Electrochemical Cells

1
Electrochemical Cells

• An electrochemical cell consists of
• Two physically separated half-cells for each
  half-reaction,
• An external circuit by which electrons generated
  by the oxidation half-cell can travel to the
  reduction half-cell,
• A salt bridge (or equivalent) to allow ions to
  move between the two half-cells so that charge
  doesnt build up in them. (That would stop the
  flow of electrons, rendering the cell useless.)

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Electrochemical Cells

• Standard notation
• With the anode (where electrons are generated) at
  the left, we describe the relationships between
  each phase in the cell.
• A single bar represents two phases in direct
  contact e.g. an electrode immersed in a solution
• A double bar represents two phases indirectly
  connected e.g. two solutions connected by a
  salt bridge.

3
Electrochemistry Meets Thermodynamics

• Recall that changes to internal energy occur via
  heat and work. The reaction in an
  electrochemical cell is a reversible process, so
  we can clarify that both the heat and work are
  reversible.
• Let us assume that the electrochemical cell is
  operating at constant pressure and temperature
  (so that qrev ?H and ?S ?H/T).
• We can divide the work into pressure-volume work
  (wrev,PV -P?V) and non-pressure-volume work -
  electrical work, in this case.

4

• So
• Recall that ?H ?U P?V
• Which is simply
• For a spontaneous reaction, the maximum amount of
  electrical work that can be done is

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Electrochemical Cells

• If the overall reaction in an electrochemical
  cell is spontaneous, energy is released in the
  form of electrical work. This energy is measured
  in relation to the number of electrons involved
  in the reaction, giving a potential, E. When 1
  Joule of energy is released by an electrochemical
  reaction involving electrons with 1 Coulomb of
  charge, the potential is 1 Volt
• This is essentially a measure of available energy
  per electron. Note that
• Energy (Joules) E (Volts) x Charge (Coulombs)

6

• A cells potential can be measured by applying
  an external voltage opposing the current flow.
  When the external voltage is sufficient to stop
  the reaction, that external voltage is termed the
  electromotive force (emf). Since the
  electromotive force must be exactly equal to the
  potential produced by the cell, the following
  terms are often used interchangeably
• Voltage (or potential)
• Electromotive force (or emf)
• Electric potential difference

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• The maximum amount of work done by a cell for a
  given amount of charge (charge q) passing
  through a potential difference (cell potential
  E)
• q is the moles of electrons (n) multiplied by
  the charge of 1 mole of electrons (F Faradays
  constant 96485 C/mol), so
• This relationship tells us that electrochemical
  cells
• - with a ve potential will be product
  favoured
• - those with a -ve potential will be reactant
  favoured.
• This allows us to calculate ?Gr from standard
  cell potentials, and to determine E for cells in
  which ?Gr is can be determined.

8
The Nernst Equation

• Under non-standard conditions we know that
• Multiplying through by -?G/nF gives us the
  Nernst equation
• so we can calculate a cells potential under
  non-standard conditions.

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Half-cells and Standard Reduction Potentials

• Its impossible to directly measure the potential
  for a half-cell since there would be no current
  and therefore no voltage. As is often the case
  in thermodynamics, we use an arbitrary zero
  reference point. Cell potential is measured
  against the standard hydrogen electrode (SHE)
• As it does for ?H, ?S, and ?G, reversing the
  reaction reverses the sign of E therefore, we
  can also say that
• The standard hydrogen electrode (shown at the
  left) is an electrode in which hydrogen gas is
  bubbled over a platinum electrode in the presence
  of 1 M H(aq).

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Standard Half-Cell Reduction Potentials
The Cu/Zn cell has a standard potential of 1.10
V This can be determined from the potentials of
the two half-cells. Each half cells standard
reduction potential is measured against the SHE.
The Zn/Zn2 has a voltage of 0.76 Vagainst a
SHE In this spontaneous cell, Zn is being
oxidized.
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Standard Half-Cell Reduction Potentials
The Cu/Cu2 has half cell has a voltage of 0.34
V against a SHE. In this case, the spontaneous
process is the reduction of Cu2. These values
have beencompiled into a generaltable of
standard reduction potentials (by convention).
12
Strongest oxidizers
13
Strongest reducing agents
14

• Like enthalpies, entropies and free energies,
  cell potentials are additive.
• e.g.

Because E? is measured in J/C, it DOES NOT CHANGE
when the reaction equation is multiplied by a
coefficient! It is the amount of charge that
flows (i.e. n) that is important.
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Some examples

• copper/lithium cell
• From the table we get the half-reactions
• Cu 2 (aq) 2 e ? Cu(s)
  E? 0.337 V
• Li (aq) e ? Li(s) E? 3.045
  V
• We now combine them in such a way as to get a
  positive overall cell potential. This means we
  must reverse the lithium equation, making it the
  anode (where the oxidation will take place.)
• Li(s) ? Li (aq) e E? 3.045 V
• now we have the cell potential for the overall
  reaction
• Cu 2 (aq) 2 Li(s) ? Cu(s)
  2 Li (aq) E?cell 3.382 V
• Note here very carefully, that the voltage was
  not doubled.

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Using the Table of Standard Reduction
Potentials You wish to oxidize Br- to
Br2 What is E for the silver/zinc cell?
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Electrochemical Cells Under Nonstandard Conditions

• We can also use a hydrogen electrode (standard or
  nonstandard) to measure reduction potentials of
  half-cells under nonstandard conditions. To do
  this, we must know the exact activities of each
  species so that we can determine Q and use the
  Nernst equation
• The cell below has a potential of -1.425 V at 25
  ?C.
• Write balanced equations for each half-cell and
  an overall chemical equation.

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Electrochemical Cells Under Nonstandard Conditions

• Knowing that E -1.425 V, calculate E? for the
  cell in the previous example.

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Electrochemical Cells Under Nonstandard Conditions

• Finally, use E? for the cell to determine the
  standard reduction potential of the Al3/Al
  half-cell.
• As noted previously, potentials can be added and
  subtracted but, because they are intensive
  properties (do not depend on quantity), they are
  never multiplied or divided by reaction
  coefficients.

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Electrochemical Cells Under Nonstandard Conditions

• Finally, we can use the standard potential for an
  electrochemical cell to determine the standard
  free energy of formation for one of the
  reactants/products. This is a convenient method
  to measure ?Gf? for new compounds/ions.
• e.g. Use the information from the previous
  example to determine ?Gf? for Al3(aq).

21
Electrochemical Cells Under Nonstandard Conditions

• If we can use cell potential to determine free
  energies then it follows that we can use free
  energies to determine cell potential.
• e.g. We wish to know whether the reaction
  described by the cell below is spontaneous and,
  if so, what is its potential.
• We can look up the standard reduction potential
  for a Cl2/Cl- half-cell, but there is no
  standard reduction potential listed for the
  S2O32-/HSO4- half-cell. We can, however, look up
  standard free energies of formation for each
  species in the reaction

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Electrochemical Cells Under Nonstandard Conditions

• So, well start by calculating the standard free
  energy change for this reaction

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Electrochemical Cells Under Nonstandard Conditions

• At this point, we can take one of two paths
• Calculate the standard potential for the cell
  (E?) then use the Nernst equation to find E.
• Calculate the free energy change under the actual
  conditions then use
• ?G -nFE to find E.
• Either way, we get the same answer and, either
  way, we need to find Q to get from standard
  conditions to actual conditions.

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Batteries

• Electrochemical cells produce a voltage, so they
  can be used to power electrical devices. The
  voltage produced depends on
• Standard cell potential (due to half-cells)
• Concentrations of reactants and products (Q in
  Nernst equation)
• Temperature (T in Nernst equation)
• The voltage does not depend on the size of the
  cell that just determines the quantity of
  available reactants (i.e. how long the cell can
  run before the concentration of reactants is too
  low for the reaction to be spontaneous).
• Typical cell potentials are 1V. If we want/need
  a larger potential, we must connect multiple
  cells in series, producing a battery

25
Batteries

• In theory, any battery can be recharged just
  apply an external potential to force the reverse
  reaction to occur, pushing the electrons
  backwards.
• In practice, this isnt always easy (or safe!)
• In some batteries, the electrodes can be damaged
  during discharge
• In some batteries, the electrodes get coated with
  resistive products which cause heating when
  current is passed through them.
• In some batteries, the desired reverse reaction
  is not the one that occurs when recharging is
  attempted generally because there is something
  else that is more easily oxidized or reduced. A
  common example is the electrolysis of water
  used to make pastes in many batteries.
• A reliable battery is a good battery. Many
  batteries contain a paste so that the solutes are
  always saturated in the small amount of water
  available. This keeps the solute concentration
  constant thereby keeping Q and E constant.

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Alkaline Batteries

• An alkaline battery has a zinc anode and a
  manganese(IV) oxide cathode. As the name
  implies, it operates under basic conditions
• Because there are no solutes in the overall
  reaction equation, Q 1 and E E?, giving a
  constant voltage.

Anode paste containing Powdered Zn, KOH, water.
Cathode paste containing MnO2, graphite and
water.
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Lead-Acid Batteries

• An lead-acid battery has a lead anode and a
  lead(IV) oxide cathode. As the name implies, it
  operates under acidic conditions (HSO4-(aq))
• The cell potential is 2 V. To get a 12 V car
  battery, six cells are connected in series.

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Fuel Cells

• We know that burning a fuel releases energy as
  heat. This energy is more efficiently harnessed
  if it is produced by oxidizing the fuel
  electrochemically as in a fuel cell. It also
  causes less pollution!
• A lot of research is currently being done to
  develop a practical hydrogen fuel cell which
  would be a very environmentally friendly power
  source as the only waste product would be water