Idea:
Develops the concept of chemical potential
and shows how it can be used to account for
the equilibrium composition of chemical
reaction.
Thermodynamic
formulations
Equilibrium composition
under any reaction
conditions
“dynamic equilibrium” -- a chemical reaction
moves toward a dynamic equilibrium in which
both reactants and products are present but have
no further tendency to undergo net change.
“spontaneous chemical reaction” -- the
direction of spontaneous change at constant
temperature and pressure is towards lower
values of the Gibbs energy G,
“equilibrium” =,The Gibbs energy minimum”
A? B
isomerization,pentane to 2-methylbutane
conversion,L-alanine to D-alaninee.g.,
–d? +d?
dnA = –d? dnB = +d?
“the extent of reaction”
“the reaction Gibbs energy” -- is defined as
the slope of the graph of the Gibbs energy
plotted against the extent of reaction
,
r
PT
G
G
difference vs,derivative?
A proof:
A reaction advances by d?,the change in G is:
dG =?AdnA +?BdnB
= –?Ad? +?Bd?
= (?B –?A)d?
,
BA
PT
r B A
G
G
Chemical potentials vary with composition,?rG changes as
the reaction proceeds;
The reaction runs in the direction of decreasing G
A >?B,the reaction A?B is spontaneous
B >?A,the reaction B?A is spontaneous
A =?B,neither direction,?rG = 0
Extent of reaction,?
Gibbs
en
erg
y,
G?
rG < 0
rG > 0
rG = 0
rG < 0,the forward reaction is spontaneous,called
“exergonic” (work producing)
rG > 0,the reverse reaction is spontaneous,called
“endergonic” (work consuming,e.g.,eletrolysing
water to H2 and O2)
rG = 0,reaction at equilibrium,neither exergonic
nor endergonic
Perfect Gas Equilibria
l n l n
ln
ln
r B A
B B A A
B
r
A
r
G
R T P R T P
P
G R T
P
G R T Q
“reaction quotient”
0,pure A
,pure B
The Standard Reaction Gibbs Energy,?rG?
Like the standard reaction enthalpy,defined as the
difference in the standard molar Gibbs energies of the
reactants and products.
,,r B m A m
f B f A
G G G
GG
At equilibrium,?rG = 0,
0 =?rG? + RT ln K
RT ln K = –?rG?
K = (PB/PA)equilibrium
tables of
thermodynamic
data
equilibrium
constant
Molecular interpretation
The minimum in the Gibbs energy,which corresponds
to?rG = 0,stems from the Gibbs energy of mixing of
two gases,namely,reactants and products.
G w/o mixing
mixing
Recall:
mixG =
nRT (xA ln xA + xB ln xB)
The General Case of a reaction
generalized extent of reaction,J = vJ
Illustration,N2(g) + 3H2(g)? 2NH3(g)
ln
r J f J
J
rr
G v G
G G RT Q
ac t i v i t i e s of pr od uc t s
Q
ac t i v i t i e s of re ac t an t s
Jv
J
J
Qa
Jv
J
J e q u ilib r iu m
Ka
- RT ln K =?rG?
Examples,calculate K
1,Calculate the equilibrium constant for the ammonia synthesis
reaction at 298 K,and show how K is related to the partial
pressures of the species at equilibrium when the overall pressure
is low enough for the gases to be treated as perfect,?fG?(NH3,g)
= –16.5 kJ/mol.
2,The standard Gibbs energy of reaction for the dissociation
H2O(g)? H2(g) + 1/2 O2(g) is +118.08 kJ/mol at 2300 K,What
is the degree of dissociation of H2O at 2300 K and 1 atm?
Answer,K = 6.0?10?5
Answer,~ 2 per cent.
The response of equilibria to the
conditions
K is unaffected by the presence of a
catalyst or an enzyme.
K is independent of the pressure at which
the equilibrium is actually established.
but does not mean that the equilibrium composition is
independent of the pressure.
increasing pressure:
1,adding inert gas,
2,compressing the gases
this addition of gas leaves all the partial pressures of the
reacting gases unchanged,that is,leaves the molar
concentrations of the original gases unchanged,means no
effect on the equilibrium composition of the system.
partial pressure changes,equilibrium moves,but the
ratio keeps constant.
The reaction responds by
reducing the number of
molecules in the gas
phases (e.g.,producing
the dimers)
N2O4? 2NO2
What is the extent of
dissociation of N2O4?
Answer,
1
1 4 /PK
The response of equilibria to temperatures
Measuring reaction enthalpy,..,..
Application:
2
ln
ln
( 1 / )
r
r
HdK
d T R T
HdK
d T R
Example:
Ag2CO3(s)? Ag2O(s) + CO2(g)
T/K 350 400 450 500
K 3.98E-4 1.41E-2 0.186 1.48
Answer,?rH? = + 79 kJ/mol
“aqueous solution”
pH = – log a(H3O+)
Acid-base equilibria in water
A Base in water:
Example,HCN
Calculate the pH of 0.2 M
HCN(aq),pKa = 9.31 Answer,pH=5.0
Acid-base Titrations
Develops the concept of chemical potential
and shows how it can be used to account for
the equilibrium composition of chemical
reaction.
Thermodynamic
formulations
Equilibrium composition
under any reaction
conditions
“dynamic equilibrium” -- a chemical reaction
moves toward a dynamic equilibrium in which
both reactants and products are present but have
no further tendency to undergo net change.
“spontaneous chemical reaction” -- the
direction of spontaneous change at constant
temperature and pressure is towards lower
values of the Gibbs energy G,
“equilibrium” =,The Gibbs energy minimum”
A? B
isomerization,pentane to 2-methylbutane
conversion,L-alanine to D-alaninee.g.,
–d? +d?
dnA = –d? dnB = +d?
“the extent of reaction”
“the reaction Gibbs energy” -- is defined as
the slope of the graph of the Gibbs energy
plotted against the extent of reaction
,
r
PT
G
G
difference vs,derivative?
A proof:
A reaction advances by d?,the change in G is:
dG =?AdnA +?BdnB
= –?Ad? +?Bd?
= (?B –?A)d?
,
BA
PT
r B A
G
G
Chemical potentials vary with composition,?rG changes as
the reaction proceeds;
The reaction runs in the direction of decreasing G
A >?B,the reaction A?B is spontaneous
B >?A,the reaction B?A is spontaneous
A =?B,neither direction,?rG = 0
Extent of reaction,?
Gibbs
en
erg
y,
G?
rG < 0
rG > 0
rG = 0
rG < 0,the forward reaction is spontaneous,called
“exergonic” (work producing)
rG > 0,the reverse reaction is spontaneous,called
“endergonic” (work consuming,e.g.,eletrolysing
water to H2 and O2)
rG = 0,reaction at equilibrium,neither exergonic
nor endergonic
Perfect Gas Equilibria
l n l n
ln
ln
r B A
B B A A
B
r
A
r
G
R T P R T P
P
G R T
P
G R T Q
“reaction quotient”
0,pure A
,pure B
The Standard Reaction Gibbs Energy,?rG?
Like the standard reaction enthalpy,defined as the
difference in the standard molar Gibbs energies of the
reactants and products.
,,r B m A m
f B f A
G G G
GG
At equilibrium,?rG = 0,
0 =?rG? + RT ln K
RT ln K = –?rG?
K = (PB/PA)equilibrium
tables of
thermodynamic
data
equilibrium
constant
Molecular interpretation
The minimum in the Gibbs energy,which corresponds
to?rG = 0,stems from the Gibbs energy of mixing of
two gases,namely,reactants and products.
G w/o mixing
mixing
Recall:
mixG =
nRT (xA ln xA + xB ln xB)
The General Case of a reaction
generalized extent of reaction,J = vJ
Illustration,N2(g) + 3H2(g)? 2NH3(g)
ln
r J f J
J
rr
G v G
G G RT Q
ac t i v i t i e s of pr od uc t s
Q
ac t i v i t i e s of re ac t an t s
Jv
J
J
Qa
Jv
J
J e q u ilib r iu m
Ka
- RT ln K =?rG?
Examples,calculate K
1,Calculate the equilibrium constant for the ammonia synthesis
reaction at 298 K,and show how K is related to the partial
pressures of the species at equilibrium when the overall pressure
is low enough for the gases to be treated as perfect,?fG?(NH3,g)
= –16.5 kJ/mol.
2,The standard Gibbs energy of reaction for the dissociation
H2O(g)? H2(g) + 1/2 O2(g) is +118.08 kJ/mol at 2300 K,What
is the degree of dissociation of H2O at 2300 K and 1 atm?
Answer,K = 6.0?10?5
Answer,~ 2 per cent.
The response of equilibria to the
conditions
K is unaffected by the presence of a
catalyst or an enzyme.
K is independent of the pressure at which
the equilibrium is actually established.
but does not mean that the equilibrium composition is
independent of the pressure.
increasing pressure:
1,adding inert gas,
2,compressing the gases
this addition of gas leaves all the partial pressures of the
reacting gases unchanged,that is,leaves the molar
concentrations of the original gases unchanged,means no
effect on the equilibrium composition of the system.
partial pressure changes,equilibrium moves,but the
ratio keeps constant.
The reaction responds by
reducing the number of
molecules in the gas
phases (e.g.,producing
the dimers)
N2O4? 2NO2
What is the extent of
dissociation of N2O4?
Answer,
1
1 4 /PK
The response of equilibria to temperatures
Measuring reaction enthalpy,..,..
Application:
2
ln
ln
( 1 / )
r
r
HdK
d T R T
HdK
d T R
Example:
Ag2CO3(s)? Ag2O(s) + CO2(g)
T/K 350 400 450 500
K 3.98E-4 1.41E-2 0.186 1.48
Answer,?rH? = + 79 kJ/mol
“aqueous solution”
pH = – log a(H3O+)
Acid-base equilibria in water
A Base in water:
Example,HCN
Calculate the pH of 0.2 M
HCN(aq),pKa = 9.31 Answer,pH=5.0
Acid-base Titrations
