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By measuring the potentials of various electrodes versus stand ard hydrogen electrode (SHE), a series of standard electrode potentials has been established. When the electrodes (metals and non-metals) in contact with their ions are arranged oh the basis of the values of their standard reduction potentials or standard oxidation potentials, the resulting series is called the electrochemical or electromotive or activity series of the elements.
By international convention, the standard potentials of electrodes are tabulated for reduction half reactions, indicating the tendencies of the electrodes to behave as cathodes towards HER. Those with positive E° values for reduction half reactions do in fact act as cathodes versus SHE, while those with negative E° values of reduction half reactions behave instead as anodes versus SHE. The electrochemical series is shown in the follow ing table.
Standard Aqueous Electrode Potentials at 25°C 'The Electrochemical Series'
Standard Electrode Reduction potential
Li+ + e- = Li
K+ + e- = K
Ca2+ + 2e- = Ca
Na+ + e- = Na
Mg2+ + 2e- = Mg
Al3+ + 3e- = Al
Zn2+ + 2e- = Zn
Cr3+ + 3e- = Cr
Fe2+ + 2e- = Fe
Cd2+ + 2e- = Cd
Ni2+ + 2e- = Ni
Sn2+ + 2e- = Sn
2H+ + 2e- = H2
Cu2+ + 2e- = Cu
I2 + 2e- = 2I-
Ag+ + e- = Ag
Hg2+ + 2e- = Hg
Br2 + 2e- = 2Br-
Cl2 + 2e- = 2Cl-
Au3+ + 3e- = Au
F2 + 2e- = 2F-
Characteristics of Electrochemical series
(!) The negative sign of standard reduction potential indicates that an electrode when joined with SHE acts as anode and oxidation occurs on this electrode. For example, standard reduction potential of zinc is -0.76 volt. When zinc electrode is joined with SHE, it acts as anode (-ve electrode) i.e., oxidation occurs on this electrode. Similarly, the +ve sign of standard reduction potential indicates that the electrode when joined with SHE acts as cathode and reduction occurs on this electrode.
(ii) The substances which are stronger reducing agents than hydrogen are placed above hydrogen in the series and have negative values of standard reduction potentials. All those substances which have positive values of reduction potentials and placed below hydrogen in the series are weaker reducing agents than hydrogen.
(iii) The substances which are stronger oxidising agents than H+ion are placed below hydrogen in the series.
(iv) The metals on the top (having high negative values of standard reduction potentials) have the tendency to lose electrons readily. These are active metals. The activity of metals decreases from top to bottom. The non-metals on the bottom (having high positive values of standard reduction potentials)
have the tendency to accept electrons readily. These are active non-metals. The activity of non-metals increases from top to bottom.
Applications of Electrochemical series
(i) Reactivity of metals:
The activity of the metal depends on its tendency to lose electron or electrons, i.e., tendency to form cation (M"+). This tendency depends on the magnitude of standard reduction potential. The metal which has high negative value (or smaller positive value) of standard reduction potential readily loses the electron or electrons and is converted into cation. Such a metal is said to be chemically active.
The chemical reactivity of metals decreases from top to bottom in the series. The metal higher in the series is more active than the metal lower in the series. For example,
(a) Alkali metals and alkaline earth metals having high negative values of standard reduction potentials are chemically active. These react with cold water and evolve hydrogen. These readily dissolve in acids forming corresponding salts and combine with those substances which accept electrons.
(b) Metals like Fe, Pb, Sn, Ni, Co, etc., which lie a little down in the series do not react with cold water but react with steam to evolve hydrogen.
(c) Metals like Cu, Ag and Au which lie below hydrogen are less reactive and do not evolve hydrogen from water.
(ii) Electropositive character of metals:
The electropositive character also depends on the tendency to lose electron or electrons. Like reactivity, the electropositive character of metals decreases from top to bottom in the electrochemical series. On the basis of standard reduction potential values, metals are divided into three groups:
(a) 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.
(b) Moderately electropositive metals: Metals having values of reduction potentials between 0.0 and about -2.0 volt are moderately electropositive. Al, Zn, Fe, Ni, Co, etc., belong to this group.
(c) Weakly electropositive metals: The metals which are below hydrogen and possess positive values of reduction potentials are weakly electropositive metals. Cu, Hg, Ag, etc., belong to this group.
(iii) Displacement reactions:
(a) To predict whether a given metal will displace another, from its salt solution. A metal higher in the series will displace the metal from its solution which is lower in the series, i.e., the metal having low standard reduction potential will displace the metal from its salt's solution which has higher value of standard reduction potential. A metal higher in the series has greater tendency to provide electrons to the cations of the metal to be precipitated.
(b) Displacement of one nonmetal from its salt solution by another nonmetal: A nonmetal higher in the series (towards bottom side), i.e., having high value of reduction potential will displace another nonmetal with lower reduction potential i.e., occupying position above 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 low value of reduction potential. Thus, Cl2 can displace bromine and iodine from bromides and iodides.
Cl2 + 2KI --> 2KC1 + I2
21- --> I2 + 2e- (Oxidation)
Cl2 + 2e- --> 2C1- (Reduction)
[The activity or electronegative character or oxidising nature of the nonmetal increases as the value of reduction potential increases.]
(c) 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.
Mn --> Mn"+ + ne- (Oxidation)
2H+ + 2e- --> H2 (Reduction)
The metal having negative values of reduction potential possess the property of losing electron or electrons. Thus, the metals occupying top positions in the electrochemical series readily liberate hydrogen from dilute acids and on descending in the series tendency to liberate hydrogen gas from dilute acids decreases.
The metals which are below hydrogen in electrochemical series like Cu, Hg, Au, Pt, etc., do not evolve hydrogen from dilute acids.
(d) Displacement of hydrogen from water: Iron and the metals above iron are capable of liberating hydrogen from water. The tendency decreases 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.
(iv) Reducing power of metals:
Reducing nature depends on the tendency of losing electron or electrons. More the negative reduction potential, more is the tendency to lose electron or electrons. Thus, reducing nature decreases from top to bottom in the electrochemical series. The power of the reducing agent increases as the standard reduction potential becomes more and more negative.
Sodium is a stronger reducing agent than zinc and zinc is a stronger reducing agent than iron.
Element Na Zn Fe
Reduction potential -2.71 -0.76 -0.44
Reducing nature decreases
Alkali and alkaline earth metals are strong reducing agents.
(v) Oxidising nature of nonmetals:
Oxidising nature depends on the tendency to accept electron or electrons. More the value of reduction potential, higher is the tendency to accept electron or electrons. Thus, oxidising nature increases from top to bottom in the electrochemical series. The strength of an oxidising agent increases as the value of reduction potential becomes more and more positive.
F2 (Fluorine) is a stronger oxidant than Cl2, Br2 and I2.
Cl2 (Chlorine) is a stronger oxidant than Br2 and I2.
Element I2 Br2 Cl2 F2
Reduction potential +0.53 +1.06 +1.36 +2.85
Oxidising nature increases
(vi) Thermal stability of metallic oxides:
The thermal stability of the metal oxide depends on its electropositive nature. As the electropositivity decreases from top to bottom, the thermal stability of the oxide also decreases from top to bottom. The oxides of metals having high positive reduction potentials are not stable towards heat. The metals which come below copper form unstable oxides, i.e., these are decomposed on heating.
Ag2O ---------> 1/2 O2
2HgO ------------> 1/2 O2
(vii) 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 com petition the ion which is stronger oxidising agent (high value of standard reduction potential) is discharged first at the cathode. The increasing order of deposition of few cations is:
K+, Ca2+, Na+, Mg2+, Al3+, Zn2+, Fe2+, H+, Cu2+, Ag+, Au3+
Increasing order of deposition
Similarly, the anion which is stronger reducing agent (low value of standard reduction potential) is liberated first at the anode.
The increasing order of discharge of few anions is:
SO42-, NO3-, OH-, Cl-, Br-, I-
Increasing order of discharge
Thus, when an aqueous solution of NaCl containing Na+, Cl-, H+ and OH" ions is electrolysed, H+ ions are discharged at cathode and CF ions at the anode, i.e., H2 is liberated at cathode and chlorine at anode.
When an aqueous solution of CuS04 containing Cu2+, , H+ and OH- ions is electrolysed, Cu2+ ions are dis charged at cathode and OH- ions at the anode.
Cu2+ + 2e- --> Cu (Cathodic reaction)
4OH- --> O2 + 2H2O + 4e- (Anodic reaction)
Cu is deposited on cathode while 02 is liberated at anode.
(viii) Corrosion of metals:
Corrosion is defined as the deterioration of a substance because of its reaction with its environment. This is also defined as the process by which metals have the tendency to go back to their combined state, i.e., reverse of extraction of metals.
Ordinary corrosion is a redox reaction by which metals are oxidised by oxygen in presence of moisture. Oxidation of metals occurs more readily at points of strain. Thus, a steel nail first corrodes at the tip and head. The end of a steel nail acts as an anode where iron is oxidised to Fe2+ ions.
Fe --> Fe2 + 2e- (Anode reaction)
The electrons flow along the nail to areas containing im purities which act as cathodes where oxygen is reduced to hydroxyl ions.
O2 + 2H2O + 4e- --> 4OH- (Cathode reaction)
The overall reaction is
2Fe + Oz + 2H2O => 2Fe(OH)2
Fe(OH)2 may be dehydrated to iron oxide, FeO, or further oxidised to Fe(OH)3and then dehydrated to iron rust, Fe203. Several methods for protection of metals against corrosion have been developed. The most widely used are (i) plating the metal with a thin layer of a less easily oxidised metal (ii) allowing a protective film such as metal oxide (iii) galvanis ing-steel is coated with zinc (a more active metal).
(ix) Extraction of metals:
A more electropositive metal can displace a less electropositive metal from its salt's solution. This principle is applied for the extraction of Ag and Au by cyanide process. Silver from the solution containing sodium argento cyanide, NaAg(CN)2, can be obtained by the addition of zinc as it is more electro-positive than Ag.
2NaAg(CN)2 + Zn --> Na2Zn(CN)4 + 2Ag
standard redox potential
The values that we have just quoted for the two cells are actually the standard electrode potentials of the Mg2+ / Mg and Cu2+ / Cu systems.
The emf measured when a metal / metal ion electrode is coupled to a hydrogen electrode under standard conditions is known as the standard electrode potential of that metal / metal ion combination. By convention, the hydrogen electrode is always written as the left-hand electrode of the cell. That means that the sign of the voltage quoted always gives you the sign of the metal electrode.
Standard electrode potential is given the symbol E°.
Prediction For Occurrence of a Redox Reaction
Any redox reaction would occur spontaneously if the free energy change (âˆ†G) is negative. The free energy is related to cell emf in the following manner:
âˆ†Go => - nFEo
where n is the number of electrons involved, F is the value of Faraday and Eo is the cel emf. âˆ†G can be negative if Eo is positive.
When Eo is positive, the cell reaction is spontaneous and serves as a source of electrical energy.
To predict whether a particular redox reaction will occur or not, write down the redox reaction into two half reactions, one involving reduction oxidation reaction and the other involving reduction reaction. Write the oxidation reaction and reduction potential value for reduction reaction. Add these two values, if the algebraic summation gives a positive value, the reaction will occur, otherwise not.
Arrhenius Theory of Electrolytic dissociation
In order to explain the properties of electrolytic solutions, Arrhenius put forth, in 1884, a comprehensive theory which is known as theory of electrolytic dissociation or ionic theory. The main points of the theory are:
(i) An electrolyte, when dissolved in water, breaks up into two types of charged particles, one carrying a positive charge and the other a negative charge. These charged particles are called ions. Positively charged ions are termed cations and negatively charged as anions.
AB --> A+ + B-
NaCl --> Na+ + CL-
K2SO4 --> 2K++ SO42-
In its modern form, the theory assumes that solid electrolytes are composed of ions which are held together by electrostatic forces of attraction. When an electrolyte is issolved in a solvent, these forces are weakened and the electrolyte undergoes dissociation into ions. The ions are solvated.
A+B- --> A+ + B-
or A+B-+ aq --> A+(aq)+B- (aq)
(ii) The process of splitting of the molecules into ions of an electrolyte is called ionization. The fraction of the total number of molecules present in solution as ions is known as degree of ionization or degree of dissociation. It is denoted by
Î±= (Number of molecules dissociated into ions)/(Total number of molecules)
It has been observed that all electrolytes do not ionize to the same extent. Some are almost completely ionized while others are feebly ionized. The degree of ionization depends on a number of factors (see 12.6).
(iii) Ions present in solution constantly re-unite to form neutral molecules and, thus, there is a state of dynamic equilibrium between the ionized the ionized and non-ionised molecules, i.e.,
AB <--> A+ + B-
Applying the law of mass action to above equilibrium
[A+ ][B- ] /[AB] =>K
K is known as ionization constant. The electrolytes having high value of K are termed strong electrolytes and those having low value of K as weak electrolytes.
(iv) When an electric current is passed through the electrolytic solution, the positive ions (cations) move towards cathode and the negative ions (anions) move towards anode and get discharged, i.e., electrolysis occurs.
The ions are discharged always in equivalent amounts, no matter what their relative speeds are.
Electrochemical cell is a system or arrangement in which two electrodes are fitted in the same electrolyte or in two different electrolytes which are joined by a salt bridge. Electrochemical cells are of two types:
(a) Electrolytic cell (b) Galvanic or voltaic cell
It is a device in which electrolysis (chemical reaction involving oxidation and reduction) is carried out by using electricity or in which conversion of electrical energy into chemical energy is done.
Galvanic or voltaic cell
It is a device in which a redox reaction is used to convert chemical energy into electrical energy, i.e., electricity can be obtained with the help of oxidation and reduction reaction. The chemical reaction responsible for production of electricity takes place in two separate compartments. Each compartment consists of a suitable electrolyte solution and a metallic conductor. The metallic conductor acts as an electrode. The compartments containing the electrode and the solution of the electrolyte are called half-cells. When the two compartments are connected by a salt bridge and electrodes are joined by a wire through galvanometer the electricity begins to flow. This is the simple form of voltaic cell.
EMF of A Galvanic Cell
Every galvanic or voltaic cell is made up of two half-cells, the oxidation half-cell (anode) and the reduction half-cell (cathode). The potentials of these half-cells are always different. On account of this difference in electrode potentials, the electric current moves from the electrode at higher potential to the electrode at lower potential, i.e., from cathode to anode. The direction of the flow of electrons is from anode to cathode.
Flow of electrons
Anode <==============> Cathode
Flow of current
The difference in potentials of the two half-cells is known as the electromotive force (emf) of the cell or cell potential.
The emf of the cell or cell potential can be calculated from the values of electrode potentials of the two half-cells constituting the cell. The following three methods are in use:
(i) When oxidation potential of anode and reduction potential of cathode are taken into account:
ECello => Oxidation potential of anode + Reduction potential of cathode
=> Eoxo (anode) + Eredo (cathode)
(ii) When reduction potentials of both electrodes are taken into account:
ECello => Reduction potential of cathode - Reduction potential of anode
=> ECathodeo - EAnodeo => Erighto - Elefto
(iii) When oxidation potentials of both electrodes are taken into account:
=> Oxidation potential of anode - Oxidation potential of cathode
ECello => Eoxo (anode) - Eredo (cathode)
It is designed to make use of the spontaneous redox reaction between zinc and cupric ions to produce an electric current (Fig.12.7). It consists of two half-cells. The half-cells on the left contains a zinc metal electrode dipped in ZnSO4 solution.
The half-cell on the right consists of copper metal electrode in a solution CuSO4. The half-cells are joined by a salt bridge that prevents the mechanical mixing of the solution.
When the zinc and copper electrodes are joined by wire, the following observations are made:
(i) There is a flow of electric current through the external circuit.
(ii) The zinc rod loses its mass while the copper rod gains in mass.
(iii) The concentration of ZnSO4 solution increases while the concentration of copper sulphate solution decreases.
(iv) The solutions in both the compartments remain electrically neutral.
During the passage if electric current through external circuit, electrons flow from the zinc electrode to the copper electrode. At the zinc electrode, the zinc metal is oxidized to zinc ions which go into the solution. The electrons released at the electrode travel through the external circuit to the copper electrode where they are used in the reduction of Cu2+ ions to metallic copper which is deposited on the electrode. Thus, the overall redox reaction is:
Zn(s) + Cu2+ Cu(s) + Zn2+(aq)
Thus, indirect redox reaction leads to the production of electrical energy. At the zinc rod, oxidation occurs. It is the anode of the cell and is negatively charged while at copper electrode, reduction takes, place; it is the cathode of the cell and is positively charged.
Thus, the above points van be summed up as:
(i) Voltaic or Galvanic cell consists of two half-cells. The reactions occurring in half-cells are called half-cell reactions. The half-cell in which oxidation taking place in it is called oxidation half-cell and the reaction taking place in it is called oxidation half-cell reaction. Similarly, the half-cell occurs is called reduction half-cell and the reaction taking place in it is called reduction half-cell reaction.
(ii) The electrode where oxidation occurs is called anode and the electrode where reduction occurs is termed cathode.
(iii) Electrons flow from anode to cathode in the external circuit.
(iv) Chemical energy is converted into electrical energy.
(v) The net reaction is the sum of two half-cell reactions. The reaction is Daniel cell can be represented as.
The net reaction is the sum of two half-cell reactions. The reaction is Daniel cell can be represented as
Oxidation half reaction, Zn(s) --> Zn2+(aq) + 2e-
Reduction half reaction, Cu2+(aq) + 2e- --> Cu (s)
Net reaction Zn(s) + Cu2+ (aq) --> Zn2+(aq) + Cu(s)
PRIMARY VOLTAIC CELL (THE DRY CELL)
In this cell, once the chemicals have been consumed, further reaction is not possible. It cannot be regenerated by reversing the current flow through the cell using an external direct current source of electrical energy. The most common example of this type is dry cell.
The container of the dry cell is made of zinc which also serves as one of the electrodes. The other electrode is a carbon rod in the centre of the cell. The zinc container is lined with a porous paper. A moist mixture of ammonium chloride, manganese dioxide, zinc chloride and a porous inert filler occupy the space between the paper lined zinc container and the carbon rod. The cell is sealed with a material like wax.
As the cell operates, the zinc is oxidised to Zn2+
Zn ---> Zn2+ + 2e- (Anode reaction)
The electrons are utilized at carbon rod (cathode) as the ammonium ions are reduced.
2NH4++2e- --> 2NH3 + H2 (Cathode reaction)
The cell reaction is
Zn+ 2 NH4+ ---> Zn2+ + 2NH3 + H2
Hydrogen is oxidized by MnO2 in the cell.
2MnO2 + H2 ---> 2MnO(OH)
Ammonia produced at cathode combines with zinc ions to form complex ion.
Zn2+ + 4NH3 ---> [Zn(NH3)4]2+
Ecell is 1.6 volt
Alkaline dry cell is similar to ordinary dry cell. It contains potassium hydroxide. The reaction in alkaline dry cell are:
Zn + 2OH- ---> Zn(OH)2 + 2e- (Anode reaction)
2MnO2 + 2H2O + 2e- ---> 2MnO(OH) + 2OH- (Cathode reaction)
Zn + 2MnO2 + 2H2O ---> Zn(OH)2 + 2MnO(OH) (Overall)
Ecell is 1.5 volt.
SECODARY VOLTAIC CELL (LEAD STORAGE BATTERY)
The cell in which original reactants are regenerated by passing direct current from external source, i.e., it is re-charged, is called secondary cell. Lead storage battery is the example of this type.
It consists of a group of lead plates bearing compressed spongy lead, alternating with a group of lead plates bearing leaf dioxide, PbO2. These plates are immersed in a solution of about 30% H2SO4. When the cell discharge; it operates as a voltaic cell. The spongy lead is oxidized to Pb2+ ions and lead plates acquire a negative charge.
Pb --> Pb2+ + 2e- (Anode reaction)
Pb2+ ions combine with sulphate ions to form insoluble lead sulphate, PbSO4, which begins to coat lead electrode.
Pb2+ + SO42- ---> PbSO4 (Precipitation)
The electrons are utilized at PbO2 electrode.
PbO2 + 4H+ + 2e- ---> Pb2+ 2H2O (Cathode reaction)
Pb2+ + SO42- ---> PbSO4 (Precipitation)
Overall cell reaction is:
Pb + PbO2 + 4H+ + 2 SO42- ---> 2PbSO4 + 2H2O
Ecell is 2.041 volt.
When a potential slightly greater than the potential of battery is applied, the battery can be re-charged.
2PbSO4 + 2H2O ---> Pb + PbO2 + 2H2SO4
After many repeated charge-discharge cycles, some of the lead sulphate falls to the bottom of the container, the sulphuric acid concentration remains low and the battery cannot be recharged fully.
Fuel cells are another means by which chemical energy may be converted into electrical energy. The main disadvantage of a primary cell is that it can deliver current for a short period only. This is due to the fact that the quantity of oxidising agent and reducing agent is limited. But the energy can be obtained indefinitely from a fuel cell as long as the outside supply of fuel is maintained. One of the examples is the hydrogen-oxygen fuel cell. The cell consists of three compartments separated by a porous electrode. Hydrogen gas is introduced into one compartment and oxygen gas is fed into another compartment. These gases then diffuse slowly through the electrodes and react with an electrolyte that is in the central compartment. The electrodes are made of porous carbon and the electrolyte is a resin containing concentrated aqueous sodium hydroxide solution. Hydrogen is oxidised at anode and oxygen is reduced at cathode. The overall cell reaction produces water. The reactions which occur are:
Anode [H2(g) + 2OH-(aq) ---> 2H2O(l) + 2e-] Ã- 2
Cathode O2(g) + 2H2O(l) + 4e- ---> 4OH-(aq)
Overall 2H2(g) + O2(g) ---> 2H20(l)
This type of cells are used in space-crafts. Fuel cells are efficient and pollution free.
If two plates of the same metal are dipped separately into two solutions of the same electrolyte and are connected with a salt bridge, the whole arrangement is found to act as a galvanic cell. In general, there are two types of concentration cells:
(i) Electrode concentration cells:
In these cells, the potential difference is developed between two like electrodes at different concentrations dipped in the same solution of the electrolyte. For example, two hydrogen electrodes at different has pressure in the same solution of hydrogen ions constitute a cell of this type.
(Pt,H2 (Pressure p1))/Anode |H+ | (H2 (Pressure p2)Pt)/Cathode
If p1, p2 oxidation occurs at L.H.S. electrode and reduction occurs at R.H.S. electrode.
Ecell = 0.0591/2 log(p1/p2) at 25o C
In the amalgam cells, two amalgams of the same metal at two different concentrations are interested in the same electrolyte solution.
(ii) Electrolyte concentration cells:
In these cells, electrodes are identical but these are immersed in solutions of the same electrolyte of different concentrations. The source of electrical energy in the cell is the tendency of the electrolyte to diffuse from a solution of higher concentration to that of lower concentration. With the expiry of time, the two concentrations tend to become equal. Thus, at the start the emf of the cell is maximum and it gradually falls to zero. Such a cell is represented in the following manner:
(C2 is greater than C1).
or (Zn|Zn2+ (C1))/Anode || (Zn2+ (C2 )|Zn)/Cathode
The emf of the cell is given by the following expression:
Ecell = 0.0591/n log C(2(R.H.S.))/C(1(L.H.S.)) at 25o C
The concentration cells are used to determine the solubility of sparingly soluble salts, valency of the cation of the electrolyte and transition point of the two allotropic forms of a metal used as electrodes, etc.
Relation between Equilibrium constant, Gibbs free energy and EMF of the cell
Concept of equilibrium in electrochemical cell
In an electrochemical cell a reversible redox process takes place, e.g., in Daniell cell:
Zn(s)+Cu2+(aq) <==> Zn2+(aq)+Cu(s)
(1) At equilibrium mass action ratio becomes equal to equilibrium constant,
i.e., Q = Ke
(2) Oxidation potential of anode = -Reaction potential of cathode
emf = oxidation potential of anode + Reduction potential of cathode = 0
Cell is fully discharged
According to Nernst equation:
E = Eo - 0.0591/n log10 Q at 25o
At equilibrium, E = 0, Q = K
0 = Eo 0.0591/n log10 K
K = Antilog [(nEo)/0.0591]
Work done by the cell
Let n faraday charge be taken out of a cell of emf E; then work done by the cell will be calculated as:
Work = Charge x Potential = nFE
Work done by the cell is equal to decrease in free energy.
-âˆ†G = nFE
Similarly, maximum obtainable work from the cell will be
Wmax = nFE°
where, Eo = standard emf or standard cell potential.
-âˆ†G = nFE
The relationship among K, âˆ†Go and Eo cell
Heat of reaction in an electrochemical cell
Let n Faraday charge flows out of a cell of emf E,
Then -âˆ†G = nFE ...... (i)
Gibbs-Helmholtz equation from thermodynamics may be given as
âˆ†G = âˆ†H + T (âˆ‚âˆ†G/âˆ‚T)P ...... (ii)
From equation (i) and (ii) we get
-nFE = âˆ†H + T (âˆ‚(-nFE)/âˆ‚T)P = âˆ†H-nFT(âˆ‚E/âˆ‚T)P
âˆ†H = -nFE + nFT(âˆ‚E/âˆ‚T)P
Here (âˆ‚E/âˆ‚T)P = Temperature coefficient of cell
Case I: When (âˆ‚E/âˆ‚T)P = 0, then âˆ†H=-nFE
Case II: When (âˆ‚E/âˆ‚T)>0, then nFE>âˆ†H, i.e., process inside the cell is endothermic.
Case III: When (âˆ‚E/âˆ‚T)<0 , then nFE<âˆ†H, i.e., process inside the cell is exothermic.
ELECTRODE AND CELL POTENTIALS /NERNST EQUATION
The electrode potential and the emf of the cell depend upon the nature of the electrode, temperature and the activities (concentrations) of the ions in solution. The variation of electrode and cell potentials with concentration of ions in solution can be obtained from thermodynamic considerations. For a general reaction such as
M1A + m2B ..... n1X + n2Y + .... .......(i)
occurring in the cell, the Gibbs free energy change is given by the equation
G => âˆ†Go + 2.303RT log10 (axn1 Ã- ayn2)/(aAm1 Ã- aBm2) ....... (ii)
where 'a' represents the activities of reactants and products under a given set of conditions and âˆ†Go refers to free energy change for the reaction when the various reactants and products are present at standard conditions. The free energy change of a cell reaction is related to the electrical work that can be obtained from the cell, i.e., âˆ†Go = -nFEcell and âˆ†Go = -nFEo. On substituting these values in Eq. (ii) we get
-nFEcell => -nFEo + 2.30eRT log10 (axn1 Ã- ayn2)/(aAm1 Ã- aBm2) ....... (iii)
or Ecell => Ecello - 2.303RT/nF log10 (axn1 Ã- ayn2)/(aAm1 Ã- aBm2) ....... (iv)
This equation is known as Nearnst equation.
Putting the values of R=>8.314 JK-1 mol-1, T => 298 K and F=>96500 C, Eq. (iv) reduces to
E => Eo - 0.0591/n log10 (axn1 Ã- ayn2)/(aAm1 Ã- aBm2) ....... (v)
=> Eo - 0.0591/n log10 ([Products])/([Reactants]) ....... (vi)
Potential of single electrode (Anode): Consider the general oxidation reaction,
M --> Mn+ + ne-
Applying Nernst equation,
Eox => Eoxo - 0.0591/n log10 [Mn+]/[M]
where Eox is the oxidation potential of the electrode (anode), is the standard oxidation potential of the electrode.
[Note: The concentration of pure solids and liquids are taken as unity.]
Eox => Eoxo - 0.0591/n log10 [Mn+]
Let us consider a Daniell cell to explain the above equations. The concentrations of the electrolytes are not 1 M.
Zn(s)+Cu2+(aq) <=> Zn2+(aq) + Cu(s)
Potential at zinc electrode (Anode)
Eox => Eoxo - 0.0591/n log10 [Zn3+]
Potential at copper electrode (Cathode)
Ered => Eredo - 0.0591/n log10 [Cu2+]
Emf of the cell
Ecell => Eox + Ered => (Eoxo + Eredo )- 0.0591/n [Zn2+/Cu2+]
The value of n = 2 for both zinc and copper.
Let us consider an example, in which the values of n for the two ions in the two half-cells are not same. For example, in the cell
The cell reaction is
Cu(s) + 2Ag+ ---> Cu2+ + 2Ag
The two half-cell reaction are:
Cu --> Cu2+ + 2e-
Ag+ + e- --> Ag
The second equation is multiplied by 2 to balance the number of electrons.
2Ag+ + 2e- --> 2 Ag
Eox => Eoxo - 0.0591/2 log10[Cu2+]
Ered => Eredo - 0.0591/2 log10[Ag+]2
Ecell = Eox + Ered => Eoxo - 0.0591/2 log10 [Cu2+]/[Ag+]2 = >
Ecell => 0.0591/2 log10 [Cu2+]/[Ag+]2