Cell Potential and Free Energy

Contributed by:
Jonathan James
The highlights are:
1. Oxidation and Reduction
2. Half reduction method
3. Electrochemistry
4. Voltaic cells
5. Cell potential
6. Electrochemical cells
7. Electroplating
8. Thermochemistry and Electrochemistry connection
1. Chapter 18
Electrochemistry
In electrochemical reactions, electrons
are transferred from one species to
Electrochemistry
2. Oxidation Numbers
Assigning oxidation
numbers to all
species allows us to
keep track of the
electrons lost or
gained.
Electrochemistry
3. Assigning Oxidation Numbers
1. Elements in their elemental form are given a zero.
2. Monatomic ions are the same as their charge.
3. Nonmetals tend to have negative oxidation
numbers, although there are some exceptions:
 Oxygen has an oxidation number of −2, except in
peroxide where it has a −1.
 Hydrogen is −1 when bonded to a metal, +1 when
bonded to a nonmetal
Electrochemistry
4. 4. In a neutral compound the sum of the ox #s is zero..
5. In a polyatomic ion is the sum of the ox #s is the
charge on the ion.
6. Nonmetals tend to have negative oxidation numbers,
although some are positive in certain compounds or
ions.
 Fluorine always has an oxidation number of −1.
 Halogens unless bonded to oxygen in a polyatomic ion.
 ClO3 - , the chlorine is a +5
Electrochemistry
5. Oxidation and Reduction
• A species is oxidized when it loses electrons.
 Here, zinc loses two electrons to go from neutral
zinc metal to the Zn2+ ion.
Electrochemistry
6. Oxidation and Reduction
• A species is reduced when it gains electrons.
 Here, each of the H+ gains an electron and they
combine to form H2.
Electrochemistry
7. Balancing Oxidation-Reduction Equations
(Half-Reaction Method)
The oxidation and reduction are treated as two separate processes.
Each one is balanced separately and then combined to balance the
overall reaction.
1. Assign oxidation numbers to determine what is oxidized and
what is reduced.
2. Write the oxidation and reduction half-reactions.
3. Balance the elements in each half reaction leaving the O
and H for last.
 Balance O by adding H2O
 Balance H by adding H+
 Balance charge by adding electrons
Electrochemistry
8. 4. Multiply the half-reactions by integers so that the electrons
gained and lost are the same.
5. Add the half-reactions, subtracting things that appear on
both sides.
6. Balance for both mass and charge.
Practice problem:
Permanganate ion(MnO4−) and oxalate ion(C2O42−)
MnO4−(aq) + C2O42−(aq) Mn2+(aq) + CO2(aq)
Electrochemistry
9. #1.) assign oxidation numbers and determine what is reduced and
what is oxidized
+7 +3 +2 +4
MnO4− + C2O42-  Mn2+ + CO2
Manganese goes from +7 to +2, it is reduced.
Carbon goes from +3 to +4, it is oxidized.
Electrochemistry
10. #2.) write out the half reactions and balance each one
Oxidation ½ rxn
C2O42−  CO2
• To balance the carbon, add a coefficient of 2 and that
also balanced the oxygen.
C2O42−  2 CO2
• To balance the charge, add 2 electrons to the right side
C2O42−  2 CO2 + 2 e−
Electrochemistry
11. Reduction ½ rxn
MnO4−  Mn2+
• Manganese is balanced.
• To balance the oxygen, add 4 waters to the right side.
MnO4−  Mn2+ + 4 H2O
• To balance the hydrogen, we add 8 H+ to the left side.
8 H+ + MnO4−  Mn2+ + 4 H2O
• To balance the charge, we add 5 e− to the left side.
5 e− + 8 H+ + MnO4−  Mn2+ + 4 H2O
Electrochemistry
12. Add the Half-Reactions
Balance for both mass and charge
C2O42−  2 CO2 + 2 e−
5 e− + 8 H+ + MnO4−  Mn2+ + 4 H2O
Balance charge, by multiplying the first reaction by 5 and the
second by 2 and then add them together.
10 e− + 16 H+ + 2 MnO4− + 5 C2O42− 
2 Mn2+ + 8 H2O + 10 CO2 +10 e−
Subtract anything that appears on both sides of the equation.
In this case it is the electrons.
16 H+ + 2 MnO4− + 5 C2O42− 2 Mn2+ + 8 H2O + 10 CO2 Electrochemistry
13. • The study of chemical reactions that produce
electricity, and chemical reactions that occur due
to electricity.
• There are many processes that take place
because of electrochemical rxns:
 Electroplating
 Electrolysis of water
 Production of aluminum metal
 Storage of electricity in batteries
Electrochemistry
14. Direct Electron Transfer
• In (redox) reactions,
electrons are
transferred and energy
is released.
• Cu gains e- and Zn
loses e-
• This type of transfer
doesn’t allow for any
useful work to be done
by the electrons.
Electrochemistry
15. • We can use the energy from
the transfer of electrons to do
work if we make the electrons
flow through an external
device.
• It provides power to do work.
• We call such a setup :
 Voltaic cell
 Battery
 Electrochemical cell
 Galvanic cell
Electrochemistry
16. Cells
• The oxidation occurs at the ANODE.
• The reduction occurs at the CATHODE.
• Electrons flow through the wire!
Electrochemistry
17. VOLTAIC CELLS
• Once even one electron flows from the anode to the
cathode, the charges(ions) in each beaker would not be
balanced and the flow of electrons would stop.
• Therefore, we use a salt bridge, usually a U-shaped tube
that contains a salt solution, to keep the charges balanced.
Only ions flow through the salt bridge!
 Cations move toward the CATHODE.
 Anions move toward the ANODE
Electrochemistry
18. • In the cell, electrons
leave the anode and
flow through the wire to
the cathode.
• As the electrons leave
the anode, the cations
formed dissolve into the
solution in the anode
compartment.
• The ANODE will
DECREASE IN SIZE
Electrochemistry
19. • As the electrons reach
the cathode, cations in
the cathode
compartment are
attracted to the now
negative cathode.
• The metal is deposited
on the cathode.
• THE CATHODE WILL
INCREASE IN SIZE.
Electrochemistry
20. CELL POTENTIAL
• The potential difference between the anode and cathode in a cell is called the cell potential, and is designated Ecell.
• It is a measure of the driving force of the redox reaction taking place in the cell.
• Cell potential is measured in volts (V).
J
1V=1
C
Electrochemistry
21. Standard Reduction Potentials
The species
with the more
positive (V)
will be
The species
lowest on the
table, and the
more negative
(V) will be Electrochemistry
22. Standard Cell Potentials
The cell potential at standard conditions can be found by
looking up the reduction potentials for each half reaction on a
table.
The standard cell potentials (net E0) of all galvanic cells
have positive values and happen spontaneously.
The oxidation half reaction will be reversed from how it
appears on the table, and the value of it’s voltage will
have a reversed sign too.
Electrochemistry
23. Cell Potentials
Ean = +0.76 V
Ecat = +0.34 V
= +0.34 V +0.76 V
= +1.10 V Electrochemistry
24. Cell Notation
25. Special Electrochemical Cell
• A metal–air electrochemical cell is a portable
electrochemical cell that uses an anode made from pure
metal and an external porous cathode that lets in oxygen
from the air, typically with an aqueous electrolyte paste.
• The big advantage here
is that you only need to
store the metal (anode)
in the battery because
the oxygen comes from
the air.
• You get a battery that is
compact and lasts
longer. Electrochemistry
26. Metal-Air ElectrochemicalCell
• It works by oxidation of
the metal at the anode
and reduction of oxygen
at the cathode to create a
current flow of electrons.
• The anode is made from
a pure metal such as
Lithium and the external
cathode is made of the
ambient air.
• An aqueous electrolyte
exists between the them.
Electrochemistry
27. Electrolytic Cells
Electrochemistry
28. Electrolytic Cells
• An electrolytic cell is an
electrochemical cell that
drives a non-spontaneous
redox reaction through an
electric current supplied by
an external source.
• They are often used to
decompose chemical
compounds, in a process
called electrolysis—the Greek
word lysis means to break up.
Electrochemistry
29. •Electrolysis of water is the
decomposition of water into oxygen
and hydrogen gas due to the
passage of an electric current.
•The reaction has a standard
potential of −1.23 V, meaning it
ideally requires a potential
difference of 1.23 volts to
split water.
•In a non-spontaneous reaction the
E0net is always less than zero.
Electrochemistry
30. Electroplating is a procedure
that uses electrolysis to apply a
thin layer of a metal over the
surface of another metal.
Electrochemistry
31. • In electroplating, the anode is made up of the
metal you want to use to coat the surface of
another metal.
• A salt solution containing the metal that makes
up the anode is used. During electrolysis, the
anode metal is oxidized and goes into solution
as positive ions.
• These positive ions are then reduced on the
surface of the cathode (the metal you are
coating)
Electrochemistry
32. Quantitative Electrochemistry
ELECTRIC CURRENT
•Electric Current is the rate of flow of Electric charges
•The SI unit of Electric Current is Ampere (A).
I = Q/T
• I = Electric current in amperes,
• Q = Amount of charge in coulombs,
• T = Time in seconds.
Electrochemistry
33. Thermochemistry and
Electrochemistry Connection
∆G Gibb’s Free Energy
n number of electrons transferred
F Faraday constant
(96,500 C/mol or J/C)
E potential difference (V)
 E is (+) then rxn is spontaneous
 E is(-) then rxn is not spontaneous
Electrochemistry
34. Practice Problem:
If the standard cell potential at 298 K is 1.10 V for the
following reaction Zn(s) + Cu2+(aq)  Zn2+(aq) + Cu(s), then what
is the change in Gibbs Free Energy?
Electrochemistry
35. Gibbs Free Energy and Equilibrium
They can be used to together to
ΔG° = - RT lnK
find E(V)
The equilibrium constant for the reaction below is 1.8 × 1019 at 298K.
What is the value of the standard cell potential for this reaction?
Ni(s) + Hg2Cl2(s)  2Hg(l) + 2Cl-(aq) + Ni2+(aq)
ΔG = -RT ln K
= - (8.314 J K-1 mol-1) (298 K) ln (1.8 × 1019)
= - 109847.8 J mol-1
= - 1.098 × 105 J mol-1
E= -ΔG°
nF
= -(-1.098 × 105 J mol-1)
(2 mol) (96500 C)
Electrochemistry
= 0.57 J/C
36. Relationships between ∆G◦, K , E ◦ cell
This one is not
on the
equation sheet
but it can be
derived by
setting the
other two
equations
equal to one
another and
simplifying.
Electrochemistry
37.