Lecture 10 Activity of chemical components.
Review



Notion of chemical potential
Notion of activity
Notion of reference state
Activity of ionic species

Debye-Huckel Model

Application to chemical equilibrium
Temperature dependence of reaction constants
Galvanic cells
Relation of equilibrium free energy change to reaction
constant
N 2  3H 2  2 NH 3
G  2  NH 3   N 2  3 H 2
u sin g
 Pi 

 1atm 
 i   i 0  RT ln 
2
  PNH
 G  G  RT ln  1 33
  PN 2 PH 2
at equilibriu m
0
  P2
NH
0
G   RT ln  1 33
  PN 2 PH 2





eq

 where G 0  2 0 NH 3   0 N 2  3 0 H 2




   RT ln( K )


This can be used to calculate the free energy change at
arbitrary concentration of reactant and products.
2
  PNH

G  G  RT ln  1 33 
  PN 2 PH 2 
2
  PNH
  RT ln( K )  RT ln  1 33
  PN 2 PH 2
 RT ln( Q / K )
0
2

 PNH
3
 denoting Q  
1

 PN PH3

 2 2





Ionic Solutes
Activity can be thought of as a measure of an effective
concentration in solution. Thus, if the solute has
tendency to associate in solution then it’s effective
concentration would be lower leading to activity
coefficient that is less than unity.
Similar situation arises with ionic species. Consider a
solution of NaCl in water; we know that the salt will
dissociate yielding Na+ cations and Cl- anions. Since the
oppositely charged species attract, cations will attract
anions and vice versa. In doing so they effectively shield
their charge. Thus apparent concentration in the
solution will be reduced. This effect was analyzed by
Debye-Huckel in 1922. Their model allows us to
calculate the activity coefficients of ions in dilute
solution. Since anions and cations are always present
stochiometrically, to maintain charge neutrality, they
defined geometrically averaged activity coefficient as
follows.
C M AN  mC  N  nA  M
    
m


1
n m n

so for NaCl, or ZnSO4
    
1


1
1 2

but for BaCl 2 orAlCl 3
  ( BaCl 2 )   
1


1
2 3


and   ( AlCl3 )   
1


1
3 4

Debye-Huckel model for activity coefficients
The result of complex calculation yields an analytical
expressions for the activity coefficients of ions in dilute
aqueous solution:
log(  i )  0.509Z i2 I 1 / 2
 i  10
I
 0.509Z i2 I 1 / 2
1
2
c
Z
i i
2 i
where Z is the charge on the ion and I is called as net
ionic strength, ci is the concentration of the i th ion. The
factor –0.0509 depends on the solvent dielectric constant
and temperature.
Thus we can see that Debye model predicts a reduction
in activity coefficients.
(1) Higher the charge, lower the activity coefficient.
(2) Higher the ionic strength. lower is the activity
coefficient.
This is one of the few instances where we have been able
to calculate the coefficients explicitly and analytically.
The model is valid only in the limit of dilute solution. In
general we do not know to calculate the activity
coefficients explicitly for other interactions such as
hydrogen boding or hydrophobic. Thus a common
practice is to set activity coefficients equal to one,
implying validity in only dilute solutions.
Importance of activity coefficients
Consider following simple dissociation reaction of acetic
acid in aqueous solution. Since it is weak acid we can
write its dissociation as a reversible chemical reaction.
CH 3 COOH  CH 3 COO   H 
K eq

a

CH 3COO 
aH 
aCH 3COOH
 c
CH 3COO 
c H   CH COO   H 
3
.
cCH 3COOH
 CH COOH
3
dilute solution :
K
c
eq

cCH COO  c H 
3
cCH 3COOH
mod erately concentrated solution
K eq
cCH COO  c H   CH COO   H 
cCH COO  c H     
3
3
3

.
debye mod el 
.
cCH 3COOH
 CH 3COOH
cCH 3COOH
1
K eq
cCH COO  c H      cCH COO  c H   2 
3
3

.

.
cCH 3COOH
1
cCH 3COOH
1
Since it is like 1:1 salt, the solution activity coefficient is
less than one. Hence the apparent rate constant is
modified and it is lesser than the one measured in very
dilute solution. For example in 0.1 molar solutions it
could differ by factor of three. Similarly, if we were to
consider the effect of added electrolyte like Na Acetate,
we can recalculate the activity coefficient using Debye
model.
Effect of temperature on the equilibrium rate constant
We know the temperature dependence of ΔG, at
constant pressure, from Gibbs Helmholtz relationship.
In addition, when a reaction is at equilibrium, we have
shown that the Gibb’s free energy is related to Reaction
constant. We may then combine both the equations to
obtain a relationship between temperature and K,
Known as Van’t Hoff relation as follows:
d (G / T ) 1 dG G S G ST  G
H

 2   2 
 2
2
dT
T dT T
T T
T
T
dT
however d (1 / T )   2
T
d (G / T )
 H  for G in chemical reaction
d (1 / T )
G (T2 ) G (T1 ) 2

  Hd (1 / T )
T2
T1
T1
T
G (T1 ) 2 HdT


assu min g H to be T indpendent
2
T1
T
T1
T

1 1
G (T1 )
 H   
T1
 T2 T1 
However
G (T )   RT ln K eq (T )
1 1
  R ln( K eq (T2 ))   R ln( K eq (T1 ))  H   
 T2 T1 
K 
H  1 1 
ln  2   
  
K
R
 1
 T2 T1 
This relation describes effect of temperature on the
equilibrium reaction rate constant.
Galvanic Cells
History of electrochemistry goes to the middle 19th century.
Pioneering work of Faraday established the connection
between chemical reactions and electron transfer processes.
The basic idea is that the Gibb’s free energy is a measure of
reversible work that system can do. In the context of
electrochemistry, we are concerned with electrical work.
w  E.I .t
dQ
But I 
 dw  E.i.dt
dt
wrev  E  i.dt  EQ
G  w  Q.E
Where E is the voltage, also referred as electromotive
force; and I is the current. Faraday discovered that for a
chemical reaction involving n electron transfer process:
Q  nF
Where F is constant, equal to 96.485kJ/mol. Thus overall
free energy change:
G  w  Q.E  nFE
Thus, by measuring maximum electrical voltage we can
determine the free energy change involved in a reaction.
Furthermore,
G  nFE
E
 G 

  S  nF
T
 T  P
E 

H  G  TS  nF   E  T


T

