CBSE Class 12 Chemistry Electrochemistry Notes Set 07

Revision Notes

Electrolytic Conductivity, Electrolytes and Kohlrausch’s Law

• Electrochemistry is the branch of chemistry which deals with the study of the production of electricity from energy released during spontaneous chemical reactions and the use of electrical energy to result in non-spontaneous chemical transformations.

• Electrolytic conduction: The flow of electric current through an electrolytic solution is called electrolytic conduction.
• Electrolyte: A substance that dissociates in solution to produce ions and hence conducts electricity in dissolved state or molten state.
  Weak electrolyte – \( \text{H}_2\text{CO}_3 \), \( \text{CH}_3\text{COOH} \), \( \text{HCN} \), \( \text{MgCl}_2 \)
  Strong electrolyte – \( \text{NaCl} \), \( \text{HCl} \), \( \text{NaOH} \)
• Degree of ionisation: It is the ratio of number of ions produced to the total number of molecules in electrolyte.
• Resistance is defined as the property of given substance to obstruct the flow of charge. It is directly proportional to the length (l) and inversely proportional to its area of cross-section (A).
  \( R \propto \frac{l}{A} \) or; \( R = \rho \frac{l}{A} \)
  \( \rho = \) Resistivity or specific resistance.
• Resistivity: If a solution is placed in between two parallel electrodes having cross sectional area ‘A’ and distance ‘l’ apart, then
  \( R = \rho \frac{l}{A} \)
  where \( \rho = \) resistivity and its SI unit is Ohm-m also Ohm-cm is used as a unit.

• Conductance: The ease with which the current flows through a conductor is called conductance. It is reciprocal of resistance. i.e.,
  \( C = \frac{1}{R} = \frac{A}{\rho l} = \kappa \frac{A}{l} \)
  The SI unit of conductance is Siemens (S).
  \( R = \rho \frac{l}{A} \)
  \( 1\text{S} = 1\text{ Ohm}^{-1} = 1\ \Omega^{-1} \)
• Conductivity: It is reciprocal of resistivity and is denoted by \( \kappa \) (Greek Kappa).
  \( \kappa = C \times \frac{l}{A} \)
  where \( C = \) Conductance of the solution
  \( l = \) Distance or length
  \( A = \) Area of cross section
  Its SI unit is \( \text{S m}^{-1} \). Also expressed as \( \text{S cm}^{-1} \).
  It depends upon the:
  (i) Nature of the material,
  (ii) Temperature,
  (iii) The number of valence electrons per atom or size of the ions produced and their solvation (electrolytes)
• Metallic conductance is the electrical conductance in metals that occurs due to the movement of electrons. It depends upon the:
  (i) Nature and structure of the metal,
  (ii) Number of valence electrons per atom,
  (iii) Temperature
• Electrolytic or ionic conductance is the conductance of electricity that occurs due to ions present in the solution. It depends upon the:
  (i) Nature of electrolyte or interionic attractions,
  (ii) Solvation of ions,
  (iii) Nature of solvent and its viscosity,
  (iv) Temperature
• Cell constant (G): It is the ratio of distance between electrodes to the cross-sectional area between electrodes.
  Cell constant (G) \( = \frac{l}{A} = \kappa \text{ in cm}^{-1} \text{ or m}^{-1} \)
  It depends on the:
  (i) Distance between the electrodes
  (ii) Area of cross section
• The resistance of electrolytic solution is determined by wheatstone bridge method where \( R_2 \) is resistance of electrolyte solution. A null point detected by P detector such that,
  Unknown \( R_2 = \frac{R_1 R_4}{R_3} \)
• Molar conductivity: It is defined as the conducting power of all the ions produced by one gram mole of an electrolyte in a solution. It is denoted by \( \Lambda_m \).
  \( \Lambda_m = \frac{\kappa}{C} \times 1000 \text{ S cm}^2 \text{ mol}^{-1} \)
  where \( \kappa = \) Conductivity
  \( C = \) Concentration of solution.
  SI unit of molar conductivity is \( \text{S m}^2 \text{ mol}^{-1} \).
• Debye Huckel Onsager equation: It is applicable for strong electrolyte:
  \( \Lambda_m = \Lambda_m^\circ - A \sqrt{C} \)
  where \( \Lambda^\circ = \) Limiting molar conductivity, \( \Lambda_m = \) Molar conductivity, \( A = \) Constant and \( C = \) Concentration of solution.
• Kohlrausch’s law of independent migration of ions: According to this law, limiting molar conductivity of an electrolyte, at infinite dilution, can be expressed as the sum of contributions from its individual ions. If the molar conductivity of the cations is denoted by \( \lambda_+^\infty \) and that of the anions by \( \lambda_-^\infty \) then the law of independent migration of ions is:
  \( \Lambda_m^\infty = v^+ \lambda_+^\infty + v^- \lambda_-^\infty \text{ or } \Lambda_m^\circ = v^+ \lambda_+^\circ + v^- \lambda_-^\circ \)
• where, \( v^+ \) and \( v^- \) are the number of cations and anions per formula of electrolyte.

Applications of Kohlrausch’s law

(i) Calculation of molar conductivities of weak electrolyte at infinite dilution.
(ii) Calculation of degree of dissociation (\( \alpha \)) of weak electrolytes:
Degree of dissociation (\( \alpha \)) \( = \frac{\Lambda_m}{\Lambda_m^\circ} \)
(iii) Determination of dissociation constant (K) of weak electrolytes:
\( K_a = \frac{C\alpha^2}{(1-\alpha)} = \frac{C\Lambda_m^2}{\Lambda_m^\circ(\Lambda_m^\circ - \Lambda_m)} \)
(iv) Determination of solubility of sparingly soluble salts:
Solubility \( = \frac{\kappa \times 1000}{\Lambda_m^\circ} \)

Redox Reactions and Electrochemical Cells, Electrode Potential and Nernst Equation

• Redox reaction: A chemical reaction in which oxidation and reduction both processes take place simultaneously is known as redox reaction. Oxidation is a process in which any substance loses one or more electrons while reduction is the process in which one or more electrons are gained by another substance.

• Galvanic cell: A device in which the redox reaction is carried indirectly and chemical energy is converted to electrical energy. It is also called galvanic cell or voltaic cell.
• Redox couple: It is defined as having together the oxidised and reduced form of a substance taking part in an oxidation or reduction half reaction.
• Galvanic cell or Voltaic cell: It consists of two metallic electrodes dipped in electrolytic solutions. Electrical energy is produced as a result of chemical reaction which takes place in this cell.
• Daniell cell: It is a type of galvanic cell which consist of two electrodes (Zn and Cu) in contact with the solution of its own ion i.e., \( \text{ZnSO}_4 \) and \( \text{CuSO}_4 \) respectively.
  \( \text{Zn(s)} + \text{Cu}^{2+}\text{(aq)} \rightleftharpoons \text{Zn}^{2+}\text{(aq)} + \text{Cu(s)} \)
  Cell is represented as,
  \( \text{Zn(s)} \mid \text{Zn}^{2+}\text{(aq)} (C_1) \parallel \text{Cu}^{2+}\text{(aq)} (C_2) \mid \text{Cu(s)} \)
• Salt Bridge and its function: It is an inverted U-shaped glass tube which contains a suitable salt in the form of a thick paste made in agar-agar. It performs following functions:
  (i) It completes inner cell circuit.
  (ii) It prevents transference of electrolyte from one half-cell to the other.
  (iii) It maintains the electrical neutrality of the electrolytes in the two half-cells.
• Electrode Potential: It is the potential developed by the electrode with respect to the standard reference electrode. By convention, the reference electrode is standard hydrogen electrode which have a potential of zero volt.
• Standard Electrode Potential: Electrode potential at 25°C, 1 bar pressure and 1 M solution is known as standard electrode potential (E°). The standard electrode potential of any electrode can be measured by connecting it to Standard Hydrogen Electrode (SHE).
  SHE has a standard potential at all temperatures. It consists of a platinum foil coated with platinum black dipped into an aqueous solution in which the \( \text{H}^+ = 1 \text{ M} \) at 25°C and 1 bar pressure.
  The potential difference between the two electrodes of a galvanic cell is called the cell potential (measured in volts). It is also called the emf of the cell when no current is flowing through the circuit.
• EMF of the cell: It is the sum of electric potential differences produced by separation of charges that occur at each phase boundary in the cell.
  \( \text{E}_{\text{cell}} = \text{E}_{\text{cathode}} - \text{E}_{\text{anode}} \)
  In terms of standard oxidation electrode potential:
  \( \text{E}^\circ_{\text{cell}} = \text{E}^\circ_{\text{cathode}} - \text{E}^\circ_{\text{anode}} \)
• where \( \text{E}^\circ_{\text{cathode}} = \) standard electrode potential of cathode
  and \( \text{E}^\circ_{\text{anode}} = \) standard electrode potential of anode
• Standard oxidation potential: It is the potential difference when given electrode is in contact with its ions having 1 molar concentration, undergoes oxidation when coupled with standard hydrogen electrode.
• Electrochemical series: It is the arrangement of the element in order of their increasing electrode potential values. The series has been established by measuring the potential of various electrodes occurs SHE.
• Nernst equation: If the concentration of species in the electrode reaction is not equal to 1 M, then we use Nernst equation. For a general electrode,
  \( \text{M}^{n+}\text{(aq)} + ne^- \rightarrow \text{M(s)} \)
  the Nernst equation can be written as
  \( \text{E}_{(\text{M}^{n+}/\text{M})} = \text{E}^\circ_{(\text{M}^{n+}/\text{M})} - \frac{\text{RT}}{n\text{F}} \ln \frac{[\text{M(s)}]}{[\text{M}^{n+}]} \)
  where \( \text{E}^\circ = \) Standard electrode potential, \( \text{R} = \) Gas constant (\( 8.31 \text{ JK}^{-1} \text{ mol}^{-1} \)), \( \text{T} = \) Temperature (\( \text{K} \)), \( n = \) Number of moles of electrons and \( \text{F} = \) Faraday (\( 96500 \text{ C} \)).
  For a cell, the electrode potential for any concentration of ions using electrode reactions is
  \( \text{M}^{n+}\text{(aq)} + ne^- \rightarrow \text{M(s)} \)
  At equilibrium,
  \( \text{E}^\circ_{\text{cell}} = \frac{0.059}{n} \log \text{K}_c \)
  Where, \( \text{K}_c = \) Equilibrium constant
  \( \text{K}_c = \frac{[\text{M(s)}]}{[\text{M}^{n+}]} \)
  For the general electrochemical cell with the net reaction,
  \( a\text{A} + b\text{B} \xrightarrow{ne^-} m\text{M} + n\text{N} \)
  the Nernst equation at 298 K can be written as
  \( \text{E}_{\text{cell}} = \text{E}^\circ_{\text{cell}} - \frac{0.059}{n} \log Q \)
  \( \text{E}_{\text{cell}} = \text{E}^\circ_{\text{cell}} - \frac{0.059}{n} \log \frac{[\text{M}]^m[\text{N}]^n}{[\text{A}]^a[\text{B}]^b} \)
  where \( \text{E}^\circ_{\text{cell}} = \text{E}^\circ_{\text{cathode}} - \text{E}^\circ_{\text{anode}} \)
• Gibbs energy:
  \( \Delta \text{G}^\circ = -n\text{FE}^\circ_{\text{cell}} \)
  For cell reaction to be spontaneous, \( \Delta \text{G} \) must be negative,
  Calculations of \( \Delta_r \text{G}^\circ \) and \( \Delta_r \text{G} \):
  \( \Delta_r \text{G}^\circ = -n\text{F} \text{E}^\circ_{\text{cell}} \)
  and \( \Delta_r \text{G} = -n\text{F} \text{E}_{\text{cell}} \)
  We also know that, Gibbs energy change is equal to the useful work done.
  For cell reaction to be spontaneous, \( \Delta \text{G} \) must be negative.
  \( \Delta \text{G}^\circ = -2.303 \text{ RT} \log \text{K} \)
   

Electrolysis, Law of Electrolysis, Batteries, Fuel Cells and Corrosion

• Electrolysis is the process of decomposition of an electrolyte when electric current is passed through either its aqueous solution or molten (fused) state. This process takes place in electrolytic cell.

• Faraday’s first law of electrolysis: The amount of chemical reaction which occurs at any electrode during electrolysis is proportional to the quantity of electricity passed through the electrolyte.
  \( m = Z \times I \times t \), where Z = Electrochemical equivalent
• Faraday’s second law of electrolysis: Amount of various substances liberated by the same quantity of electricity passed through the electrolytic solution is proportional to their chemical equivalent weights.
  \( \frac{w_1}{E_1} = \frac{w_2}{E_2} \)
• Products of electrolysis depend on
  (i) Physical state of material.
  (ii) Types of electrode being used.
• Battery is a combination of galvanic cells in series and used as a source of electrical energy.
  Types of batteries:
  (i) Primary batteries are non-chargeable batteries such as Leclanche cell and Dry cell.
  (ii) Secondary batteries are chargeable cells involving reversible reaction. Example, Lead storage battery and Nickel-cadmium cells.
• Dry cell (Leclanche cell): The anode consists of a zinc container and the cathode is a graphite electrode surrounded by powdered \( \text{MnO}_2 \) and C. The space is filled with paste of \( \text{NH}_4\text{Cl} \) and \( \text{ZnCl}_2 \).
  At anode: \( \text{Zn(s)} \rightarrow \text{Zn}^{2+}\text{(aq)} + 2\text{e}^- \)
  At cathode: \( \text{MnO}_2\text{(s)} + \text{NH}_4^+\text{(aq)} + 2\text{e}^- \rightarrow \text{MnO(OH)} + \text{NH}_3 \)
  The net reaction: \( \text{Zn} + \text{NH}_4^+\text{(aq)} + \text{MnO}_2 \rightarrow \text{Zn}^{2+} + \text{MnO(OH)} + \text{NH}_3 \)
• Lead storage battery:
  Anode - Spongy lead
  Cathode - Lead packed with Lead dioxide
  Electrolyte - Aqueous solution of \( \text{H}_2\text{SO}_4 \) (38%)
  Discharge reaction of cell:
  At anode: Following reaction takes place at anode
  \( \text{Pb(s)} + \text{SO}_4^{2-}\text{(aq)} \rightarrow \text{PbSO}_4\text{(s)} + 2\text{e}^- \)
  Reaction at cathode: \( \text{PbO}_2 \) filled in lead grid gets reduced to \( \text{Pb}^{2+} \) ions which combines with \( \text{SO}_4^{2-} \) ions to form \( \text{PbSO}_4\text{(s)} \).
  Complete cathode reaction is as follows:
  \( \text{PbO}_2\text{(s)} + 4\text{H}^+\text{(aq)} + \text{SO}_4^{2-}\text{(aq)} + 2\text{e}^- \rightarrow \text{PbSO}_4\text{(s)} + 2\text{H}_2\text{O(l)} \)
  Complete cell reaction: \( \text{Pb(s)} + \text{PbO}_2\text{(s)} + 2\text{H}_2\text{SO}_4\text{(aq)} \rightarrow 2\text{PbSO}_4\text{(s)} + 2\text{H}_2\text{O(l)} \)
  Recharge reaction of cell: It changes the direction of electrode reaction. \( \text{PbSO}_4 \) accumulated at cathode gets reduced to Pb.
  At cathode: \( \text{PbSO}_4\text{(s)} + 2\text{e}^- \rightarrow \text{Pb(s)} + \text{SO}_4^{2-}\text{(aq)} \)
  At anode: \( \text{PbSO}_4 \) gets oxidised to \( \text{PbO}_2 \)
  \( \text{PbSO}_4\text{(s)} + 2\text{H}_2\text{O} \rightarrow \text{PbO}_2\text{(s)} + 4\text{H}^+\text{(aq)} + \text{SO}_4^{2-}\text{(aq)} + 2\text{e}^- \)
• Complete cell reaction would be as follows:
  \( \text{PbSO}_4\text{(s)} + 2\text{H}_2\text{O(l)} \xrightarrow{\text{charge}} \text{Pb(s)} + \text{PbO}_2\text{(s)} + 2\text{H}_2\text{SO}_4\text{(aq)} \)
• Conventions for representing the galvanic cell:
  (i) Double vertical line is used for salt bridge. Left hand side of the double line is anode and the cathode is on the right hand side.
  (ii) A single vertical line is used to separate metal and the electrolytic solution.
  (iii) If there is no metallic surface involved, we write Pt.
  Example:
  \( \text{Zn(s)} + \text{Cu}^{2+}\text{(aq)} \rightarrow \text{Zn}^{2+}\text{(aq)} + \text{Cu(s)} \)
  \( \text{Zn(s)} \mid \text{Zn}^{2+}\text{(aq)} \parallel \text{Cu}^{2+}\text{(aq)} \mid \text{Cu(s)} \)
• Fuel cells: Electrical cells that are designated to convert the energy from the combustion of fuels such as hydrogen, carbon monoxide or methane directly into electrical energy are called fuel cells.
  In the cell:
  Anode: \( [\text{H}_2\text{(g)} + 2\text{OH}^-\text{(aq)} \rightarrow 2\text{H}_2\text{O(l)} + 2\text{e}^-] \times 2 \)
  Cathode: \( \text{O}_2\text{(g)} + 2\text{H}_2\text{O(l)} + 4\text{e}^- \rightarrow 4\text{OH}^-\text{(aq)} \)
  Net reaction: \( 2\text{H}_2\text{(g)} + \text{O}_2\text{(g)} \rightarrow 2\text{H}_2\text{O(l)} \)
• Corrosion: The process of slow conversion of metals into their undesirable compounds (usually oxide) by reaction with moisture and other gases present in the atmosphere.
  Rusting of iron:
  \( \text{Fe(s)} + 2\text{H}^+\text{(aq)} + \frac{1}{2}\text{O}_2\text{(aq)} \rightarrow \text{Fe}^{2+}\text{(aq)} + \text{H}_2\text{O(l)} \)
  \( 2\text{Fe}^{2+}\text{(s)} + \frac{1}{2}\text{O}_2\text{(g)} + 2\text{H}_2\text{O(l)} \rightarrow \text{Fe}_2\text{O}_3\text{(s)} + 4\text{H}^+ \)
  \( \text{Fe}_2\text{O}_3 + x\text{H}_2\text{O} \rightarrow \text{Fe}_2\text{O}_3\cdot x\text{H}_2\text{O} \text{ (Rust)} \)
  Prevention of Corrosion:
  (i) Barrier protection: By covering the surface with paint or a thin film of grease or by electroplating.
  (ii) Sacrificial protection: By galvanization.
  (iii) Alloying.

Know the Terms

• Superconductors: Materials with a zero resistance

• Limiting molar conductivity: Molar conductivity when concentration approaches zero

• Electrolyte: Substance that dissociates into electrically conducting ions.

• Over voltage: It is the difference between the potential required for the evolution of a gas and its standard reduction potential.

Know the Formulae

• Current (I) \( = \frac{\text{Potential difference (V)}}{\text{Resistance (R)}} \)

• Resistance (R) \( = \rho \frac{l}{A} \)
• Conductance (C) \( = \kappa \frac{A}{l} \)
• Specific conductivity (\( \kappa \)) \( = C \times \frac{l}{A} = \frac{\text{Cell constant}}{\text{R}} \)
• Cell constant (G*) \( = \frac{l}{A} \)
• For strong electrolyte, \( \Lambda_m = \Lambda_m^\circ - A \sqrt{C} \)
  \( \Lambda^\circ = v_+ \Lambda_+^\circ + v_- \Lambda_-^\circ \)
• Degree of dissociation (\( \alpha \)) \( = \frac{\Lambda_m^c}{\Lambda_m^\circ} \)
• \( K = \frac{C\alpha^2}{(1-\alpha)} = \frac{C(\Lambda_m^c)^2}{\Lambda_m^\circ(\Lambda_m^\circ - \Lambda_m^c)} \)
• Solubility \( = \frac{\kappa \times 1000}{\Lambda_m^\circ} \)
• \( \text{E}_{\text{cell}} = \text{E}_{\text{cathode}} - \text{E}_{\text{anode}} \)
• \( \text{E}^\circ_{\text{cell}} = \text{E}^\circ_{\text{cathode}} - \text{E}^\circ_{\text{anode}} \)
• Nernst equation:
  \( \text{E}_{\text{cell}} = \text{E}^\circ_{\text{cell}} - \frac{2.303 \text{ RT}}{n\text{F}} \log \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b} \)
  \( \text{E}_{\text{cell}} = \text{E}^\circ_{\text{cell}} - \frac{0.0591}{n} \log \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b} \) at 298 K
• \( \Delta_r \text{G}^\circ = -n\text{FE}^\circ_{\text{cell}} \)
• \( \Delta_r \text{G}^\circ = -2.303 \text{ RT} \log \text{K}_c \)
• \( Q = It \)
• \( m = ZIt \)