for any process (not limited to
chemical reaction systems) to occur (spontaneous process).
• DG°<0 indicates a specified reaction has tendency to proceed; however, it
CANNOT tell how fast that reaction will occur - reaction kinetics tell the rxn rate.
• A process/reaction proceeds always in the direction of MINIMISING Gibbs free
energy. This is a very important concept.
• A process/reaction will stop at DG°0, this is called equilibrium state.
Chemical Reaction
reaction can proceed in the direction specified
reaction at equilibrium (no further change occurs)
reaction will NOT proceed (it can proceed backward!)







D


D


D
0
0
0
T
T
T
G
G
G
for a reaction
at constant T,
P, we have

7. Standard Free-Energy Changes
7

8. Factors Affecting ΔG
17 March 2023 PH 101: PHYSICAL CHEMISTRY 8

9. 9
Important Notes about DS, DH and DG
• DS, DH and DG are widely used in analysing various systems. Our current discussion of
these function is limited to the application to a reaction system.
• A clear definition of the reaction conditions is necessary before start calculation of
these properties.
• There are many ways these thermodynamic properties can be determined. Only most
commonly used ones in relation to a chemical reaction are given.
• It is very important to understand the study a chemical reaction by means of
thermodynamics tells only state - a ‘snapshot’ of system, and how a process proceeds
from one state to another (reversible-irreversible, with or without work done /
exchange heat with surrounding). There is no factor of time involved.
Chemical Reaction

10. 10
• For a chemical reaction vAA + vBB D vCC + vDD
when G°T =0, we say the reaction is in chemical reaction equilibrium
- What is a chemical reaction equilibrium?
Example 1: NH3(aq)+H2O(l) D NH4
+(l)+OH-(aq)
At constant T and P, when t
Example 2: 2NO(g) + O2(g) D 2NO2(g)
At constant T and P, when t
The concentration of a gas is usually measured as partial pressure
At an equilibrium the reaction quotient becomes constant
Chemical Reaction - The Equilibrium
t
NO2
NO
O2
t
NH4
NH3
constant
2
2
2
2

O
NO
NO
P
P
P
constant
O]
][H
[NH
]
][OH
[NH
2
3
4



reaction quotient

11. 11
Equilibrium Constant (1)
• Definition of equilibrium constant, K
The equilibrium constant is the reaction quotient at G°T =0.
• Expressions of equilibrium constant for various reactions
– gas phase 2NO(g) + O2(g) D 2NO2(g)
– gas-solid phase CaCO3(s) D CaO (s)+CO2(g)
– liquid phase NH3(aq)+H2O(l) D NH4
+(l)+OH-(aq)
– liquid-solid Cu(OH)2(s) D Cu2+(aq)+2OH- (aq)
– gas-liquid NH3(g)+H2O(l) D NH4OH(aq)
– general vAA + vBB D vCC + vDD
Chemical Reaction equilibrium
2
2
2
2
O
NO
NO
p
P
P
P
K 
O]
][H
[NH
]
][OH
[NH
2
3
4



c
K
2
CO
p P
K 
2
2
]
][OH
[Cu 


c
K
3
1 NH
p P
/
K 
B
A
D
C
B
A
D
C
v
B
v
A
v
D
v
C
v
v
v
v
c
P
P
P
P
D
C
K 

[B]
[A]
]
[
]
[

12. 12
• Equilibrium constant, Kp, and Gibbs free energy DG
A gas phase reaction vAA + vBB  vCC + vDD
– When at equilibrium, assuming all the gases follow the ideal gas law
at P=1 atm, DG°=S(viG°i)prod-S(viG°i)reac=0
and at any P(1) DG=S(viGi)prod-S(viGi)reac=0
– when reaction occurs at constant temperature (isothermal reaction)
dG=VdP-SdT dG=VdP dG=RTdP/P DG=RTln(P/P0)
– G° is defined at P0=1 atm, so that DG=G-G°=RTln(P/1) Gi=Gi°+RTlnPi
S(vi(G°i+RTln(PCPD))prod-S(vi (G°i+RTln(PAPB))reac=0
S(viG°i)prod-S(vi G°i)reac=-[S(viRTln(PCPD))prod-S(vi RTln(PAPB))reac]
– By definition:
Equilibrium Constant (2)
Chemical Reaction equilibrium





















D B
A
D
C
B
A
D
C
v
B
v
A
v
D
v
C
v
B
v
A
v
D
v
C
P
P
P
P
ln
RT
)
atm
/
P
(
)
atm
/
P
(
)
atm
/
P
(
)
atm
/
P
(
ln
RT
G
p
K
RT
G ln



D









B
A
D
C
v
B
v
A
v
D
v
C
p
P
P
P
P
K
T=const PV=RT intergration

13. 17 March 2023 PHYSICAL CHEMISTRY 13
Free Energy and Chemical Equilibrium
DG = DG0 + RT lnQ
R is the gas constant (8.314 J/K•mol)
T is the absolute temperature (K)
Q is the reaction quotient
At Equilibrium
DG = 0 Q = K
0 = DG0 + RT lnK
DG0 =  RT lnK

14. 14
• Equilibrium constant, Kc, and Gibbs free energy DG
– Ideal solution (liquid and solid)
Raoult’s law Pi=xiPi* or xi=Pi / Pi* where
thus for a solution we can also write Gi=(Gi°+RTln xi) (compare to gas Gi=Gi°+RTlnPi)
which lead to, in a similar way, the relation between DG and Kc,
• Summary of G calculation for ideal gas and solution
– For a pure substance at const T & P, G=G°+RTlnP (1)
– For a mixture of ideal gas at const T and P G =SGi=S(Gi°+RTln Pi) (2-1)
– For a mixture of ideal solution at const T and P G =SGi=S(Gi°+RTln xi) (2-2)
 For a situation that a mixture (gas or solution) under concern is not ideal, the Pi or xi cannot be
related to G by expressions (2-1) & (2-2). How do you calculate G?
Equilibrium Constant (3)
Chemical Reaction equilibrium
Pi - vapour pressure of component i
xi - mole fraction of component i in solution
Pi* - equil. vapour pressure of pure component i
B
A
D
C
B
A
D
C
B
A
D
C
v
v
v
v
v
v
v
v
v
B
v
A
v
D
v
C
K
K
RT
RT
x
x
x
x
RT
G
[B]
[A]
[D]
[C]
where
)
ln(
[B]
[A]
[D]
[C]
ln
ln c
c 























D

15. Delta G is mainly influenced by G0. If G0 is very
negative, G will be too. When this happens, the
reaction favors the formation of products.
According to le chatlier’s principle, RT lnQ will then
slowly become positive and equal in magnitude to G.
This will cause the reaction to move to equilibrium.
This also happens when G is very positive. lnQ will
cause the reaction to move towards equilibrium
again.
K= equilibrium constant
17 March 2023 PH 101: PHYSICAL CHEMISTRY 15

16. Free Energy and Chemical Equilibrium
17 March 2023 PH 101: PHYSICAL CHEMISTRY 16

17. Free Energy and Chemical Equilibrium
17 March 2023 PH 101: PHYSICAL CHEMISTRY 17

18. Free Energy and Chemical Equilibrium
17 March 2023 PH 101: PHYSICAL CHEMISTRY 18

19. …..Ending
Thanks for your attention!
17 March 2023 PH 101: PHYSICAL CHEMISTRY 19