A series of electrodes or half cells arranged in order of their increasing standard oxidation potentials or in the decreasing order of their standard reduction potentials is called an electromotive force series or electrochemical series. Electrochemical series is also known as e.m.f. series

Characteristics Electrochemical Series:

• In this series, all reduction potentials are given on hydrogen scale whose, Eo is taken as zero.
• The standard reduction potential of an element is a measure of the tendency of that element to get reduced.
• The element which has greater reduction potential gets reduced easily.  While the elements with low reduction potential will get easily oxidized
• Elements that lose electrons more easily have lower (negative) reduction potential and those which lose electrons with greater difficulty or instead of losing they accept electrons more easily have a higher (positive) reduction potential.
• In EMF series elements having higher (+ ve), the reduction potential is placed at the top.  While those having lower (-ve) reduction potential are placed at the bottom.  SHE has the middle position in the electrochemical series.
• The substances which are stronger reducing agents than hydrogen are placed below the hydrogen in the series and have negative standard reduction potential. The substances which are weaker reducing agents than hydrogen are placed above the hydrogen in the series and have positive standard reduction potential. Thus as we move down the group strength of reducing agent increases while the strength of the oxidizing agent decreases.
• Metal at the bottom is the most active metal. As we move down in the series activity and electropositivity of metals increase. Nonmetal at the Top is the most active nonmetal. As we move down in the series activity and electronegativity of nonmetal decreases.

Applications of Electrochemical Series:

For Choosing Elements as Oxidising Agents:

The elements which have more electron-accepting tendency are oxidizing agents. Elements at the top of the electrochemical series have higher (+ ve) reduction potential.  Hence they gain an electron from other elements and oxidize them.  So they are good oxidizing agents.

Element (F₂) at the topmost position of electrochemical series which has the highest reduction potential is the strongest oxidizing agent. Oxidizing power decreases from top to bottom in the series.

e.g. The elements like Cu, Ag, Hg, Br₂, Cl₂, etc. are good oxidizing agents. F₂ is the strongest oxidizing agent.

For Choosing Elements as Reducing Agents:

The elements which have more electron losing tendency are reducing agents. The elements at the bottom in the electrochemical series have lower (- ve) reduction potential. Hence they lose electrons readily and supply to other elements and reduce them. So bottom elements in electrochemical series are reducing agents.  Reducing strength goes on increasing from top to bottom in the series.

Element (Li) having the bottom-most position has the lowest reduction potential hence it is the strongest reducing agent.

e.g. The element like Zn, Cd, Ni, K, etc. are good reducing agents.

For Studying displacement reaction:

One metal can be displaced from a salt solution by another metal is known as a redox reaction. Elements having higher reduction potential will gain electrons and that having lower reduction potential will lose electrons. Hence element lower in electrochemical series can displace an element placed higher in electrochemical series from its salt solution.

Example-1:

Zn displaces Cu from CuSO₄, because, zinc is placed lower in electrochemical series and has lower reduction potential while Cu is placed higher in electrochemical series and has higher reduction potential.  Hence zinc can easily displace copper from CuSO₄

Zn + CuSO₄ → ZnSO₄ + Cu    i.e.

Zn + Cu⁺⁺_(aq) → Zn ⁺⁺_(aq) +  Cu

Example-2:

Fe displaces Cu from CuSO₄ because Fe is placed lower in electrochemical series and has lower reduction potential while Cu is placed higher in electrochemical series and has higher reduction potential.  Hence Fe can easily displace copper from CuSO₄.

Fe + CuSO₄ → FeSO₄(aq)+ Cu  i.e.

Fe + Cu⁺⁺_(aq) → Fe⁺⁺_(aq) +  Cu

To predict whether a given metal will displace another, from its salt solution:

A metal lower in the series will displace the metal from its solution which is higher in the series, i.e., the metal having low standard reduction potential will displace the metal from its salt’s solution which has a higher value of standard reduction potential. A metal lower in the series has a greater tendency to provide electrons to the cations of the metal to be precipitated.

Displacement of one nonmetal from its salt solution by another nonmetal:

A nonmetal higher in the series having the high value of standard reduction potential will displace another nonmetal with lower reduction potential i.e., occupying the position below in the series. The nonmetal’s which possess high positive reduction potentials have the tendency to accept electrons readily. These electrons are provided by the ions of the nonmetal having the low value of reduction potential. Thus, Cl2 can displace bromine and iodine from bromides and iodides.

Displacement of hydrogen from dilute acids by metals:

The metal which can provide electrons to H⁺ ions present in dilute acids for reduction evolve hydrogen from dilute acids. The metal having negative values of reduction potential possess the property of losing electron or electrons. Thus, the metals occupying lower positions in the electrochemical series readily liberate hydrogen from dilute acids and on ascending in the series tendency to liberate hydrogen gas from dilute acids decreases.

The metals which are above hydrogen in electrochemical series like Cu, Hg, Au, Pt, etc., do not evolve hydrogen from dilute acids.

Displacement of hydrogen from water:

Iron and the metals below iron are capable of liberating hydrogen from water. The tendency increases from top to bottom in electrochemical series. Alkali and alkaline earth metals liberate hydrogen from cold water but Mg, Zn and Fe liberate hydrogen from hot water or steam.

For Calculation of standard EMF of cell ( E^o_cell):

From the standard electrode potential values, it is easy to calculate EMF of cell. Standard oxidation potential values are given in EMF series. Eo  cell is calculated using formula:

E^o_cell =    E^o_{red (cathode)}    –    E^o_{red (anode)}

e.g. in Daniell cell,

Now, From the series, E^o_Zn  = – 0.763 V ,  E^o_Cu =  + 0.337 V

E^o_cell =    E^o_{red (cathode)}    –    E^o_{red (anode)}

∴  E^o_cell =    E^o_{red (Cu)}    –    E^o_{red (Zn)}

∴  E^o_cell =     0.337  –  ( -0.763)

∴  E^o_cell =     0.337  + 0.763

∴  E^o_cell =     1.10 V

For Checking Spontaneity of Redox Reactions:

If cell is assembled such that one electrode has higher positive oxidation potential and other has lower negative oxidation potential then redox cell reaction will be spontaneous and cell will have positive EMF.  On the contrary if EMF of cell is negative then redox cell reaction will be non spontaneous.

e.g. in Daniell cell,

Now, From the series, E^o_Zn  = – 0.763 V ,  E^o_Cu =  + 0.337 V

E^o_cell =    E^o_{red (cathode)}    –    E^o_{red (anode)}

∴  E^o_cell =    E^o_{red (Cu)}    –    E^o_{red (Zn)}

∴  E^o_cell =     0.337  –  ( -0.763)

∴  E^o_cell =     0.337  + 0.763

∴  E^o_cell =     1.10 V

Since cell has positive EMF, following redox cell reaction is spontaneous.

Zn + Cu⁺⁺_(aq) → Zn ⁺⁺_(aq) +  Cu

Thus higher the positive EMF of the cell, the more is the spontaneity of the redox cell reaction.

For Construction of a Cell:

Various cells can be constructed by combining standard electrodes given in EMF series as per the requirement of e.m.f.

e.g If a cell of e.m.f. 1.1 V is required, then from e.m.f. series we can locate zinc and copper electrode whose combination gives required e.m.f.

For Corrosion Treatment:

When two metals which are in contact with each other are exposed to the atmosphere, the element lower in series will be oxidized. i.e. it is rusted and destroyed.

If there is a scratch on the galvanized sheet of iron, and iron is exposed then zinc is rusted and iron is protected. This is because in e.m.f. series zinc is below the iron. But if there is a scratch on the tin-plated iron, iron gets rusted because in e.m.f. series iron is below tin.

To Find Reactivity of Metals:

As we move down in the electrochemical series reactivity of metal increases. Alkali metals and alkaline metals at the bottom are highly reactive. They can react with cold water and evolve hydrogen. They can dissolve in acid-forming salt.

Metals like Fe, Pb, Sn, Ni, Co which are in little higher in the series do not react with cold water but react with steam and evolve hydrogen. Metals like Cu, Ag, and Au which lie above the hydrogen are less reactive and do not react with water in any form to evolve hydrogen.

To Ascertain Electropositivity of Metals:

Strongly electropositive metals:

Metals having standard reduction potential near about -2.0 volt or more negative like alkali metals, alkaline earth metals are strongly electropositive in nature.

Moderately electropositive metals:

Metals having values of standard reduction potentials between 0.0 and about -2.0 volt are moderately electropositive. Al, Zn, Fe, Ni, Co, etc., belong to this group.

Weakly electropositive metals:

The metals which are above hydrogen and possess positive values of standard reduction potentials are weakly electropositive metals. Cu, Hg, Ag, etc., belong to this group.

To Find Thermal Stability of Metallic Oxides:

The thermal stability of the metal oxide depends on its electropositive nature. As the electropositivity increases from top to bottom, the thermal stability of the oxide also increases from top to bottom.

The oxides of metals having high positive reduction potentials are not stable towards heat. The metals which are above copper form unstable oxides, i.e., these are decomposed on heating.

To Determine the Products of Electrolysis:

In case two or more types of positive and negative ions are present in solution, during electrolysis certain ions are discharged or liberated at the electrodes in preference to others.

In general, in such competition, the ion which is the stronger oxidizing agent (higher value of standard reduction potential) is discharged first at the cathode. e.g. In a mixture of copper and silver ions, silver will be deposited first because the reduction potential of silver is higher than copper.

• The increasing order of deposition of few cations is: K⁺, Ca⁺⁺, Na⁺, Mg⁺⁺+, Al⁺⁺⁺, Zn⁺⁺, Fe⁺⁺, H⁺, Cu⁺⁺, Ag⁺, Au⁺⁺⁺.
• The anion which is a stronger reducing agent (low value of standard reduction potential) is liberated first at the anode.
• The increasing order of discharge of few anions is SO₄^– –, NO₃^–, OH^–, Cl^–, Br^–, I^–
• When an aqueous solution of NaCl containing Na⁺, Cl^–, H^+, and OH- ions is electrolyzed, H+ ions are discharged at cathode and Cl- ions at the anode, i.e., H2 is liberated at cathode and Cl2 at the anode.
• When an aqueous solution of CuS04 containing Cu++, H+ and OH- ions is electrolyzed, Cu⁺⁺ ions are dis­charged at the cathode and OH^– ions at the anode.

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In this article, we shall study the use of the Nernst equation to find e.m.f. of cell and electrodes.

Convention Followed While Calculation of Cell Potential (e.m.f.):

• In the symbolic representation of the cell, the right-hand side electrode is the cathode (positive electrode) and the left-hand side is the anode (negative electrode).
• All standard potentials are reduction potentials that are they refer to a reduction reaction.
• The cathode has a higher standard potential than the anode.
• For spontaneous reaction to take place the cell potential should be positive.

Illustrations for Use of Nernst Equation:

When Reactions are given:

Example – 1: 

Cr_(s) + 3Fe³⁺ _(aq) → Cr³⁺_(aq) + 3Fe²⁺ _(aq)

The cell formation is

Cr_(s)| Cr³⁺_(aq)|| Fe²⁺_(aq),Fe ³⁺_(aq)| Pt

The half cell reactions are

Cr_(s) → Cr³⁺(aq)+ 3e^–  (Oxidation)

Fe³⁺_(aq)+ 3e^– → Fe²⁺_(aq)(Reduction)

Hence n = 3

Nernst equation is

Example – 2:  

Al³⁺(aq) + 3e-  → Al_(s) ,

Here n = 3,  Nernst equation is

When Type of Electrode is Given:

Redox Electrode:

Example – 1:  

Pt | Sn²⁺, Sn⁴⁺

The Reduction reaction is

Sn⁴⁺_(aq)+ 2e^– → Sn²⁺_(aq)(Reduction),

Hence n = 2, Nernst equation is

Example – 2:

Pt | Fe²⁺, Fe³⁺

The Reduction reactions are

Fe³⁺_(aq) + 1e^– →  Fe ²⁺_(aq)(Reduction)

Hence n = 1, Nernst equation is

Metal Metal Ion Electrode:

Example – 1: 

Zn_(s)| Zn⁺⁺_(aq)

Reduction reaction for it is

Zn_(s)  →  Zn⁺⁺_(aq)     +   2e^–

Here n = 2,  Nernst equation is

Example – 2:

Al_(s)| Al³⁺_(aq)

The reduction reaction is

Al³⁺(aq) + 3e-  → Al_(s)

Here n = 3,  Nernst equation is

Metal Sparingly Soluble Salt Electrode:

Example – 1:

Cl^– _(aq) | AgCl_(s)| Ag

The Reduction reaction is

AgCl_(s)+ e^– → Cl^– _(aq) + Ag_(s) (Reduction)

Hence n = 1, Nernst equation is

Gas Electrode:

Example – 1:

Cl^– _(aq) |   Cl_2(g), (1 atm)| Pt

The Reduction reaction is

½ Cl_2(g) + e ^–  →   Cl^– _(aq)  (Reduction)

Hence n = 1, Nernst equation is

Important Terms:

Half-Cell:

An electrode in contact with an electrolyte containing its own ions is called a half cell. e.g. In Daniel cell, the zinc rod dipped in zinc sulphate solution is called zinc half cell.

Half-Cell Reaction:

The reaction taking place in a half cell or reaction taking place at each electrode is called half-cell reaction. e.g. In Daniel cell in zinc half cell oxidation takes place. Therefore the half-cell reaction is

Zn_(s)  →  Zn⁺⁺_(aq)     +   2e^–

Cell:

A combination of two half-cells such that oxidation takes place at one half cell and reduction takes place at other half-cell is called the cell. e.g. A Daniel cell is formed by the combination of zinc half cell and copper half cell. Oxidation takes place at zinc half cell and the reduction takes place at the copper half cell.

Single Electrode Potential:

The difference of potential between the electrode and its salt solution around it at equilibrium is called a single electrode potential. Electrode potential depends upon

• Nature of the element/ metal,
• Concentration or activity of ions in solution
• Temperature and
• Pressure in case of gas.

Standard Electrode Potential (E°):

The difference of potential between the electrode and its salt solution around it containing ion concentration at a unit activity at 298 K is called standard electrode potential.

Oxidation  Electrode Potential (E_ox):

The difference of potential between the electrode and its salt solution around it at equilibrium and at constant temperature due to oxidation is called oxidation potential.

Standard Oxidation Potential (E°_ox):

The difference of potential between the electrode and its salt solution around it containing ion concentration at a unit activity at 298 K  due to oxidation is called standard oxidation potential (S.O.P.).

Reduction Electrode Potential (E°_red):

The difference of potential between the electrode and its salt solution around it at equilibrium and at constant temperature due to reduction is called reduction potential.

Standard Reduction Potential (E°_red):

The difference of potential between the electrode and its salt solution around it containing ion concentration at a unit activity at 298 K  due to reduction is called standard reduction potential (S.R.P.).

Standard e.m.f. of Cell:

The algebraic sum of the standard oxidation potential of one electrode (anode) and the standard reduction potential of another electrode (cathode) is called the standard e.m.f. of a cell.

Note:

The oxidation potential of electrode is equal to the reduction potential of the electrode with the opposite sign

Gibb’s Energy Change:

In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the maximum or reversible work that may be performed by a thermodynamic system at a constant temperature and pressure (isothermal, isobaric).

As the cell reaction in an electrochemical cell progresses, electrons move through a wire connecting the two electrodes until the equilibrium point of the cell reaction is reached, at which point the flow of electrons ceases. Just cell performs the work. In electrochemistry, the maximum amount of electrical work a galvanic cell can do at constant temperature and pressure is Gibb’s free energy.

The amount maximum work a galvanic cell can do is given as

Electrical work = Amount of charge (nF) × Cell potential (E_cell)

Electrical work = n F E_cell

The reversible electrical work done in a galvanic cell reaction is equal to the decrease in its Gibb’s energy

Thus,     Electrical work = – ΔG

∴ – ΔG = n F E_cell

∴ ΔG = –  n F E_cell

The standard Gibb’s energy change is given by

ΔG° = –  nFE°_cell

Gibb’s energy is an extensive property, which depends on the amount of substance. But the electrical potential is an intensive property which does not depend on the amount of substance. Thus E°_cell remains constant. Thus if ΔG° changes there is the corresponding change in the number of electrons. It can be explained as follows

ΔG° = –  n F E°_cell 

If the stoichiometric equation of redox reaction is multiplied by 2, then the standard Gibb’s energy ΔG° gets doubled and the number of electrons ‘n’ also gets doubled.

From (1) and (2) we can see that the e.m.f. of cell in both cases is the same. It shows that electrical potential is an intensive property that does not depend on the amount of substance.

Relation between Standard Cell Potential and Equilibrium Constant:

The Gibb’s free energy of a galvanic cell is given by

G° = –  n F E°_cell

By thermodynamical and equilibrium concept

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In this article, we shall study the Nernst theory of electrode potential, Nernst equation, and its use.

Single Electrode or Half cell or Electrode Couple:

A single electrode or half cell or electrode couple is produced when a metal is dipped in the solution of its own ions.

e.g. Cu | Cu⁺⁺_(aq),   Zn| Zn⁺⁺_(aq) etc

A single vertical line indicates physical contact between the metal and its ions. Sometimes a couple is produced from gas and solution of its ions. In such cases noble metal like platinum is used as a conductor to adsorb the gas.

e.g. Pt| H_2(g) | H⁺_(aq)

Concept of electrode potential (Nernst Theory):

Nernst in 1889 gave his theory of electrode potential. An electrode is a couple of active element, and its ionic solution. When metal is immersed in its salt solution it shows two opposite tendencies called de-electronation (oxidation) and electronation (reduction).

Metals have a tendency to pass into solution as cations and liberate electrons.  This process is oxidation or de – electronation. The tendency of a metal to pass into its salt solution in the form of cations liberating electrons is called the solution pressure of metal (P_s). There is a reverse tendency of cations to deposit on the electrode by taking electrons.  This process is called as electronation or reduction. The tendency of the ions in the solution to be deposited back on the surface of the metal by taking electrons is called an osmotic pressure of ions (P_o).

Nernst suggested the mechanism of the establishment of the difference of potential in a cell.  His theory is based on the theory of electrolytic dissociation and his ideas of solution pressure and formation of the electrical double layer.

De-electronation:

The process in which an atom or ion of an element loses one or more electrons is called de-electronation. De-electronation takes place at the electrode when the solution pressure of metal is greater than its osmotic pressure.

Electrons released in oxidation are accumulated on the electrode and solution, on the other hand, acquires excess positive charge because of the excess of cations. This gives rise to the electrical double layer at the electrode surface. Because of this electrical double layer, a potential difference is set up.  As this potential is due to the oxidation, it is called oxidation potential.

e.g. In Daniel cell solution pressure of zinc is more.  Zinc passes into its ion solution as Zn ⁺⁺ ions and electrons released in oxidation get accumulated on the zinc rod. Thus de-electronation takes place at zinc half cell in a Daniel cell.

Zn_(s)     →      Zn⁺⁺_(aq)     +   2e^–

Thus at zinc electrode, a negative potential is developed which is due to the oxidation.

Electronation:

The process in which an atom or ion of an element gains one or more electrons is called electronation.  Electronation takes place at the electrode when the osmotic pressure of metal is greater.

Due to electronation the electrode loses electrons continuously and acquires a positive charge. And the solution, on the other hand, acquires an excess negative charge.  Thus electrical double layer is set up across the surface of the metal. Because of the electrical double layer potential difference is set up. As this potential is due to reduction it is called a reduction potential.

e.g. In Daniel cell osmotic pressure of copper ions is more. Cu⁺⁺ ions from solution take electrons and deposited on the surface of the metal. Thus due to reduction, there is a removal of electrons from the metal surface. Thus electronation takes place at the copper half-cell in Daniel cell.

Cu⁺⁺_(aq)     +   2e^–    →  Cu_(s)

Thus at the copper electrode, a positive potential is developed due to reduction.

Rate of Electronation or De-electronation:

The rate of de-electronation and electronation differs from metal to metal.  There are three possibilities.

P_s > P_o: When the solution pressure is greater than the osmotic pressure. The rate of de-electronation is greater than the rate of electronation. The electrode undergoes oxidation. Thus negative potential develops on the electrode and it acts as an anode.

P_o > P_s: When the osmotic pressure is greater than the solution pressure. The rate of electronation is greater than the rate of de-electronation. The electrode undergoes a reduction. Thus positive potential develops on the electrode and it acts as a cathode.

P_s = P_o: When the solution pressure is equal to the osmotic pressure. The rate of electronation is equal to the rate of de-electronation. Thus there is no double layer formation and hence no potential is developed on the electrode.  Such an electrode is called the null electrode.

Nernst Equation:

For single electrode potential: Let M be the metal, ‘n’ be the number of electrons involved in the electrode.  Then the reactions are,

M    →   Mⁿ⁺ +   n e^–    (oxidation)   OR

Mⁿ⁺  +    n e^–    → M    (reduction)

According to the Nernst equation at 25° C

Where, E^o = standard oxidation potential

E = oxidation potential

R = 8.314 J K^–1 mol ^–1

n = no. of electrons involved in electrode reaction.

F = Faraday’s constant = 96500 C

T = temperature in K

[Oxidation state] = concentration of Mⁿ⁺ ions in mol dm^-3

[Reduced state] = activity of pure metal = 1

This expression gives variation of electrode potential with respect to electrolyte concentration.

The first part of the equation represents standard state electrochemical conditions and the second term is a correction for non-standard state electrochemical conditions.

Mathematical expression for EMF of a cell:

Let us consider general cell reaction

aA   +   bB  →  cC   +  dD

Let ‘n’ be the number of electrons in cell reaction.

Then according to Nernst equation, EMF of cell is given by

Calculation of Cell Potential Using Nernst Equation:

Consider a cell

Zn_(s)| Zn⁺⁺_(aq)|| H⁺_(aq) (1 M)|H_2(g) (1 atm.) | Pt  +

Oxidation reaction at anode:

Zn_(s)  →  Zn⁺⁺_(aq)     +   2e^–

Reduction reaction at anode: 

2H⁺_(aq) + 2e^–    → H_2(g)

Net cell reaction:   

Zn_(s)  + 2H⁺_(aq) → Zn⁺⁺_(aq)  + H_2(g)

The e.m.f. of a cell at 25 °C by Nernst equation is given by

Where concentrations are in mol dm^-3 and pressure is in atm.

Calculation of Electrode Potential Using Nernst Equation:

Consider an electrode  Zn_(s)| Zn⁺⁺_(aq)

Reduction reaction for it is

Zn_(s)  →  Zn⁺⁺_(aq)     +   2e^–

The electrode potential at 25 °C by Nernst equation is given by

at 25 °C. Where concentrations are in mol dm^-3 and pressure is in atm.

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