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Electromotive Force (EMF)
Skills to develop
- Explain electromotive force.
- Construct the reference hydrogen electrode and explain why it is a reference.
- Distinguish reduction potentials from oxidation potentials.
- Calculate the standard potential from the reduction potentials.
Electromotive Force (EMF)
The electromotive force (EMF) is the maximum potential difference
between two electrodes of a galvanic or voltaic cell. This quantity
is related to the tendency for an element, a compound or an ion to
acquire (i.e. gain) or release (loss) electrons. For example, the maximum
potential between Zn and Cu of a well known cell
Zn (s) | Zn2+ (1 M) || Cu2+ (1 M) | Cu (s)
has been measured to be 1.100 V. A concentration of 1 M in an ideal solution
is defined as the standard condition, and 1.100 V is thus the
standard electromotive force,
DEo, or
standard cell potential for the Zn-Cu galvanic cell.
The standard cell potential, DEo,
of the a galvanic cell can be evaluated from the
standard reduction potentials
of the two half cells Eo.
The reduction potentials are measured against the standard hydrogen
electrode (SHE):
Pt (s) | H2 (g, 1.0 atm) | H+ (1.0 M).
Its reduction potential or oxidation potential is defined to be exactly
zero.
The reduction potentials of all other half-cells measured in volts
against the SHE are the difference in electrical potential
energy per coulomb of charge.
Note that the unit for energy J = Coulomb volt, and the Gibbs free energy
G is the product of charge q and potential difference E:
G in J = q E in C V
for electric energy calculations.
Evaluating Standard Cell Potential DE°
of Galvanic Cells
A galvanic cell consists of two half-cells. The convention in writing
such a cell is to put
the (reduction) cathode on the right-hand side,
and the (oxidation) anode on the left-hand side.
For example, the cell
Pt | H2 | H+ || Zn2+ | Zn
consists of the oxidation and reduction reactions:
H2 = 2 e + 2 H+ . . . . anode (oxidation) reaction
Zn2+ + 2 e = Zn . . . . cathode (reduction) reaction
If the concentrations of H+ and Zn2+ ions are
1.0 M and the pressure of H2
is 1.0 atm, the voltage difference between the two electrodes would be
-0.763 V
(the Zn electrode being the negative electrode).
The conditions specified above are called the
standard conditions and the EMF so obtained is
the standard reduction potential.
Note that the above cell is in reverse order compared to that given
in many textbooks, but this arrangement gives the
standard reduction potentials directly, because the Zn half
cell is a reduction half-cell. The negative voltage indicates
that the reverse chemical reaction is spontaneous.
This corresponds to the fact that
Zn metal reacts with an acid to produce H2 gas.
As another example, the cell
Pt | H2 | H+ || Cu+ | Cu
consists of an oxidation and a reduction reaction:
H2 ® 2 e + 2 H+ . . . . anode reaction
Cu2+ + 2 e ® Cu . . . . cathode reaction
and the standard cell potential is 0.337 V. The positive potential indicates
a spontaneous reaction,
Cu2+ + H2 ® Cu + 2 H+
but the potential is so small that the reaction is too slow to be observed.
Example 1
What is the potential for the cell
Zn | Zn2+(1.0 M) || Cu2+(1.0 M) | Cu
Solution
From a table of
standard reduction potentials we have
the following values
Cu2+ + 2 e ® Cu . . . E° = 0.337 - - - (1)
Zn ® Zn2+ + 2 e . . . E* = 0.763 - - - (2)
Add (1) and (2) to yield
Zn + Cu2+ ® Zn2+ + Cu . . . DE° = E° + E* = 1.100 V
Note that E* is the oxidation standard potential, and E° is the reduction
standard potential, E* = - E°. The standard cell potential is represented
by dE°.
Discussion
The positive potential confirms your observation that zinc metal reacts
with cupric ions in solution to produce copper metal.
Example 2
What is the potential for the cell
Ag | Ag+(1.0 M) || Li+(1.0 M) | Li
Solution
From the table of standard reduction potentials, you find
Li+ + e ® Li . . . E° = -3.045, - - - (3)
Ag = Ag+ + e . . . E* ® -0.799, - - - (4)
According to the convention of the cell, the reduction reaction is on the
right. The cell on your left-hand side is an oxidation process. Thus, you
add (4) and (3) to obtain
Li+ + Ag ® Ag+ + Li . . . dE° = -3.844 V
Discussion
The negative potential indicates that the reverse reaction should be
spontaneous.
Some calculators use a lithium battery. The atomic weight of Li is 6.94,
much lighter than Zn (65.4).
Summary
- The electromotive force (EMF) is the maximum potential difference
between two electrodes of a galvanic or voltaic cell.
-
The standard reduction potential of Mn+, 1 M / M
couple is the standard cell potential of the galvanic cell:
Pt | H2, 1 atm | H+, 1 M || Mn+, 1 M | M
-
The standarde oxidation potential of M | Mn+, 1 M
couple is the standard cell potential of the galvanic cell:
M | Mn+, 1 M || H+, 1 M | H2, 1 atm | Pt
-
If the cell potential is negative, the reaction is reversed.
In this case, the electrode of the galvanic cell should be written
in a reversed order.
Confidence Building Questions
-
In which cell does reduction takes place? The right-hand cell or
the left-hand cell in the notation
| left | left+ || right+ | right |?
Answer... Right
Consider...
Oxidation takes place in the left hand cell.
Reduction takes place in the Right hand cell or cathode.
-
Reduction potentials of half cells are measured against what?
- The zinc half cell Zn | Zn2+ 1 M.
- The hydrogen half cell Pt | H2 | H+ 1 M.
- The hydrogen half cell H+ 1 M | H2 | Pt.
- The copper half cell Cu2+ 1 M | Cu.
- The hydrogen half cell Pt | H2 | H+ 10-7 M.
Answer... B.
Consider...
Pt | H2 | H+ 1 M || right+ | right
gives the reduction potential.
- Is the potential for the battery
Pt | H2 | H+ || Cl2 | Cl- | Pt
positive or negative?
Answer... Positive
Consider...
Cl2 + 2 e ® 2 Cl- . . .E° = 1.36
H2 ® 2 H+ + 2 e . . . E° = 0.00
----------------------------------
Cl2 + H2 ® 2 HCl . . . DE° = 1.36 V
The reaction is spontaneous.
© cchieh@uwaterloo.ca