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Though there are a number of methods for balancing oxidation – reduction reactions, two methods are very important. These are, (1) Oxidation number method (2)  Ion – electron method (1) Oxidation number method : The method for balancing redox reactions by oxidation number change method was developed by Johnson. In a balanced redox reaction, total increase in oxidation number must be equal to the total decrease in oxidation number. This equivalence provides the basis for balancing redox reactions. This method is applicable to both molecular and ionic equations. The general procedure involves the following steps, (i) Write the skeleton equation (if not given, frame it) representing the chemical change. (ii) Assign oxidation numbers to the atoms in the equation and find out which atoms are undergoing oxidation and reduction. Write separate equations for the atoms undergoing oxidation and reduction. (iii) Find the change in oxidation number in each equation. Make the change equal in both the equations by multiplying with suitable integers. Add both the equations. (iv) Complete the balancing by inspection. First balance those substances which have undergone change in oxidation number and then other atoms except hydrogen and oxygen. Finally balance hydrogen and oxygen by putting H2O molecules wherever needed. The final balanced equation should be checked to ensure that there are as many atoms of each element on the right as there are on the left. (v) In ionic equations the net charges on both sides of the equation must be exactly the same. Use H+ ion/ions in acidic reactions and OH– ion/ions in basic reactions to balance the charge and number of hydrogen and oxygen atoms. The following example illustrate the above rules, Step : I \[Cu+HN{{O}_{3}}\to Cu{{(N{{O}_{3}})}_{2}}+N{{O}_{2}}+{{H}_{2}}O\] (Skeleton equation) Step: II  Writing the oxidation number of all the atoms. \[\overset{0}{\mathop{Cu}}\,\,\,+\,\,\overset{+1}{\mathop{H}}\,\overset{+5}{\mathop{N}}\,{{\overset{\,-2}{\mathop{O}}\,}_{3}}\,\,\,\to \,\,\,\overset{+2}{\mathop{Cu}}\,\,{{(\,\overset{+5}{\mathop{N}}\,{{\overset{-2}{\mathop{O}}\,}_{3}})}_{2}}\,\,+\,\,\overset{+4}{\mathop{N}}\,{{\overset{-2}{\mathop{O}}\,}_{2}}\,+\,\,{{\overset{+1}{\mathop{H}}\,}_{2}}\overset{-2}{\mathop{O}}\,\] Step: III Change in oxidation number has occurred in copper and nitrogen. \[\overset{0}{\mathop{Cu}}\,\to \overset{+2}{\mathop{Cu}}\,\,{{(N{{O}_{3}})}_{2}}\]                                     ......(i) \[H\overset{+5}{\mathop{N}}\,{{O}_{3}}\to \overset{+4}{\mathop{N}}\,{{O}_{2}}\]                                        ......(ii) Increase in oxidation number of copper     = 2 units per molecule Cu Decrease in oxidation number of nitrogen = 1 unit per molecule HNO3 Step: IV  To make increase and decrease equal, equation (ii) is multiplied by 2. \[Cu+2HN{{O}_{3}}\to Cu\,{{(N{{O}_{3}})}_{2}}+2N{{O}_{2}}+{{H}_{2}}O\] Step: V     Balancing nitrate ions, hydrogen and oxygen, the following equation is obtained. \[Cu+4HN{{O}_{3}}\to Cu\,{{(N{{O}_{3}})}_{2}}+2N{{O}_{2}}+2{{H}_{2}}O\] This is the balanced equation. (2) Ion-electron method (half reaction method) Jette and LaMev developed the method for balancing redox-reactions by ion electron method in 1927. It involves the following steps (i) Write down the redox reaction in ionic form. (ii) Split the redox reaction into two half reactions, one for oxidation and other for reduction. (iii) Balance each half reaction for the number of atoms of each element. For this purpose, (a) Balance the atoms other than H and O for each half reaction using simple multiples. (b) Add water molecules to the side deficient in oxygen and H+ to the side deficient in hydrogen. This is done in acidic or neutral solutions. (c) In alkaline solution, for each excess of oxygen, add one water molecule to the more...

(1) Definition : Charge on an atom produced by donating or accepting electrons is called oxidation number or oxidation state. It is the number of effective charges on an atom. (2) Valency and oxidation number : Valency and oxidation number concepts are different. In some cases (mainly in the case of electrovalent compounds), valency and oxidation number are the same but in other cases they may have different values. Points of difference between the two have been tabulated below
Oxidation number Valency
O.N. is the charge (real or imaginary) present on the atom of the element when it is in combination. It may have plus or minus sign. It is the combining capacity of the element. No plus or minus sign is attached to it.
O.N. of an element may have different values. It depends on the nature of compound in which it is present. Valency of an element is usually fixed.
O.N. of the element may be a whole number or fractional. Valency is always a whole number.
O.N. of the element may be zero. Valency of the element is never zero except of noble gases.
(3) Oxidation number and Nomenclature (i) When an element forms two monoatomic cations (representing different oxidation states), the two ions are distinguished by using the ending-ous and ic. The suffix – ous is used for the cation with lower oxidation state and the suffix – ic is used for the cation with higher oxidation state. For example : Cu+ (oxidation number +1) cuprous                       Cu2+ (oxidation number +2) cupric (ii) Albert Stock proposed a new system known as Stock system. In this system, Roman numeral written in parentheses immediately after the name of the element indicates the oxidation states. For example,  
Cu2O Copper (I) oxide SnO    Tin (II) oxide
FeCl2 Iron (II) chloride Mn2O7 Manganess (VII) oxide
K2Cr2O7  Potassium dichromate (VI) Na2CrO4 Sodium chromate (VI)
V2O5 Vanadium (V) oxide CuO Copper (II) oxide
SnO2 Tin (IV) oxide FeCl3 Iron (III) chloride
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(1) Definition : The substance (atom, ion or molecule) that gains electrons and is thereby reduced to a low valency state is called an oxidising agent, while the substance that loses electrons and is thereby oxidised to a higher valency state is called a reducing agent.        Or An oxidising agent is a substance, the oxidation number of whose atom or atoms decreases while a reducing agent is a substance the oxidation number of whose atom increases. (2) Important oxidising agents (i) Molecules made up of electronegative elements. Example :  O2, O3 and X2 (halogens). (ii) Compounds containing an element which is in the highest oxidation state. Example : , etc. (iii) Oxides of elements,  etc. (iv) Fluorine is the strongest oxidising agent. (3) Important reducing agents (i) All metals e.g. Na, Zn, Fe, Al, etc. (ii) A few non-metals e.g. C, H2, S etc. (iii) Hydracids : HCl, HBr, HI, H2S etc. (iv) A few compounds containing anelement in the lower oxidation state (ous). Example :  etc. (v) Metallic hydrides e.g. NaH, LiH etc. (vi) Organic compounds like HCOOH and (COOH)2 and their salts, aldehydes, alkanes etc. (vii) Lithium is the strongest reducing agent in solution. (viii) Cesium is the strongest reducing agent in absence of water. Other reducing agents are  and KI. (ix) Hypo prefix indicates that central atom of compound has the minimum oxidation state so it will act as a reducing agent. Example :  (hypophosphorous acid). (4) Substances which act as oxidising as well as reducing agents Examples : H2O2,SO2,H2SO3,HNO2,NaNO2,Na2SO3,O3 etc. (5) Tips for the identification of oxidising and reducing agents (i) If an element is in its highest possible oxidation state in a compound, the compound can function as an oxidising agent. Example : etc. (ii) If an element is in its lowest possible oxidation state in a compound, the compound can function only as a reducing agent.  Example :  etc. (iii) If an element is in its intermediate oxidation state in a compound, the compound can function both as an oxidising agent as well as reducing agent. Example : etc. (iv) If a highly electronegative element is in its highest oxidation state in a compound, that compound can function as a powerful oxidising agent. Example :  etc. (v) If an electronegative element is in its lowest possible oxidation state in a compound or in free state, it can function as a powerful reducing agent. Example :  etc. (6) Equivalent weight of oxidising and reducing agents Equivalent weight of a substance (oxidant or reductant) is equal to molecular weight divided by number of electrons lost or gained by one molecule of the substance in a redox reaction. Eq. wt. of O. A. \[=\frac{Molecular\,\,weight}{No.\,\,of\,\,electrons\,\,gained\,\,by\,\,one\,\,molecule}\]                           \[=\frac{Molecular\,\,weight}{Change\,\,O.N.\,\,per\,\,mole}\] Eq. wt. of R. A.   \[=\frac{Molecular\,\,weight}{No.\,\,of\,\,electrons\,\,lost\,\,by\,\,one\,\,molecule}\]                                \[=\frac{Molecular\,\,weight}{Change\,\,in\,\,O.N.\,\,per\,\,mole}\] Equivalent weight of few oxidising/reducing agents
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(1) Oxidation : Oxidation is a process which involves; addition of oxygen, removal of hydrogen, addition of non-metal, removal of metal, Increase in +ve valency, loss of electrons and increase in oxidation number. (i)  Addition of oxygen : 2Mg + O2 \[\to \]2MgO                     (ii) Removal of hydrogen : H2S+Cl2\[\to \]2HCl + S      (iii) Addition of Non-metal : Fe + S \[\to \] FeS               (iv) Removal of metal : 2KI+H2O2\[\to \]2KOH+I2 (v) Increase in +ve valency : \[F{{e}^{2+}}\,\to \,F{{e}^{3+}}+{{e}^{-}}\]                         (vi) Loss of electrons (also known as de-electronation) (a) \[{{H}^{0}}\to {{H}^{+}}+{{e}^{-}}\]            (Formation of proton) (b) \[MnO_{4}^{2-}\to MnO_{4}^{-}+{{e}^{-}}\]      (De-electronation of \[MnO_{4}^{2-}\]) (c) \[2F{{e}^{0}}\to 2Fe_{{}}^{3+}+6{{e}^{-}}\]      (De-electronation of iron) (vii) Increase in oxidation number (a) \[M{{g}^{0}}\to M{{g}^{2+}}\]                         (From 0 to +2) (b) \[{{\left[ F{{e}^{+2}}{{(CN)}_{6}} \right]}^{4-}}\to {{\left[ F{{e}^{+3}}{{(CN)}_{6}} \right]}^{3-}}\]   (From +2 to +3) (c) \[2C{{l}^{-}}\to Cl_{2}^{0}\]                             (From –1 to 0) (2) Reduction : Reduction is just reverse of oxidation. Reduction is a process which involves; removal of oxygen, addition of hydrogen, removal of non-metal, addition of metal, decrease in +ve valency, gain of electrons and decrease in oxidation number. (i) Removal of oxygen : \[CuO+C\to Cu+CO\]            (ii) Addition of hydrogen : \[C{{l}_{2}}+{{H}_{2}}\to 2HCl\] (iii) Removal of non-metal  \[2HgC{{l}_{2}}+SnC{{l}_{2}}\to H{{g}_{2}}C{{l}_{2}}+SnC{{l}_{4}}\] (iv) Addition of metal : \[HgC{{l}_{2}}+Hg\to H{{g}_{2}}C{{l}_{2}}\] (v) Decrease in +ve valency  (a) \[F{{e}^{3+}}\,\to \,F{{e}^{2+}}\]     (+ve valency decreases) (b) \[{{[Fe\,{{(CN)}_{6}}]}^{3-}}\to {{[Fe{{(CN)}_{6}}]}^{4-}}\] (–ve valency increases) (vi) Gain of electrons (also known as electronation) (a) \[Z{{n}^{2+}}(aq)+2{{e}^{-}}\to Zn(S)\] (Electronation of \[Z{{n}^{2+}}\]) (b) \[P{{b}^{2+}}+2{{e}^{-}}\to P{{b}^{0}}\] (Electronation of \[P{{b}^{2+}}\]) (c) \[{{[Fe{{(CN)}_{6}}]}^{3-}}+{{e}^{-}}\to {{[Fe{{(CN)}_{6}}]}^{4-}}\]                     (Electronation of \[{{[Fe{{(CN)}_{6}}]}^{3-}}\]) (vii) Decrease in oxidation number (a) \[M{{g}^{2+}}\to M{{g}^{0}}\]                         (From +2 to 0) (b) \[{{\left[ Fe{{(CN)}_{6}} \right]}^{3-}}\to {{\left[ Fe{{(CN)}_{6}} \right]}^{4-}}\]               (From +3 to +2) (c) \[Cl_{2}^{0}\to 2C{{l}^{-}}\]                             (From 0 to –1) (3) Redox-reactions (i) An overall reaction in which oxidation and reduction takes place simultaneously is called redox or oxidation-reduction reaction. These reactions involve transfer of electrons from one atom to another. Thus every redox reaction is made up of two half reactions; One half reaction represents the oxidation and the other half reaction represents the reduction. (ii) Types of redox reaction (a) Direct redox reaction : The reactions in which oxidation and reduction takes place in the same vessel are called direct redox reactions. (b) Indirect redox reaction : The reactions in which oxidation and reduction takes place in different vessels are called indirect redox reactions. Indirect redox reactions are the basis of electro-chemical cells. (c) Intermolecular redox reactions : In which one substance is oxidised while the other is reduced. For example, \[2\,Al+F{{e}_{2}}{{O}_{3}}\to A{{l}_{2}}{{O}_{3}}+2Fe\] Here, Al is oxidised to \[A{{l}_{2}}{{O}_{3}}\] while \[F{{e}_{2}}{{O}_{3}}\]is reduced to Fe. (d) Intramolecular redox reactions : In which one element of a compound is oxidised while the other is reduced. For example, \[2\,KCl{{O}_{3}}\xrightarrow{\Delta }2\,KCl+3\,{{O}_{2}}\] Here, \[C{{l}^{+5}}\] in \[KCl{{O}_{3}}\] is reduced to \[C{{l}^{-1}}\] in KCl while \[{{O}^{2-}}\] in \[KCl{{O}_{3}}\] is oxidised to \[O_{2}^{0}\].

(1) Molecular equations : When the reactants and products involved in a chemical change are written in molecular forms in the chemical equation, it is termed as molecular equation. Example :  \[Mn{{O}_{2}}+4\,HCl\to MnC{{l}_{2}}+2{{H}_{2}}O+C{{l}_{2}}\] In above example the reactants and products have been written in molecular forms, thus the equation is termed as molecular equation. (2) Ionic equations : When the reactants and products involved in a chemical change are ionic compounds, these will be present in the form of ions in the solution. The chemical change is written in ionic forms in chemical equation, it is termed as ionic equation. Example, \[Mn{{O}_{2}}+4\,{{H}^{+}}+4\,C{{l}^{-}}\]\[\to \]\[\,M{{n}^{2+}}+2C{{l}^{-}}+2{{H}_{2}}O+C{{l}_{2}}\] In above example the reactants and products have been written in ionic forms, thus the equation is termed as ionic equation. (3) Spectator ions : In ionic equations, the ions which do not undergo any change and equal in number in both reactants and products are termed as spectator ions and are not included in the final balanced equations. Example, \[Zn+2{{H}^{+}}+2C{{l}^{-}}\,\]\[\to \]\[Z{{n}^{2+}}+{{H}_{2}}+2C{{l}^{-}}\]    (Ionic equation) \[Zn+2{{H}^{+}}\] \[\to \]\[Z{{n}^{2+}}+{{H}_{2}}\]                           (Final ionic equation)            In above example, the \[C{{l}^{-}}\] ions are the spectator ions and hence are not included in the final ionic balanced equation.

(1) When metals are exposed to atmospheric conditions, they react with air or water in the environment to form undesirable compounds (usually oxides). This process is called corrosion. Almost all metals except the least active metals such as gold, platinum and palladium are attacked by environment i.e., undergo  corrosion. For example, silver tarnishes, copper develops a green coating, lead or stainless steel lose their lusture due to corrosion. Corrosion causes enormous damage to building, bridges, ships and many other articles made of iron. Thus corrosion is a process of deterioration of a metal as a result of its reaction with air or water (environment) surrounding it. In case of iron, corrosion is called rusting. Chemically, rust is hydrated form of ferric oxide, \[F{{e}_{2}}{{O}_{3}}\]. \[x{{H}_{2}}O\]. Rusting of iron is generally caused by moisture, carbon dioxide and oxygen present in air. It has been observed that rusting takes place only when iron is in contact with moist air. Iron does not rust in dry air and in vacuum. (2) Factors which affect corrosion : The main factors which affect corrosion are More the reactivity of metal, the more will be the possibility of the metal getting corroded. The impurities help in setting up voltaic cells, which increase the speed of corrosion Presence of electrolytes in water also increases the rate of corrosion Presence of \[C{{O}_{2}}\]in natural water increase rusting of iron. (v) When the iron surface is coated with layers of metals more active than iron, then the rate of corrosion is retarded. A rise in temperature (with in a reasonable limit) increases the rate of corrosion. (3) Classification of corrosion process : Depending upon the nature of corrosion, and the factors affecting it, the corrosion may be classified as follows. (i) Chemical corrosion : Such corrosion, generally takes place when (a) Reactive gases come in contact with metals at high temperatures e.g., corrosion in chemical industry. (b) Slow dissolution of metal takes place when kept in contact with non conducting media containing organic acids. (ii) Bio-chemical corrosion or Bio-corrosion: This is caused by the action of microorganisms. Soils of definite composition, stagnant water and certain organic products greatly favour the bio-corrosion. (iii) Electrochemical corrosion : It occurs in a gaseous atmosphere in the presence of moisture, in soils and in solutions. (4) Mechanism of rusting of iron : Electrochemical theory of rusting. The overall rusting involves the following steps, (i) Oxidation occurs at the anodes of each electrochemical cell. Therefore, at each anode neutral iron atoms are oxidised to ferrous ions. At anode : \[Fe(s)\xrightarrow{{}}F{{e}^{2+}}(aq)+2{{e}^{-}}.\] Thus, the metal atoms in the lattice pass into the solution as ions, leaving electrons on the metal itself. These electrons move towards the cathode region through the metal. (ii) At the cathodes of each cell, the electrons are taken up by hydrogen ions (reduction takes place). The \[{{H}^{+}}\] ions are obtained either from water or from acidic substances (e.g. \[C{{O}_{2}})\] in water \[{{H}_{2}}O\xrightarrow{{}}{{H}^{+}}+O{{H}^{-}}\]  more...

(1) The standard reduction potentials of a large number of electrodes have been measured using standard hydrogen electrode as the reference electrode. These various electrodes can be arranged in increasing or decreasing order of their reduction potentials. The arrangement of elements in order of increasing reduction potential values is called electrochemical series.It is also called activity series, of some typical electrodes. (2) Characteristics of Electrochemical series (i) 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 value 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. Standard reduction electrode potentials at 298K   (3) Application 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 \[({{M}^{n+}})\]. 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 more...

The electrical work (electrical energy) is equal to the product of the EMF of the cell and electrical charge that flows through the external circuit i.e., \[{{W}_{\max }}=nF{{E}_{cell}}\]                                                                ......(i) According to thermodynamics the free energy change \[(\Delta G)\] is equal to the maximum work. In the cell work is done on the surroundings by which electrical energy flows through the external circuit, So \[-{{W}_{\max ,}}=\Delta G\]                                                                     ......(ii) from eq. (i) and (ii) \[\Delta G=-nFE_{cell}^{{}}\] In standard conditions  \[\Delta {{G}^{0}}=-\,nFE_{cell}^{0}\] Where \[\Delta {{G}^{0}}=\]standard free energy change But \[E_{cell}^{0}=\frac{2.303}{nF}RT\,\log {{K}_{c}}\] \[\therefore \]\[\Delta {{G}^{0}}=-nF\times \frac{2.303}{nF}RT\,\log \,{{K}_{c}}\] \[\Delta {{G}^{0}}=-\text{ 2}\text{.303 RT log }{{\text{K}}_{\text{c}}}\text{ }\]or \[\Delta G=\Delta G{}^\circ +2.303RT\log Q\] \[\Delta {{G}^{0}}=-RT\,\ln \,{{K}_{c}}\,\,\,\,\,\,\,\,(2.303\,\log X=\ln \,X)\]

(1) Nernst’s equation for electrode potential The potential of the electrode at which the reaction, \[{{M}^{n+}}(aq)+n{{e}^{-}}\to M(s)\] takes place is described by the equation,  \[{{E}_{{{M}^{n+}}/M}}=E_{{{M}^{n+}}/M}^{0}-\frac{RT}{nF}\ln \frac{[M(s)]}{[{{M}^{n+}}(aq.)]}\] or\[{{E}_{{{M}^{n+}}/M}}=E_{{{M}^{n+}}/M}^{0}-\frac{2.303\,\,RT}{nF}\log \frac{[M(s)]}{[{{M}^{n+}}(aq)]}\] above eq. is called the Nernst equation. Where, \[{{E}_{{{M}^{n+}}/M}}\]= the potential of the electrode at a given concentration, \[E_{{{M}^{n+}}/M}^{0}\] = the standard electrode potential R =  the universal gas constant, \[8.31\ J\,{{K}^{-1}}\,mo{{l}^{-1}}\] T= the temperature on the absolute scale, n = the number of electrons involved in the electrode reaction, F = the Faraday constant : (96500 C), \[[M(s)]\]= the concentration of the deposited metal, \[[{{M}^{n+}}(aq)]\]= the molar concentration of the metal ion in the solution, The concentration of pure metal M(s) is taken as unity. So, the Nernst equation for the \[{{M}^{n+}}/M\] electrode is written as,  \[{{E}_{{{M}^{n+}}/M}}=E_{{{M}^{n+}}/M}^{0}-\frac{2.303\,\,RT}{nF}\log \frac{1}{[{{M}^{n+}}(aq)]}\] At 298 K, the Nernst equation for the  \[{{M}^{n+}}/M\] electrode can be written as, \[{{E}_{{{M}^{n+}}/M}}=E_{{{M}^{n+}}/M}^{0}-\frac{0.0591}{n}\log \frac{1}{[{{M}^{n+}}(aq)]}\] For an electrode (half - cell) corresponding to the electrode reaction, Oxidised form \[+n{{e}^{-}}\to \]Reduced form The Nernst equation for the electrode is written as, \[{{E}_{half-cell}}=E_{half-cell}^{0}-\frac{2.303\,RT}{nF}\log \frac{[\text{Reduced form }]}{\text{ }\!\![\!\!\text{ Oxidised form }\!\!]\!\!\text{ }}\] At 298 K,  the Nernst equation can be written as, \[{{E}_{half-cell}}=E_{half-cell}^{0}-\frac{0.0591}{n}\log \frac{[\text{Reduced form }]}{\text{ }\!\![\!\!\text{ Oxidised form }\!\!]\!\!\text{ }}\] (2) Nernst’s equation for cell EMF For a cell in which the net cell reaction involving n electrons is, \[aA+bB\to cC+dD\] The Nernst equation is written as, \[{{E}_{cell}}=E_{cell}^{0}-\frac{RT}{nF}\text{ln}\frac{{{\text{ }\!\![\!\!\text{ C }\!\!]\!\!\text{ }}^{\text{c}}}{{[D]}^{d}}}{{{[A]}^{a}}{{[B]}^{b}}}\] Where, \[E_{cell}^{0}=E_{cathode}^{0}-E_{anode}^{0}\].  The \[E_{cell}^{o}\] is called the standard cell potential. or  \[{{E}_{\text{cell}}}=E_{cell}^{o}-\frac{2.303\,RT}{nF}\log \frac{{{[C]}^{c}}{{[D]}^{d}}}{{{[A]}^{a}}{{[B]}^{b}}}\] At 298 K, above eq. can be written as, or \[{{E}_{\text{cell}}}=E_{cell}^{o}-\frac{0.0592}{n}\log \frac{{{[C]}^{c}}{{[D]}^{d}}}{{{[A]}^{a}}{{[B]}^{b}}}\] It may be noted here, that the concentrations of A, B, C and D referred in the eqs. are the concentrations at the time the cell emf is measured. (3) Nernst’s equation for Daniells cell :  Daniell’s cell consists of zinc and copper electrodes. The electrode reactions in Daniell’s cell are, At anode :                    \[Zn(s)\to Z{{n}^{2+}}(aq)+2{{e}^{-}}\] At cathode : \[C{{u}^{2+}}(aq)+2{{e}^{-}}\to Cu(s)\] Net cell reaction :        \[Zn(s)+C{{u}^{2+}}(aq)\to Cu(s)+Z{{n}^{2+}}(aq)\] Therefore, the Nernst equation for the Daniell’s cell is, \[{{E}_{cdll}}=E_{cell}^{0}-\frac{2.303\,RT}{2F}\log \frac{[Cu(s)][Z{{n}^{2+}}(aq)]}{[Zn(s)][C{{u}^{2+}}(aq)]}\] Since, the activities of pure copper and zinc metals are taken as unity, hence the Nernst equation for the Daniell’s cell is, \[{{E}_{cdll}}=E_{cell}^{0}-\frac{2.303\,RT}{2F}\log \frac{[Z{{n}^{2+}}(aq]}{[C{{u}^{2+}}(aq)]}\] The above eq. at 298 K is, \[{{E}_{cdll}}=E_{cell}^{o}-\frac{0.0591}{2}\log \frac{[Z{{n}^{2+}}(aq]}{[C{{u}^{2+}}(aq)]}V\] For Daniells cell,  \[E_{cell}^{0}=1.1\,V\] (4) Nernst's equation and equilibrium constant        For a cell, in which the net cell reaction involving n electrons is,  \[aA+bB\to cC+dD\]                                                           The Nernst equation is \[{{E}_{Cell}}=E_{cell}^{0}-\frac{RT}{nF}\ln \,\frac{{{[C]}^{c}}{{[D]}^{d}}}{{{[A]}^{a}}{{[B]}^{b}}}\]                                        .....(i) At equilibrium, the cell cannot perform any useful work. So at equilibrium, \[{{E}_{Cell}}\]is zero. Also at equilibrium, the ratio \[\frac{{{[C]}^{c}}{{[D]}^{d}}}{{{[A]}^{a}}{{[B]}^{b}}}={{\left[ \frac{{{[C]}^{c}}{{[D]}^{d}}}{{{[A]}^{a}}{{[B]}^{b}}} \right]}_{equilibrium}}={{K}_{c}}\]

(1) “The difference in potentials of the two half – cells of a cell known as electromotive force (emf) of the cell or cell potential.” The difference in potentials of the two half – cells of a cell arises due to the flow of electrons from anode to cathode and flow of current from cathode to anode. \[Anode\underset{Flow\,\,of\,\,current}{\overset{Flow\,\,of\,\,electrons}{\longleftrightarrow}}Cathode\] (2) The emf of the cell or cell potential can be calculated from the values of electrode potentials of two the 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 \[E_{\text{cell}}^{0}=\] Oxidation potential of anode + Reduction potential of cathode \[=E_{\text{ox}}^{0}\,(\text{anode})+E_{\text{red}}^{\text{0}}(\text{cathode})\] (ii) When reduction potentials of both electrodes are taken into account \[=E_{\text{Cathode}}^{\text{0}}-E_{\text{Anode}}^{\text{0}}\]\[=E_{\text{right}}^{\text{o}}-E_{\text{left}}^{o}\] (iii) When oxidation potentials of both electrodes are taken into account \[E_{\text{cell}}^{o}=\] Oxidation potential of anode – Oxidation potential of cathode \[=E_{\text{ox}}^{0}(\text{anode})-E_{\text{ox}}^{0}(\text{cathode})\]       (3) Difference between emf and potential difference
Emf Potential difference
It is the potential difference between two electrodes when no current is flowing in the circuit. It is the difference of the electrode potentials of the two electrodes when the cell is under operation.
It is the maximum voltage that the cell can deliver. It is always less then the maximum value of voltage which the cell can deliver.
It is responsible for the steady flow of current in the cell. It is not responsible for the steady flow of current in the cell.
(4) Cell EMF and the spontaneity of the reaction :         We know, \[\Delta G=-nF{{E}_{cell}}\]
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