Download Galvanic Cells

Lecture 11:
Review

Debye Huckel Theory

Galvanic Cells
Today

Galvanic Cells

Application of thermodynamics to biochemistry
o Thermodynamics of metabolism
o Biological Redox Reactions
o DNA formation
Galvanic Cells
Free energy associated with an electron transfer reaction
G  w  Q.E  nFE
Since ΔG depends on temperature, we can evaluate the entropy
and enthalpy associated with the process as follows:
G  nFE
E
 G 

  S  nF
T
 T  P
E 

H  G  TS  nF   E  T


T


A simplest example of electron transfer process is oxidationreduction. Consider following reduction process:
Li   e  Li
This process is thermodynamically not favored. We find the
electrical voltage at which this reaction can be driven is at
3.045Volts, which is termed as the reduction potential. Since
process does not occur spontaneously we assign a negative sign to
it. Table 4.1 depicts a series of reduction potentials. As in the
case of free energy change involved in chemical reactions, we can
use these potentials to determine the free energy involved in
chemical
oxidation/reduction.
Cu 2  2e  Cu 0
E 0  0.337
Zn 0  Zn 2  2e
 E 0  0.7628
Cu 2  Zn  Zn 2  Cu 0
ERe action  1.100V  G  nFE  212kJ
Thus, the reaction will take place spontaneously.
Galvanic Cells
Consider an example of pair of redox reactions coupled to
form an electrochemical cell. At one electrode H2 gas is
oxidized to yield H+ ions while at other electrode O2 gas is
reduced to provide OH- ion. Hydrogen gas gives its
electron to the electrode on the left and oxygen gas receives
this extra electron.
Thus, a voltage difference develops across the electrode,
which can be calculated using the net sum of the free
energy change involved in the reaction between hydrogen
and oxygen. The exact reverse of the process would involve
application of potential difference between the two
electrodes, sufficiently strong to cause an evolution H2 at
cathode and O2 at anode. The first is an example of battery
second is an example of electrolysis.
Concentration dependence of E
Following our usual prescription for concentration
dependence of Gibbs free energy, we can derive one of the
most famous equations in electrochemistry, the Nernst
equation.
G  G 0  RT ln Q
RT
E  E0 
ln Q u sin g G   nFE
nF
for
aA  bB  cC  dD
aCc aDd
RT  aCc aDd 
0
Q  a b E  E 
ln  a b 
a A aB
nF  a A aB 
for Cu / Zn reaction
1
1
1




a
a
a

2
RT
.
059
Cu
0
0
Zn
Zn  2
EE 
ln  1 1   E 
log  1 
nF  aCu
a
n
 2 Zn 
 aCu  2 

Here, I have set the activity of pure metals to unity and
converted ln to log. Thus, E measurements as a function of
Zn+2 and Cu+2 concentration will allow us to determine

E0 hence the reaction constant since



G 0  nFE 0  RT ln( K eq )
And from the slope we can determine n the number of
electrons transferred.
Conversely if we know n, E0, we can determine the
activity coefficients.
Thermodynamics of metabolism
As we have learned, the complete oxidation of glucose by
oxygen is a process involving G=-2878kJ/mole. However,
in biological systems the process is controlled
Step 1: If we were to calculate the G for the first step, in
absence of hydrolysis of ATP to form ADP, the reaction
would have positive G. Since
ATP  H 2O   ADP  Phosphate G  31kJ / M
So the reaction is made possible by coupling this hydrolysis
reaction with the glucose phosphorylation. This coupling
involves a use of hexokinase enzyme, which also speeds up
the rate of the reaction.
Step 2: Note that G for the conversion of glucose to
fructose phosphate is positive, yet the reaction is possible if
the concentration of the product is low:
G  G 0  RT ln Q
 [ fructose  P] 
G   RT ln K eq  RT ln 

[Glu cos e  P] 
Thus if the ratio is low, the ln term will make a negative
contribution to total G making it possible to synthesize
fructose-6-phosphate.
Step 3: Similar to Step 1.
Step 4: Here, we see that the reaction is bit more complex
in that two products are formed and can interconvert with
positive G. The fact that glyceraldehyde is consumed in
subsequent reactions drives its concentration to sufficiently
low levels; which makes the interconversion
thermodynamically favored. The overall process has G=80.6 kJ, implying a large chemical potential of glucose is
effectively trapped in puruvate and NADH. The latter can,
under conditions of high muscular energy demand, convert
pyruvate to lactate with release of –25kJ of free energy.
Biological Oxidation/Reduction processes
Consider following reactions involving reduction of
NAD(+).
Clearly, not a spontaneous process but driven by demand.
But oxidation of NADH can result in formation of ATP in
Mitochondria.
2 NADH  2H   O2  2 NAD   2H 2 O
However, the actual process of oxidation is complex
involving three membrane-bound proteins:
Step 2
Step 3.
DNA pairing
Binary interactions between nuclear base pairs
Ionic Effects Protein-Nucleic Acid Binding
The structure of DNA contains negatively charged
phosphate groups in its backbone. Na(+) ions in cells
partially neutralize this charge by binding to these
groups. Let the fraction of PO4 bound by Na ions be ψ
(For DNA it is 0.88). When a protein binds to the
nucleic acid, it replaces these bound counterions
(n/mole). Then we can write:
Hence by studying K(obs) as a function of Na ion
concentration allows a determination of n, the number
of PO4 groups on the DNA, the protein interacts with!