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Calculating Cell Potentials
Definitions
• Cell Potential: The voltage that can be
generated when two compounds are
brought together, with one oxidizing and
the other being reduced.
• Voltage: The energy per electron. Strictly
speaking, it is the energy (Joules) per
coloumb (6 x 1018) positive charge.
Reduction Potential
• When an atom gains an electron, there is a
change in energy. This can be measured on an
absolute scale and is referred to as electron
affinity. It is measured in kJ/mole of atoms
• In reduction-oxidation reactions, chemists have
found it much more useful to measure the
energy change of the electrons. So they use a
scale of electron volts (eV).
Standard Reduction Potential
• Since there can never be a reduction
without an oxidation, the easiest way to
calculate energy change in redox reaction
is with a relative scale.
• The scale compares how every atom or
ion will reduce relative to a common atom.
• The common atom was (because it is very
common and very simple) chosen to be
hydrogen.
Reduction of Atoms and Ions with
Hydrogen
• All Atoms are
REDUCED and
H2 is Oxidized
• H2 – 2e AND
Zn02+
S2-
0 ++2e
2- 00
Cu
Zn
S2+
2e
SCu
Zn
2e
2e
2e
0
Cu2+
2H
H2+
Standard Reduction Potential
• Each Reduction has a
certain energy change
• The energy released
is the difference
between hydrogen
being oxidized and the
other element being
reduced
Zn2+ + 2e  Zn0
E0 = -0.76 volts
Zn02+
2e
2H
H2+
Standard Reduction Potential
• Some atoms and ions are
less active than hydrogen
• They hold onto electrons
more strongly, and so are
easier to reduce
• They have a positive
reduction potential
2H
H2+
Cu2+ + 2e  Cu0
E0
2e
= +0.34 volts
0
Cu2+
Oxidation Potential
• Oxidation is the exact
opposite of reduction
• The energy released is
the difference between
hydrogen being
reduced and the other
element being oxidized
• The potential is the
same value, but
opposite in sign
Zn0  Zn2+ + 2e
E0 = +0.76 volts
0
Zn2+
2e
2H
H2+
Potential Difference between two
Elements
• The easiest way to
calculate the potential
between any two
elements is to think of
them going through
hydrogen
• The zinc is oxidized
• The copper is reduced
Zn0  Zn2+ + 2e
Cu2+ + 2e  Cu0
0
Zn2+
2e
2H
H+2
2e
0
Cu2+
Calculating Potential Difference
• The calculation
0
Zn2+
becomes simple
• The difference
between any two
elements equals
• the reduction of one
and the oxidation of
the other
Ecell = Ered + Eox
0
Cu2+
=
H2
Calculating Cell Potential
• To keep it a bit more consistent with other
work:
Ecell = Ered + Eox
is translated to :
Ecell = Ered (of reduced) – Ered (of oxidized)
– So….
Calculating Potential Difference
• The calculation:
0
Zn2+
Zn0  Zn2+ + 2e
+0.76 (Oxidation)
E0 = -0.76 volts
Cu2+ + 2e  Cu0
E0
= +0.34 volts
1.10
H2
Ecell = Ered - Ered
1.10 =
0.34 (Reduction)
0.34 - (-0.76)
0
Cu2+
Positive Potential Difference
• If the Cell Potential Difference (Voltage) is
positive
– The reaction is spontaneous. The reaction, as
written, will happen by itself
– It releases energy
– These happen in voltaic cells
– It is the same as a negative DG
(The sign is reversed because voltage is
measured for positive charges and electrons
are negative.)
Negative Potential Difference
• If the Cell Potential Difference (Voltage) is
negative
– The reaction is not spontaneous.The
reaction, as written, will not happen by itself
– These happen in electrolytic cells
– It absorbs energy
– It is the same as a positive DG
(The sign is reversed because voltage is
measured for positive charges and electrons
are negative.)
Spontaneous Redox
• Batteries
• Rusting
Non-Spontaneous
• Electroplating (Zinc and silver plating)
• Purifying pure elements
• Rechargeable Batteries