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At anode: Zn (s) Zn2+ (aq.) + 2 e- (oxidation)
At cathode: Cu2+ (aq.) + 2e- Cu (s) (Reduction)
Net reaction: Zn (s) + Cu 2+ (aq.) Zn2+ (aq.) + Cu (s)
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Electrochemical Cells
An electrochemical cell consists of two electrodes, or metallic conductors, in contact with an electrolyte, an ionic
conductor (which may be a solution, a liquid, or a solid).
An electrode and its electrolyte comprise an electrode compartment. The two electrodes may share the same
compartment. If the electrolytes are different, the two compartments may be joined by a salt bridge, which is a tube
containing a concentrated electrolyte solution (almost always potassium chloride in agar jelly) that completes the
electrical circuit and enables the cell to function.
There are two types of electrochemical cells:
1. Galvanic cells
2. Electrolytic cells
• Both types contain two electrodes, which are solid metals connected to an external circuit that provides an electrical
connection between the two parts of the system
• The oxidation half-reaction occurs at one electrode (the anode), and the reduction half-reaction occurs at the other
(the cathode). When the circuit is closed, electrons flow from the anode to the cathode. The electrodes are also
connected by an electrolyte, an ionic substance or solution that allows ions to transfer between the electrode
compartments, thereby maintaining the system’s electrical neutrality.
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Galvanic and Electrolytic Cells
A galvanic cell (left)
transforms the energy released
by a spontaneous redox
reaction into electrical energy.
The oxidative and reductive
half-reactions occur in separate
compartments that are
connected by an external
electrical circuit; in addition, a
second connection that allows
ions to flow between the
compartments (shown here as a
vertical dashed line to
represent a porous barrier) is
necessary to maintain electrical
neutrality. The potential
difference between the
electrodes causes electrons to
flow from the reductant to
the oxidant through the
external circuit, generating an
electric current.
In an electrolytic cell
(right), an external source
of electrical energy is used
to generate a potential
difference between the
electrodes that forces
electrons to flow, driving
a nonspontaneous redox
reaction; only a single
compartment is employed
in most applications. In
both kinds of
electrochemical cells, the
anode is the electrode at
which the oxidation half-
reaction occurs, and the
cathode is the electrode at
which the reduction half-
reaction occurs
Fig. Electrochemical Cells
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Electrolytic Cell vs Galvanic Cell
At anode: Cl- ½ Cl2 (g) + e-
At cathode: Na+ + e- Na
At anode: Zn (s) Zn2+ (aq.) + 2 e-, E0 = 0.76 V
At cathode: Cu2+ (aq.) + 2e- Cu (s), E0 = 0.34 V
Net reaction: Zn (s) + Cu 2+ (aq.) Zn2+ (aq.) + Cu (s)
The cell potential, Ecell = 0.34 + 0.76 = 1.1 V
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Electrolytic cell Electrochemical cell
Electrical energy is converted to chemical energy Chemical energy is converted into electrical
energy
An input of energy is required for the redox
reactions to proceed in these cells, i.e. the
reactions are non-spontaneous
The redox reactions that take place in these cells
are spontaneous in nature
Anode is positive and cathode is negative
electrode
Anode is negative and cathode is positive
electrode
The external battery supplies the electrons. The
electrons enter through the cathode and come out
through the anode
The electrons are supplied by species getting
oxidized. They move from anode to the cathode
in the external circuit
9. Types of Reversible Electrodes
1. Metal-Metal ion electrodes: A metal rod dipped in a solution containing its own ions
e.g., A Zn rod dipped in a solution of zinc sulphate
Electrode reaction: Mz+ (aq) + z e- M (s)
2. Gas electrodes
e.g., Hydrogen electrode
Hydrogen gas bubbled in a solution of an acid (HCl) forms this type of electrode.
H+ (aq) + e- H2 (g)
3. Metal- insoluble metal salt electrodes
A metal and a sparingly soluble salt of the same metal dipped in a solution of a soluble salt
having the same anion
e.g., Calomel electrode consists of mercury, mercurous chloride (Hg2Cl2 (s)) and a solution of
potassium chloride
Hg2Cl2 (s) + e- 2 Hg (l) + 2 Cl- (aq)
4. Redox electrodes
The potential is developed in these electrodes due to the presence of ions of the same
substance in two different valence states
e.g., A platinum wire inserted in a solution containing Fe2+ and Fe3+ ions
Fe3+ (aq) + e- Fe2+ (aq)
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Cell Notation
• The anode is written on the left hand side and it is represented by writing metal or solid phase first and then the metal
ions. The two are separated by semicolon or a vertical line.
Eg., Zn(s); Zn2+ (aq) or Zn(s) Zn2+(aq)
• The cathode is written on the right hand and it is
represented by writing metal ions first and the metal.
The two are separated by semicolon or vertical line.
Eg., Cu2+(aq);Cu(s) or Cu2+ Cu(s)
• When a salt bridge is used, it is indicated by two vertical lines separating the two half cells
Eg., Anode Cathode
• The above convention is used as
Eg., Zn(s); Zn2+ (aq) Cu2+(aq);Cu(s)
Fig. A cell diagram
11. Representation of the Cell (Galvanic Cell)
The electrode on the right is written in the order:
Ion, electrode (e.g., Cu2+, Cu) (involving reduction)
e.g., Cu2+ (aq) + 2e- Cu (s)
The electrode on the left is written in the order:
Electrode, ion (e.g., Zn, Zn2+) (involving oxidation)
e.g., Zn (s) Zn2+ (aq) + 2e -
The net reaction: Cu2+ (aq) + Zn (s) Cu(s) + Zn2+ (aq)
Thus, the galvanic cell can be represented as:
Zn (s), Zn2+ (aq) / Cu2+ (aq), Cu (s)
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The cell potential, Ecell, is the measure of the potential difference between two half cells in an
electrochemical cell. The potential difference is caused by the ability of electrons to flow from one half cell
to the other.
Electrons are able to move between electrodes because the chemical reaction is a redox reaction. A redox
reaction occurs when a certain substance is oxidized, while another is reduced.
During oxidation, the substance loses one or more electrons, and thus becomes positively charged.
Conversely, during reduction, the substance gains electrons and becomes negatively charged.
This relates to the measurement of the cell potential because the difference between the potential for the
reducing agent to become oxidized and the oxidizing agent to become reduced will determine the cell
potential.
The cell potential (Ecell) is measured in voltage (V), which allows us to give a certain value to the cell
potential.
Cell Potential
15. The half-cell reaction with a lower reduction potential is
subtracted from the one with a higher electrode potential if both
half cell reactions are presented as reduction reactions.
(i) Cu2+ (aq) + 2e- Cu (s); Eel
0 = 0.34 V
(ii) Zn (s) Zn2+ (aq) + 2e- Eel
0 = -0.76 V
Subtracting Eq. (ii) from Eq. (i), we get
Cu2+ (aq) + Zn (s) Cu(s) + Zn2+ (aq)
The cell potential, Ecell
0 = 0.34 – (- 0.76) V
= 1.10 V
Determination of Cell Potential
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Relationship between Cell Potentials and Free Energy
The maximum cell potentials is directly related to the free energy difference between the reactants and the products in
the cell
∆G = -nFE0 ........................ (1)
where, G – Gibbs free energy
n – No of moles transferred per mole of reactant and product
F – Faraday=96,485 coulombs
E0 – Standard potential
The equation (1) is derived by terms of
The maximum amount of work that can be produced by an electrochemical cell, Wmax, is equal to the product of the
cell potential,E0, and total charge transferred during the reaction
Wmax = -nFE0 ....................... (2)
Work is expressed as a negative number because work is being done by the system on the surroundings.
∆G0 is also the measure of the maximum amount of work that can be performed during chemical reaction (∆G=Wmax
there must be a relationship between the potential of an electrochemical cell and the change in free energy, ∆G
∆G0 = -nFE0
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Nernst Equation
Gibb's Free Energy
The Gibb's free energy G is the negative value of maximum electric work,
∆G = - W
= - q ∆E
A redox reaction equation represents definite amounts of reactants in the formation of also definite amounts of products.
The number (n) of electrons in such a reaction equation, is related to the amount of charge transferred when the reaction is
completed.
Since each mole of electron has a charge of 96,485 C (known as the Faraday's constant, F),
q = nF and, ∆G = - nF∆E
At standard conditions, ∆G° = - n F∆E°
The General Nernst Equation
The general Nernst equation correlates the Gibb's Free Energy ∆G and the EMF of a chemical system known as the galvanic
cell. For the reaction
a A + b B = c C + d D and
[C]c [D]d Q = --------- [A]a [B]b
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It has been shown that
∆G = ∆G° + RT ln Q and
∆G = - nF∆E
Therefore
- nF∆E = - nF∆E° + R T ln Q
Where, R – is the gas constant (8.314 J mol-1 K-1), T- temperature (in K), Q- reaction quotient,
and F- Faraday constant (96485 C) respectively.
Thus, we have ∆E = ∆E°-R T/ n F ln [C]c [D]d/ [A]a [B]b
This is known as the Nernst equation.
The equation allows us to calculate the cell potential of any galvanic cell for any concentrations.
Some examples are given in the next section to illustrate its application.
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Applications of Nernst equation
• In many situations, accurate determination of an ion concentration by direct measurement of a cell potential is impossible
due to the presence of other ions and a lack of information about activity coefficients.
• In such cases it is often possible to determine the ion indirectly by titration with some other ion. For example, the initial
concentration of an ion such as Fe2+ can be found by titrating with a strong oxidizing agent such as Ce4+. The titration is
carried out in one side of a cell whose other half is a reference electrode:
Pt(s) | Fe2+, Fe3+ || ......................... (1)
Initially the left cell contains only Fe2+. As the titrant is added, the ferrous ion is oxidized to Fe3+ in a reaction that is virtually
complete:
Fe2+ + Ce4+ → Fe3+ + Ce3+ ............ (2)
The cell potential is followed as the Fe2+ is added in small increments. Once the first drop of ceric ion titrant has been added,
the potential of the left cell is controlled by the ratio of oxidized and reduced iron according to the Nernst equation
...................... (3)
which causes the potential to rise as more iron becomes oxidized.
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When the equivalence point is reached, the Fe2+ will have
been totally consumed (the large equilibrium constant
ensures that this will be so), and the potential will then be
controlled by the concentration ratio of Ce3+/Ce4+.
The idea is that both species of a redox couple must be
present in sufficient concentrations to poise an electrode
(that is, to control its potential according to the Nernst
equation.)
If one works out the actual cell potentials for various
concentrations of all these species, the resulting titration
curve looks much like the familiar acid-base titration
curve.
The end point is found not by measuring a particular cell
voltage, but by finding what volume of titrant gives the
steepest part of the curve.
Fig. Potentiometric titration graph
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Application of Nernst Equation-Redox Reaction
• From the thermodynamic point of view, the redox reactions occurring in electrochemical cells are not
spontaneous since external energy is used to produce these reactions (∆G>0, ∆E<0).
• The Nernst equation is suitable for use in electrochemical cells to determine quantities such as potential,
concentration, number of electrons transferred during the process, as well as the electric charge (q= ∆G/nF)
where according to reaction
Oxidations : Zn -> Zn 2+ + 2e-
Reductions : 2H+ + 2e- -> H2 (gas)
The overall reaction: Zn + 2H+ -> Zn 2+ + H2 (gas)
The cell voltage is the sum of potentials of both half reactions written in their current states
E0 = 0.76V + 0 = 0.76V
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Since pH is actually defined in terms of hydrogen ion activity and not its concentration, a hydrogen electrode allows a
direct measure of {H+} and thus of –log {H+}, which is the pH.
Application of Nernst Equation-pH
The potential between a pH glass electrode and a reference electrode is defined by the Nernst equation, which is as
follows for a pH measurement:
E = E0 + 2.3 RT / F * log aH+
E0 is the standard potential at aH+ = 1mol/L.
The factor 2.3 RT/F is summarized as the Nernst potential EN and is identical to the change in potential per pH unit. The
value of EN depends on the absolute temperature T Kelvin. (EN is often referred to as the slope factor):
Temperature EN Value (mV)
0 °C EN = 54.2 mV
25 °C EN = 59.2 mV
50 °C EN = 64.1 mV
Fig. 18: Different sources of potential in a combination electrode
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In order to measure E1 and assign a definite pH value to it, all other single potentials E2 - E6 have to be constant.
• A thermodynamic equilibrium of the hydrogen ion
arises at the phase boundary between the
measuring solution and the outer gel layer.
• If the activity of the hydrogen ions is different in
the two phases, a hydrogen ion transport will occur.
This leads to a charge at the phase layer, which
prevents any further H+ transport.
Fig. 19: A model representing the pH potentials at the glass membrane
• A thermodynamic equilibrium of the hydrogen ion arises at the phase boundary between the measuring solution and the
outer gel layer. If the activity of the hydrogen ions is different in the two phases, a hydrogen ion transport will occur. This
leads to a charge at the phase layer, which prevents any further H+ transport.
• This resulting potential is responsible for the different hydrogen ion activities in the solution and in the gel layer:
The number of hydrogen ions in the gel layer is given by the silicic acid skeleton of the glass membrane and can be
considered a constant and independent of the measuring solution.
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The potential in the outer gel layer is transmitted to the inside of the glass membrane by the Li+ ions found in the glass
membrane, where another phase boundary potential arises:
The total membrane potential is equal to the difference of the two phase boundary potentials
When H+ activity is identical in the two gel layers (the ideal case) and the H+ activity of the
inner electrolyte is kept constant, the following equation is true:
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• A solubility equilibrium exists when a chemical compound in the solid state is in chemical
equilibrium with a solution of that compound.
• The equilibrium is an example of dynamic equilibrium in that some individual molecules migrate between
the solid and solution phases such that the rates of dissolution and precipitation are equal to one another.
When equilibrium is established, the solution is said to be saturated. The concentration of the solute in a
saturated solution is known as the solubility.
• Solubility is temperature dependent. A solution containing a higher concentration of solute than the
solubility is said to be supersaturated. A supersaturated solution may be induced to come to equilibrium by
the addition of a "seed" which may be a tiny crystal of the solute, or a tiny solid particle, which initiates
precipitation.
• There are three main types of solubility equilibria.
1. Simple dissolution.
2. Dissolution with dissociation.
3. Constant is known in this case as a solubility product.
4. Dissolution with reaction.
Solubility equilibria (Ksp)
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H 2 (g) + 1/2 0 2 (g) → H 2O (l)
Δf H° 298 . = - 286 kJ mol-1
Since entropy is a state function, entropy values are additive in the same way as enthalpy values:
Δf S = ∑Vi S i
where Vi are stoichiometric coefficients in the chemical equation for the formation of one mole of the compound from
the elements. We find the following valued for absolute entropies, given in the units
J mol-1 K-1 S° 298 (H 2 ,g) = 131 , S° 298 (O2 ,g) = 205, S° 298 (H 2O,l) = 70
Thus the standard entropy of formation for liquid water, Δf S° 298 will be:
Δf S° 298 = - 131 - 1/2 x 205 + 70 = - 163.5 1 J mol-1 K-1
Gibbs Free Energy:
Δf G° 298 = Δ f H° 298 - TΔf S° 298 = - 286 - 298 x (-163.5/1000) = - 237 kJ mol-1 (Spontaneous)
Gibbs’s Free Energy for Water Formations
