ELECTROCHEMISTRY - Wits Structural Chemistry

w max = ∆G
Before Equilibrium
The Cell Potential
Consider a galvanic cell reaction:
The cell can do electrical work by driving
e − ’s through the external circuit.
The larger the potential difference between the
two electrodes, the more work can be done by
each e−.
Measure E cell by applying an opposing
potential s.t. the reaction occurs reversibly
and the composition is constant (no nett
current flows).
∆G = −nFE cell
for electrical work for a
reversible reaction
At Equilibrium
No more work can be done
E cell = 0 V
The composition in electrode compartment is expressed by:
the reaction quotient, Q
the equilibrium constant, K
Derive Nernst equation:
RT
E = E
o − ln Q
nF
Applies to:
∆G = −nFE
Half-reactions
RT
E
nF
and
Cells
RT
nF
o
o
= Ered
− lnQred
E = Ecell
− lnQrxn
Half-cell reaction written as a
reduction reaction.
Nernst Equation
o
∆G
= ∆G
+ RT ln Q
2.303 RT
E = E
o − log Q
nF
E
o
cell
= E
o
cathode
− E
o
anode
NOTE: E o used in the calculations are always for the reduction reactions.
loge
x
log x =
10
loge
10
2 .303 log x = ln x
0.05916
E = E
o − log Q at 25°C
n
E o = standard cell potential all reactants and products in their standard states,
thus all activities = 1
∆G = −nFE
Do Self-test 6.7
Standard Reduction Potentials in H 2 O at 25 o C
The cell reaction is spontaneous
if E cell > 0
At equilibrium:
∆G = 0 E cell = 0 and Q = K
Strong oxidising
agent
Gibbs free energy, G
∆G < 0
E > 0
∆G = 0
E = 0
∆G > 0
E < 0
RT
E = E
− lnQ
nF
RT
0 E − lnK
nF
= nF
ln K = E
RT
E > 0
spontaneous
reduction
reactants
Extent of reaction
products
The steeper the slope, the greater
the driving power of the cell.
Recall:
∆G°= –RT ln K
∆G°= –nFE°
E < 0 nonspontaneous
reduction
Strong reducing
agent
Example 1
Consider the Daniell cell:
Using the standard reduction potentials, calculate the equilibrium constant at 25 °C.
Standard reduction potentials at 25 °C:
Cu 2+ + 2e - → Cu(s)
Zn 2+ + 2e - → Zn(s)
Zn(s)
ZnSO 4 (aq) CuSO 4 (aq) Cu(s)
E o = +0.34 V
E o = −0.76 V
Do Self-test 6.8
Metal/metal ion:
e.g. Zn(s) in zinc ion solution
M(s) | M n+ (aq)
Metal-insoluble salt: M(s) | MX(s) | X - (aq)
e.g. silver-silver chloride electrode
−
Ag(s)
AgCl(s) Cl (aCl)
AgCl(s) + e - Ag(s) + Cl - (aq)
Inert electrode: Pt(s) | M n+ (aq), M p+ (aq)
e.g. Pt immersed in a solution containing a redox couple
4 + 3+
Pt(s) Ce (aq),Ce (aq)
Ce 4+ + e - Ce 3+
o RT a
E = E − ln
F a
Gas electrode:
Zn 2+ + 2e - Zn(s)
Pt(s) | X 2 (g) | X +/− (aq)
e.g. a standard hydrogen electrode
+
Pt(s)
H2(g)
H (aq)
2H + + 2e - H 2 (g)
Types of Electrodes
E
E
RT
2F
o
= E − ln
2+
RT
F
o
= E − ln a
−
Cl
RT
2F
1
a
p
3+
Ce
4+
Ce
o
H2
E = E − ln
2
a
Zn
+
H
2