Electrochemistry

Definition ,Electrolyte

1. 1 ELECTRO CHEMISTRY Mr.M.RAGU Assistant Professor of Chemistry Vivekananda College Tiruvedakam West – 625234 Madurai - Tamilnadu Physical chemistry

2. 2 Introduction Electrochemistry is the branch of chemistry which deals with the transformation of electrical energy to chemical energy and vice versa. In brief it deals with the chemical applications of electricity . Electrical Energy Chemical Energy

3. 3 Eletrolytic cell and Electrochemical cell Electrolytic cell: A device which converts electrical energy to chemical energy Electrochemical cell: A device which converts chemical energy to electrical energy

4. 4

5. 5

6. 6

7. 7

8. 8

9. 9

10. 10

11. 11

12. 12

13. 13

14. 14 Types of Conductors Electrical Conductors: Substances which allow electric current to pass through them are known as electrical conductors. Eg . All metals, graphite, fused salts, aqueous solutions of acids and bases Semi conductors: The substances which partially conduct electricity are called semi- conductors. The conducting properties of semi-conducting properties are increased by the addition of certain impurities called “ dopping ”. Ex : ‘Si’ and Ge on addition of V group elements like P produces n-type semi- conductor. Non-conductors or Insulators: The substances which do not allow electricity are called non- conductors. . Eg . Rubber, wood, paper, all non-metals except carbon.

15. 15 Differences between metallic conduction and electrolytic conduction

16. 16 Conductance The capacity of a conductor to allow the passage of current through it called conductance. It is a property of conductor which facilitates flow of electricity through it.

17. 17 Specific Conductance (k) The reciprocal of specific resistance (ρ) is called as specific conductance. This may be defined as the conductance of 1cm 3 of a material and denoted by k (kappa). Units: Ohm -1 Cm. -1

18. 18 Equivalent Conductance If one gram equivalent weight of an electrolyte is dissolved in V ml of the solvent, the conductivity of all ions produced from one gram equivalent of an electrolyte at the dilution V is known as equivalent conductance. This is denoted by the symbol Zeq Z eq = K×V V = Volume of electrolytic solution in milliliters containing 1g equivalent wt of an electrolyte V = 1000 / C = 1000 / Normality of the electrolyte solution Let C be the concentration of a solution containing gm equivalent of electrolyte per liter and the volume V of the solution will be 1000/C. Z eq = Let C be the concentration of a solution containing gm equivalent of electrolyte per liter and the volume V of the solution will be 1000/C. Units: ohm -1 cm 2 eq -1 or Scm 2 eq -1

19. 19 Molar Conductance( µ) Molar conductance is defined as the conductance of an electrolyte solution containing 1 mole of an electrolyte. It is denoted by Zm . If Vml is the volume of solution containing 1 g mole of the electrolyte . µ m = K × V m V = 1000 / M = 1000 / Molarity of the electrolyte solution UNITS: ohm -1 cm 2 mol -1

20. 20 Cell Constant It is a constant, characteristic of the cell in which the electrolyte is taken and its value depends on the distance between the electrodes and area of cross-section of the electrodes Specific conductance =

21. The electrolytic conductors are further sub-classified into three types as follows. (a) Strong Electrolytes : Strongelectrolytes are substances , which ionise completely almost at alldilutions . HCl , NaOH , NaCl , KCl , etc ., (b) Weak Electrolytes Weak electrolytes are substances, which ionise to a small extent even at high dilutions. CH 3 COOH , NH 4 OH , CaCO 3 , etc., (c) Non Electrolytes Non electrolytes are substances, which do not ionise at any dilutions. Glucose, sugar, alcohol, petrol, etc ., Types of Electrolytic Conductors

22. Difference between strong and weak electrolyte 22

23. 23

24. 24

25. 25

26. 26

27. Cell Terminology CURRENT Current is the flow of electrons through a wire or any conductor. ELECTRODE Electrode is a material (or) a metallic rod/bar/strip which conducts electrons. ANODE Anode is the electrode at which oxidation occurs.

28. (iv) CATHODE Cathode is the electrode at which reduction occurs . (v) ELECTROLYTE Electrolyte is a water soluble substance forming ions in solution, and conduct an electric current . (vi) ANODE COMPARTMENT Anode compartment is the compartment of the cell in which oxidation half-reaction occurs. It contains the anode . (vii) CATHODE COMPARTMENT Cathode compartment is the compartment of the cell in which reduction half reaction occurs. It contains the cathode. (ix) CELL Cell is a device consisting two half cell. The two half cells are connected through one wire.

29. Variation of Conductance with dilution The conductance increases with increase in the concentration of the electrolyte to a certain maximum level and decreases on further increase in the concentration. This is because, on increase in the concentration, the population of free ions increases and these cons get closer and the electrostatic force of attractions and the viscosity of the electrolyte increases. These factors tend to reduce the conductance of the solution. But equivalent conductances are inversely proportional to the conc. Of electrolyte and hence increases with increase in dilution. In case of strong electrolyte, a gradual and linear change in ^ (or) µ with square root of concentration is observed. But in case of weak electrolytes, there is a significant change of ^ (or) ‘µ’ with . At higher concentrations, they show low ^ (or) µ and at higher dilutions (low cons). They show higher ^ (or) µ 29

30. 30 Equivalent conductivity of any electrolyte at any dilution is directly proportional to the charge carried by the ions and their velocities. The conductivity is thus given by the products of charge and velocity of individual ions. At infinite dilution the ionization is complete and the solution containing one equivalent of various electrolytes contains equivalent number of ions. Hence at infinite dilution total charge carried by all ions is same in every case. Because the total charge is constant at infinite dilution, the Λα must depend exclusively on ionic velocities. Defining the ionic velocity or mobility as the speed with which a charged a particle at infinite dilution moves under a potential gradient of one volt per cm, we have, λ + α u+ λ − α u- Or λ + = ku + λ − = ku Where k is a proportionality constant and u+ and u- represent the ionic velocities at infinite dilution. Since 1 equivalent of an ion under unit potential gradient carries a charge of 1 Faraday per sec., the proportionality constant k = 96500 coulombs. Therefore, u+ = λ + /k and u- = λ − /k Ionic conductivity is expressed in S cm2 , while ionic mobility is expressed in cm s-1 . Calculated ionic mobilities of few common ions at 25 o C are given in Table Ionic Conductivity and Ionic Mobilities

31. 31

32. 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 1.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 . 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 dissolved in a solvent, these forces are weakened and the electrolyte undergoes dissociation into ions. The ions are solvated . The process of splitting of the molecules into ions of an electrolyte is called  ionization . .

33. 2.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 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.

34. 35

35. 3.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.

36. AB   A +  + B -    NaCl   Na +  + Cl -    (Both ions are equal) AB 2    A 2+  + 2B - BaCl 2    Ba 2+  + 2Cl - (Anions are double that of cations) A 2 B  2a +  + B 2- Na 2 SO 4   2Na +  + (Anions are double that of cations 4.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 . 5.The ions are discharged always in equivalent amounts, no matter what their relative speeds are. 6.The electrolytic solutions is always neutral in nature as the total charge on one set of ions is always equal to the total charge on the other set of ions. However, it is not necessary that the number of two sets of ions must be equal always .

37. 7.The properties of electrolytes in solution are the properties of ions present in solution. For example, acidic solution always contains H +  ions while basic solution contains OH -  ions and characteristic properties of solutions are those of H -  ions and OH -  ions respectively . 8.The ions act like molecules towards depressing the freezing point, elevating the boiling point, lowering the vapour pressure and establishing the osmotic pressure . 9.The conductively of the electrolytic solution depends on the nature and number of ions as the current is carried through solution by the movement of ions.

38. Evidences in Favour of Ionic Theory Ions Present in Solid Electrolytes X-ray diffraction studies have shown that electrolytes are composed of ions. For example , A crystal of NaCl does not contain NaCl units but Na +  and Cl -  ions. Each Na +  ion is surrounded by six Cl -  ions and each Cl -  ion in turn is surrounded by six Na +  and Cl - ions . The ionic compounds behave as good conductors in fused state. It can only be possible of ions are already present in ionic solids .

39. Ohm's Law Applicability The electrolytic solutions like metallic conductors obey Ohm's law, i.e., the strength of the current flowing conductor is directly proportional to potential difference (E) applied across the conductor and is inversely proportional to the resistance of the conductor.  Mathematically , I = E/R This can only be possible if ions are already present in the solution and no part of the current has only directive effect on the ions.

40. Ionic Reaction Evidence for the existence of ions in aqueous solutions of electrolytes is furnished by well known reactions in inorganic chemistry. A white precipitate of silver chloride is obtained whenever Ag +  ions come in contact with chloride ions. Ag +   + Na +   Cl -   → AgCl + Na +  + NO 3 - But no precipitation occurs when AgNO 3  solution is added to CCl 4 , CHCl 3  or C 2 H 5 Cl as these substances being non-electrolytes do not furnish Cl -  ions in solution. An acid which gives all tests of H+ ions in aqueous solution, does not give the same tests when dissolved in any organic solvent because no ionization of the acid occurs in the common reaction.

41. Heat of Neutralization When one gram equivalent of a strong acid is neutralized by one gram equivalent of a strong base, the heat evolved is always the same, i.e., 13.7 kcal. This can be explained on the basis of Arrhenius theory that an acid furnished H +  ions and base OH -  ions when dissolved in water and the process of neutralization involves the common reaction. H +  + OH -   H 2 O + 13.7 kcal. Thus, heat of neutralization is actually the heat of formation of H 2 O from H +  and OH -  ions.

42. Abnormal Colligative Properties The abnormal behavior towards colligative properties as observed in the case of electrolytes can be explained on the basis of ionic theory. When an electrolyte is dissolved in water, the number of molecules actually dissolved due to ionization. The can't Hoff factor , is always more than one, i.e.,  i = 1 + (n-1)   where 'n' is the number of ions produced by the ionization of one molecule of the electrolyte and ' is the degree of ionization.

43. Colour of Solution The color of the electrolytes in solution. If any, is due to their ions, the CuSO 4  is blue in solution due to the presence of Cu 2+  ions. Potassium permanganate (KMnO 4 ) is purple in solution due to the presence of   ions.

44. Explanation of Some Other Phenomena Ionic theory provides satisfactory explanations regarding various phenomena such as electrolysis, conductivity, salt hydrolysis, solubility product, etc.

45. Limitations of Arrhenius Theory Ostwald's dilution law which is based on Arrhenius theory is not applicable to strong electrolytes. Strong electrolytes conduct electricity infused state, i.e., in absence of water. this is in contradiction of Arrhenius theory according to which the presence of solvent is a must for ionization. Arrhenius theory assumes independent existence of ions but fails to account for the factors which influence the mobility of the ions.

46. 47

47. Ostwald dilution law According to Arrhenius theory of electrolyte dissociation, the molecules of an electrolyte in solution are constantly splitting up into ions and the ions are constantly reuniting to form unionized molecules. Therefore , a dynamic equilibrium exists between ions and unionized molecules of the electrolyte in solution . It was pointed out by Ostwald that like chemical equilibrium, law of mass action van be applied to such systems also. Consider a binary electrolyte AB which dissociates into A+ and B- ions and the equilibrium state is represented by the equation:

48. Ionic Equilibria The Ostwald’s Dilution Law: Wilhelm Ostwald’s dilution law is a relationship between the dissociation constant ( Kp /Kc) and the degree of dissociation of a weak electrolyte (acids, bases). The fraction of the amount of the electrolyte in solution present as free ions is called the Degree of Dissociation. Where, K p is dissociation constant, α is degree of dissociation, c(A - ) is concentrations of anions, c(K + ) concentration of cations , c is overall concentration, c(KA) is concentration of associated electrolyte.

49. According to the Arrhenius Theory of Dissociation, An electrolyte dissociates into ions in the water solutions These ions are in a state of equilibrium with the undissociated molecules. These equilibrium is called Ionic equilibrium Or The molecules of an electrolyte in solution are constantly splitting up into ions and the ions are constantly reuniting to form unionized molecules. Therefore, a dynamic equilibrium exists between ions and unionized molecules of the electrolyte in solution.

50. If one mole of electrolyte be dissolved in V litre of the solution then C = 1/V Where V is known as the Dilution For the solution. Therefore, Kc = α 2 / (1 - α ) V For weak electrolytes, Put (1 - α ) = 1 , Therefore α = √ Kc.V Or α = K’√V It implies that, the degree of dissociation is proportional to the square root of the dilution. For Strong electrolytes, α 2+ α Kc-KcV =0

51. Limitations of Ostwald's dilution law The law holds good only for weak electrolytes and fails completely in the case of strong electrolytes. The value of 'α' is determined by conductivity measurements by applying the formula Λ/Λ∞. The cause of failure of Ostwald's dilution law in the case of strong electrolytes is due to the following factors“ (i ) The law is based on the fact that only a portion of the electrolyte is dissociated into ions at ordinary dilution and completely at infinite dilution. Strong electrolytes are almost completely ionized at all dilutions and Λ/Λ∞ does not give accurate value of 'α'. (ii) When concentration of the ions is very high, the presence of charges on the ions appreciably effects the equilibrium. Hence, law of mass action its simple form cannot be strictly applied in the case of string electrolytes.

52. Theory of Strong Electrolytes (Debye- Huckel Theory) The Debye– Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes. The main ideas of the theory are given below: The strong electrolyte is completely ionized at all dilutions. Since oppositely charged ions attract each other It suggests that anions and cations are not uniformly distributed in the solution of an electrolyte but that the cation tend to be found in the vicinity of anions and vice-versa. Degree in equivalent conductance with increase in concentration is due to fall in mobilities of the ions to greater inter-ionic effect and vice-versa.

53. DEBYE-HUCKEL THEORY The first successful attempts to explain the variation of equivalent conductance of strong electrolytes with dilution was made by Debye and Huckel (1923). The fundamental idea underlying their work is that because of electrical attraction among the oppositely charged ions.

54. INTERIONIC EFFECTS The electrical attractions among the oppositely charged ions which affect the speed of an ion in the electric field are called “interionic effects”. There are two such effects :- Relaxation effect or Asymmetry effect Electrophoretic effect

55. RELAXATION EFFECTS OR ASYMMETRY EFFECTS - - + _ - - - - - - - - - - - - - + + (a) (b) Symmetrical ionic atmosphere around a positive ion Ionic atmosphere becoming asymmetrical when central ion moves FIG:1

56. ELECTROPHORETIC EFFECT _ _ _ _ _ _ _ + FIG:2

57. DEBYE-HUCKEL-ONSAGER EQUATION Debye and huckel (1923)derived a mathematical expression for the variation of equivalent conductance with concentration. This equation was further improved by Onsager(1926-1927) and is known as Debye- Huckel -Onsager equation. Λ c = Λ -[82.4/(DT) 1/2 ή +8.20X10 5 /(DT) 3/2 λ ] √C Where Λ c =Equivalent conductance at concentration c. Λ =Equivalent conductance at infinite dilution. D = Diectric constant of the medium. ή =Coefficient of viscosity of the medium. T =Temperature of the solution in degree absolute. c = Concentration of the solution in moles/ litre . As D and ή are constant for a particular solvent.Therefore,at constant temperature, the above equation can be written in the form: Λ c = Λ -(A+B Λ ) √ c where A and B are constants for a particular solvent

58. VERIFICATION OF THE ONSAGER EQUATION Two tests can be readily performed to verify the onsager equation.These are:- The plot of Λ c vs √ c should be linear. The slope of the line should be equal to A+B Λ , calculated by substituting the value of various constants directly. Equivalent conductance √ concentration c HCI ACID KCl AgNO 3 NaCl FIG:3 TESTS OF ONSAGER EQUATION

59. TRANSPORT NUMBER The fraction of the total current carried by an ion is called its transport number or Hittorf’s number. Transport number of anion n a = u a u a + u c Transport number of cation n C = u C u a +u c

60. MIGRATION OF IONS AND TRANSPORT NO The movement of ions towards the oppositely charged electrode is called migration of ions. KNO 3 SOLUTION KNO 3 SOLUTION IN JELLY CHARCOAL POWDER CuCr 2 O 7 SOLUTION IN JELLY (GREEN) Cu 2+ (Blue) Cr 2 O 7 2 - (YELLOW) FIG:4 DEMONSTRATION OF THE MIGRATION OF IONS

61. DETERMINATION OF TRANSPORT NUMBERS BY HITTORF’S METHOD Hittorf’s method:- Principle:- The method is based upon the principle that the fall in concentration around an electrode is proportional to the speed of the ion moving away from it. n c =Number of gram equivalent lost from the anodic compartment Number of gram equivalent deposited in the voltameter

62. APPARATUS FOR THE DETERMINATION OF TRANSPORT NUMBER FIG:7 HITTORF’S TRANSPORT NO. APPARATUS FOR THE DETERMINATION OF TRANSPORT NO VARIABLE RESISTANCE EXPERIMENTAL SOLUTION MILLI-AMMETER VOLTAMETER OF COULOMETER

63. HITTORF’S THEORETICAL DEVICE According to faraday’s second law of electrolysis, when the same quantity of electricity is passed through solution of different electrolytes, the ions are always liberated in equivalent amounts. To explain this ,consider a cell containing the solution and provided with the anode A and the cathode C.Let the solution lying between the electrodes A and C be divided into three compartment. Before electrolysis suppose there are 13 pairs of ions.

64. WHEN ELECTRODES ARE NOT ATTACKED:- The following different cases may be considered Case 1:When only anion moves. Case 2: When cations and anions move at the same rate. Case 3: when cations move at double the speed of the anions ---------------------------------------------------------- ---------------------------------------------------------- A C a b I II III IV ANODIC COMPARTMENT CENTRAL COMPARTMENT CATHODIC COMPARTMENT + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ 2 + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ 2 2 2 1 FIG: 5 MIGRATION VELOCITY OF IONS AND CHANGE IN CONCENTRATION WHEN ELECTRODES ARE NOT ATTACKED + _

65. CONCLUSION Fall in concentration around any electrode is directly proportional to the speed of the ions moving away from it. It means: Fall in con. around anode =Speed of cation No. of ions liberated on both the electrodes is equal.

66. CASE IV:- WHEN ELECTRODES ARE ATTACKABLE ---------------------------------------------------------- ---------------------------------------------------------- A C a b I II III IV ANODIC COMPARTMENT CENTRAL COMPARTMENT CATHODIC COMPARTMENT + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ + + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ + + + + + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ 2 + + + + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ 2 2 2 1 FIG: 6 MIGRATION VELOCITY OF IONS AND CHANGE IN CONCENTRATION WHEN ELECTRODES ARE ATTACKED + _

67. CONCLUSION Fall in conc. In the anodic compartment due to migration of Ag + ions=(x-y)gram equivalents Fall in conc. around cathode=Increase in conc. Around anode=y gram equivalents Thus, the speed ratio will be given by: Speed of Ag + ions/Speed of Nitrate ion=x-y/y

68. DETERMINATION OF TRANSPORT NUMBERS BY HITTORF’S METHOD Hittorf’s method:- Principle:- The method is based upon the principle that the fall in concentration around an electrode is proportional to the speed of the ion moving away from it. n c =Number of gram equivalent lost from the anodic compartment Number of gram equivalent deposited in the voltameter

69. APPARATUS FOR THE DETERMINATION OF TRANSPORT NUMBER FIG:7 HITTORF’S TRANSPORT NO. APPARATUS FOR THE DETERMINATION OF TRANSPORT NO VARIABLE RESISTANCE EXPERIMENTAL SOLUTION MILLI-AMMETER VOLTAMETER OF COULOMETER

70. FACTORS ON WHICH TRANSPORT NUMBER DEPENDS Nature of the ion Nature of the other ion present Hydration of the ions Concentration Temperature

71. The moving boundary method The moving boundary method is based on the direct observation of migration of ions under the influence of applied potential. This method is very accurate and has been used in recent years for precision measurements . The apparatus used consists of a long vertical tube fitted with two electrodes at the two ends (Fig. 25.7). The tube is filled with a solution of cadmium chloride (CdCl2) at the lower end and hydrochloric acid at the upper end in a way that there is a sharp boundary between the two (due to difference in their refractive indices ). The platinum cathode dipped in HCl solution is inserted at the top and the anode (cadmium stick) is introduced at the bottom. On passing electric current through the apparatus, hydrogen gas is evolved at the cathode and H+ ions move toward the anode . The H+ ions are replaced by Cd2+ ions and hence the boundary line moves in the upward direction. By noting the length through which the boundary moves and the quantity of electricity passed through the cell, the transport number of H+ ion can be calculated . In general, if the transport number of a cation A+ is to be determined, the electrolyte AX solution is taken in the upper part of the apparatus and a layer of another electrolyte BX having the common ion X– is introduced in the lower part of the apparatus. The electrolyte BX is selected so that the velocity of B+ ion is less than that of A+ ion. In such a case, the situation is described in Fig. 25.8 . 72

72. Kohlrausch Law : 73 From a study of the equivalent conductances of different electrolytes at infinite dilution (λ∝), Kohlrausch discovered that each ion contributes to the conductance of the solution. In 1875, he enunciated a generalisation which is called the Kohlrausch’s Law . It states that : the equivalent conductance of an electrolyte at infinite dilution is equal to the sum of the equivalent conductances of the component ions . The law may be expressed mathematically as : λ ∝ = λa + λc where λa is the equivalent conductance of the anion and λc that of the cation. For example, the equivalent conductance of NaCl at infinite dilution at 25°C is found to be 126.45. The equivalent conductance of Na+ and Cl– ion is 50.11 ohm– 1 and 76.34 ohm– 1 respectively. Thus, – Cl Na λ =λ +λ ∞ ( NaCl ) + or 126.45 = 50.11 + 76.34 This is in conformity with the Kohlrausch’s Law .

73. Applications of Kohlrausch’s Law 74

74. 75 From the experimental results, he noticed, replacement of Sodium by Potassium ion, irrespective of the nature of anion, gives the same difference in equivalent conductance. Similarly, replacement of chloride by hydroxide ion, irrespective of the cation, gives the same difference in equivalent conductance at infinite dilutions. Basing on similar observations, kohlrausch advised a hypothesis called law of independent migration of ions. This law states that at infinite dilution each ion makes a definite contribution towards the equivalent conductivity of an electrolyte, irrespective of nature of the co-ion with which it is associated in the solution. Therefore equivalent conductivity at infinite dilution is made up of two independent terms, called ion conductivities, characteristic of each ionic constituent of an electrolyte in solution. We can express the same conclusion mathematically as Λ0 = λ 0 + + λ - 0 Where λ 0 + and λ - 0 are the contributions of cation and anion (or) ionic conductance of anion respectively.

75. Applications of Kohlrausch law: 1. Determination of equivalent conductance for weak electrolytes at infinite dilutions: 2. Determination of equivalent conductance for sparingly soluble salt ( AgCl ): 3. Determination of the solubility of sparingly soluble salt: 4. Determination of degree of dissociation & calculate the ionic product of water. 1. Determination of equivalent conductance for weak electrolytes at infinite dilutions: We can easily calculate the equivalent conductance of strong electrolyte at infinite dilution graphically by extrapolation to zero concentration, but impossible for weak electrolytes like acetic acid, ammonium hydroxide, because ( i ) Even at high dilutions they are not fully dissociated, and (ii) Can’t obtain straight line curve. So Kohlrausch gave a simple method of calculating Λ0 for weak electrolytes from measurements of strong electrolytes. e.g Equivalent conductance of acetic acid is obtained from the knowledge of equivalent conductance of HCl , CH3COONa & NaCl at infinite dilutions. λ 0 CH3COO- + λ 0H + = λ 0 Cl- +λ 0CH3COO- + λ 0 Na+ - (λ 0Na+ +λ 0Cl- ) i.e Λ0 CH3COOH = Λ0 HCl + Λ0CH3COONa - Λ0NaCl Similarly Λ0NH4OH = Λ0 NH4Cl + Λ0NaOH - Λ0 NaCl 2. Determination of equivalent conductance for sparingly soluble salt ( AgCl ): The equivalent conductance of sparingly soluble salt ( AgCl ) also can be obtained by the similar method. _______________________________________________________________________________ I B.Tech Engineering Chemistry (Unit-I) Electrochemistry By… B.SRINIVAS 4 www.hitam.webs.com Λ0AgCl = Λ0 NH4Cl + Λ0 AgNO3 - Λ0 NH4NO3 3. Determination of the solubility of sparingly soluble salt: The solubility of the sparingly soluble salts like Gal, BaSO4 can calculate by using the following relation. Λ0 = 1000 k S S = Solubility in gm eq lit – K is determined by using Wheatstone bridge, Λ0 is calculated using Kohlrausch’s law, Λ0 (salt) = Λ0 + + Λ0 – 4. Determination of degree of dissociation: Degree of dissociation (α ) is the fraction of the total number of molecules ionized into ions. α = No. of molecules ionized into ions Total number of molecules taken This equation may be written as Λ = α = No. of molecules ionized into ions at a particular dilution Λ0 Total no. of Molecules taken Λ, can be obtained from conductivity measurements, Λ0can calculated using Kohlrausch’s law. Thus degree of dissociation (α ), is the ratio of the equivalent conductivity at particular dilution to the equivalent conductivity at infinite dilution. Similarly we may calculate the ionic product of water. 76

76. Ammonia has a C 3 axis. Note that there are two operations associated with the C 3 axis. Rotation by 120 o in a clockwise or a counterclockwise direction provide two different orientations of the molecule.

77. Mirror Planes The reflection of the water molecule in either of its two mirror planes results in a molecule that looks unchanged.

78. Mirror Planes The benzene ring has a C 6 axis as its principal axis of rotation. The molecular plane is perpendicular to the C 6 axis, and is designated as a horizontal plane, σ h . C 6 .

79. If reflection of all parts of a molecule through a plane produces an indistinguishable configuration, the plane is a plane of symmetry 80 Plane of Symmetry ( σ )

80. 81 There are three types of mirror planes s v => vertical mirror plane which contains the principle axis . s h => horizontal mirror plane which is perpendicular to the principle axis. s d => mirror plane bisects dihedral angle made by the principal axis of Plane of Symmetry ( σ ) Con

81. The inversion operation projects each atom through the center of inversion, and across to the other side of the molecule. 82 Centre of Symmetry ( i )

82. Centre of Symmetry ( i ) Con

83. Rotation about an axis, followed by reflection through a plane perpendicular to this axis If rotation through a bout an axis, followed by reflection through a plane perpendicular to that axis, yields an indistinguishable configuration, the axis is an n -fold rotation – reflection axis, also called an n-fold improper rotation axis . It is denoted by the symbol S n . 84 84 Improper axis of Rotation (S n )

84. This operator applies a clockwise rotation on the molecule followed by a reflection in a plane perpendicular to that axis of rotation . S n = σ h C n Example : Methane

85. 86 A collection of symmetry elements are called group. There are 1 . Finite group 2 . Infinite group 3. Abelian group 4. Non – Abelian group 5. Order Centre of Symmetry ( i ) Con Groups

86. Finite Group : A group containing a finite or limited number of elements is called a finite group. Ex: C 2 v group order is 4 C 3 v group order is 6 Infinite Group: A group containing a infinite or unlimited number of elements is called a infinite group. Ex: Linear molecules belong to this group. Abelian Group: A group in which all the elements commute is called an Abelian group. Two elements A and B commute if AB = BA. The set of numbers. The set of symmetry operations of water molecule represents an Abelian group since they obey the commutative law. 87

87. Non - Abelian Group: A group is said to be non-Abelian if all the elements do not commute with one another. The symmetry operations of the ammonia molecule provide an example for the non – Abelian group. E, C’3. δ V δ V’ and δ V’’ do not obey the commute law. 88

88. Cyclic group: A group is said to be cyclic if all the elements of a group can be generated from one element. Ex : H 2 O 2 Order: The total number of elements are called order. 89

89. Definition: All the symmetry operations present in a molecule form a group is called Point group. 90 Point Group

90. 1 . E 2. C n 3. σ n 4.i 5. S n 91 Multiplication Table C 2v water molecule

91. 92 Multiplication Table C 3 v Ammonia molecule

92. Point Group = the set of symmetry operations for a molecule Group Theory = mathematical treatment of the properties of the group which can be used to find properties of the molecule Assigning the Point Group of a Molecule Determine if the molecule is of high or low symmetry by inspection Low Symmetry Groups Point Groups

93. B. High Symmetry Groups

94. If not, find the principle axis If there are C 2 axes perpendicular to C n the molecule is in D If not, the molecule will be in C or S If  h perpendicular to C n then D nh or C nh If not, go to the next step If  contains C n then C nv or D nd If not, D n or C n or S 2n If S 2n along C n then S 2n If not C n

95. Flow chart for determining point groups .

96. The determination of point groups of molecules axis = C 2 only one rotational two σ v but no σ h mirror planes means point group is C 2v The point group of the water molecule is C 2v

97. The point group of the carbon dioxide molecule We start at the top of the flow-chart, and can see that the CO 2 molecule is linear, and has a center of inversion ( i ) so it is D ∞h . Note the C ∞ principal rotation axis. i C ∞ D ∞h

98. Other linear molecules: H I C≡O All have a C ∞ axis N 2 O 2 F 2 H 2 D ∞h C ∞v i i HC≡N The bottom row have no i and so are C ∞v The top row of linear molecules all have a center of inversion ( i ) and so are D ∞h .

99. The C s point group: C s σ chloro-difluoro-iodo- methane I F Cl C F

100. Most land animals have bilateral symmetry, and belong to the C s point group: Mirror planes ( σ ) C s

101. The C 1 point group: chloro-iodo-amine B romo-chlor o - f l uo r o - iod o - methane Molecules that have no symmetry elements at all except the trivial one where they are rotated through 360º and remain unchanged, belong to the C 1 point group. In other words, they have an axis of 360º/360º = 1-fold, so have a C 1 axis. Examples are: I Br F Cl C I Cl H N C 1 C 1

102. Other C nv molecules: C 2v C 3v C 4v ammonia water σ v σ v σ v Vanadyl tetrafluoride (VOF 4 ) V

103. These ha v e a C n axis as their only s y m m etry ele m ent. I mp o rtant examples are (hydrogens omitted for clarity): The C n point groups: C 3 C 3 C 3 C 3 C 3 C 3 triphenyl phosphine viewed down C 3 axis Cobalt(III) tris-glycinate viewed down C 3 axis triphenyl phosphine viewed from the side Cobalt(III) tris-glycinate viewed from the side

104. The D nh point groups: σ h four C 2 axes at rt. angles to C 4 axis C 2 C 2 C 2 C 2 C 4 princ i pal axis mirror plane at rt. angles to C 4 axis D 4h

105. Examples of molecules belonging to D nh point groups: D 2h D 3h D 3h D 3h D 4h D 4h D 5h D 5h C 2 C 3 C 3 C 3 C 4 C 4 C 5 C 5

106. C 6 principal axis C 2 C 2 C 2 C 6 C 2 σ v σ v Benzene, an example of the D 6h point group: σ h C 6 principal axis C 6 principal axis D 6h

107. The D n point groups: C 2 C 2 C 2 principal axis D 2 these have a principal n -fold axis, and n 2-fold axes at right angles to it, but no mirror planes. [Cu(en) ] 2+ complex 2 with H-atoms omitted for clarity. (en = ethylene diamine) N N Cu C

108. Some further views of the symmetry elements of [Cu(en) 2 ] 2+ , point group D 2 : C 2 [Cu(en) 2 ] 2+ complex with H-atoms omitted for clarity. (en = ethylene diamine) C 2 C 2 C 2 C 2 C 2 principal axis C 2 principal axis C 2 principal axis C 2 principal axis C 2 C 2 C 2 D 2

109. C 2 C 2 C 2 C 3 principal axis Some views of the symmetry elements of [Co(en) 3 ] 3+ , point group D 3 . C 3 principal axis C 2 axis view down the C 3 axis of [Co(en) 3 ] 3+ showing the three C 2 axes. D 3 view down one of the three C 2 axes of [Co(en) 3 ] 3+ at right angles to C 3

110. Molecules belonging to the D nd point groups C 3 axis These have mirror planes parallel to the principal axis, but not at right angles to it. C 5 axis Staggered form of ethane Staggered form of ferrocene σ v planes contain the principal axis D 3d D 5d

111. The D 4d point group: C 2 C 2 C 2 C 2 C 4 principal axis C 4 principal axis σ v C 2 σ v σ v σ v C 4 principal axis [ZrF 8 ] 4- Square antiprism As predicted by VSEPR, the [ZrF 8 ] 4- anion has a square anti-prismatic structure. At left is seen the C 4 principal axis. It has four C 2 axes at right angles to it, so it has D 4 symmetry. One C 2 axis is shown side-on (center). There are four σ v mirror planes (right), but no mirror plane at right angles to C 4 , so the point group does not rate an h , and is D 4d . D 4d

112. [K(18-crown-6)] + , an example of a D 3d point group: The complex cation [K(18-crown-6)] + above is an important structure that has D 3d symmetry. It has a C 3 principal axis with 3 C 2 axes at right angles to it, as well as three σ v mirror planes that contain the C 3 axis, but no σ h mirror plane (because it’s not flat, as seen at center), so is D 3d . D 3d σ v σ v C 3 principal axis K + 3 C principal axis σ v C 2 C 2 C 2 C 2 C 2 C 2

113. 114 References

114. 115 Thank you Mr.M.RAGU Assistant Professor of Chemistry Vivekananda College Tiruvedakam West – 625234 Madurai - Tamilnadu