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• Electrolytes : Definition, Strong and weak electrolytes and their conductance measurement, Ions and electrical conductivity by ions • Kohlrausch law of Independent Migration of Ions • Applications of Kohlrausch law • Transference No. and its determination using Moving Boundary Method • Factors affecting transport number

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• Electrolytes : Definition, Strong and weak electrolytes and their conductance measurement, Ions and electrical conductivity by ions • Kohlrausch law of Independent Migration of Ions • Applications of Kohlrausch law • Transference No. and its determination using Moving Boundary Method • Factors affecting transport number

- 1. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar • Electrolytes : Definition, Strong and weak electrolytes and their conductance measurement, Ions and electrical conductivity by ions • Kohlrausch law of Independent Migration of Ions • Applications of Kohlrausch law • Transference No. and its determination using Moving Boundary Method • Factors affecting transport number CONDUCTOR : It is a substance which allows an electric current to flow through it. Conductors are of two types: NON-ELECTROLYTES : ✓ Aqueous solution does not conduct electricity Examples are solutions of cane sugar, glucose, urea etc. ELECTROLYTES : A chemical compound which dissociates into positively charged cations and negatively charged anions in the solution state or in molten state which can conduct electricity is called electrolyte. ✓ solution in water conducts electric current ✓ Conduction by the movement of ions Examples are salts, acids and bases Strong Electrolyte : • Highly ionized in the solution • Only free ions of the compound are present • Solution is Good conductor of electricity • Molar conductance increases slightly on dilution • Ostwald’s dilution law is not applicable Example - HCl, HBr , H2SO4, NaOH, NaCl , KOH etc Weak Electrolytes • Only feebly ionized in the solution • Free ions as well as molecules of the compound are present • Solution is poor conductor of electricity • Molar conductance increases rapidly with dilution • Ostwald’s dilution law isapplicable Example - H2CO3, CH3COOH, NH4OH, NH3, Aniline ,HCOOH , HF , C6H5COOH etc TYPES OF ELECTROLYTES
- 2. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar VARIATION OF EQUIVALENT AND MOLAR CONDUCTANCE WITH CONCENTRATION The variation of equivalent conductance with dilution can be studied by plotting a graph of 𝜆 against √𝐶 . ✓ The 𝜆 value of strong electrolyte shows a linear variation with concentration ✓ For other electrolyte variation of 𝜆 with concentration is not small ✓ For the experimental observation, Kohlrausch suggested equation 𝝀𝒄 = 𝝀∞ − 𝒃√𝑪 Where 𝝀𝒄 is equivalent conductance at concentration ‘c’ 𝝀∞ is equivalent conductance at infinite dilution or zero concentration Value of ‘b’ and 𝝀∞ constant for a given electrolyte ✓ Incase of weak electrolyte ionisation is incomplete hence value of 𝝀 decreases with increase in concentration. Thus conductivity is proportional to degree of dissociation of electrolyte ( 𝜶 ) ✓ Degree of dissociation is defined as fraction of total electrolyte that has dissociated into ions. At infinite dilution electrolyte is completely dissociated, hence according to Arrhenius, degree of dissociation can be written as Kohlrausch law of Independent Migration : Kohlrausch studied molar conductivity at infinite dilution for different electrolytes having an ion common and concluded that each ion contributes a characteristic Set 1 Set 2 Electrolyte 𝝀∞ Difference Electrolyte 𝝀∞ Difference KCl 0.0150 0.0023 KCl 0.0150 0.0005 NaCl 0.0127 KNO3 0.0145 KNO3 0.0145 0.0023 NaCl 0.0127 0.0005 NaNO3 0.0122 NaNO3 0.0122 KOH 0.0271 0.0023 HCl 0.0426 0.0005 NaOH 0.0248 HNO3 0.0421
- 3. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar value of its own to molar conductivity at infinite dilution irrespective of the nature of other ion present. In Set 1 , the common difference between the molar conductance at infinite dilution is due to difference in 𝝀∞ values of K+ and Na+ . In Set 2 , the common difference between the molar conductance at infinite dilution is due to difference in 𝝀∞ values of 𝐶𝑙− and 𝑁𝑂3 − . On the basis of this observation , Kohlrausch stated the law of independent migration of ions “ At infinite dilution , when all the forces of interaction between ions disappear, each ion migrates independently of its co-ion and contributes a definite value to the total conductance of the electrolyte solution.” This contribution is independent of nature of other ion with which it is associated. In mathematical form Kohlrausch stated the law – “ The value of the molar conductance of an electrolyte at infinite dilution is equal to the sum of the conductances of the constituent ions at infinite dilution”. In other words, a given ion will have same value of limiting equivalent conductance in all its salt solution. Mathematically, the law can be given 𝝀𝒎 ∞ = 𝝂+ 𝝀+ ∞ + 𝝂− 𝝀− ∞ Where 𝝂+ and 𝝂− are the numbers of cation and anions produced by each formula unit of the electrolyte. Example : For different electrolytes the law can be written as 1) 𝝀𝒎 ∞(𝑵𝒂𝑪𝒍) = 𝝀𝑵𝒂+ ∞ + 𝝀𝑪𝒍− ∞ ; 𝝂+ = 𝟏 , 𝝂− = 𝟏 2) 𝝀𝒎 ∞(𝑩𝒂𝑪𝒍𝟐) = 𝝀𝑩𝒂+𝟐 ∞ + 𝟐 𝝀𝑪𝒍− ∞ ; 𝝂+ = 𝟏 , 𝝂− = 𝟐 3) 𝝀𝒎 ∞(𝑵𝒂𝟐𝑺𝑶𝟒) = 𝟐 𝝀𝑵𝒂+ ∞ + 𝝀𝑺𝑶𝟒 −𝟐 ∞ ; 𝝂+ = 𝟐 , 𝝂− = 𝟏
- 4. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar Applications of Kohlrausch law : 1) Determination of degree of ionisation : Degree of ionisation is the fraction of total electrolyte that has dissociated into ions. ∝= 𝑁𝑜. 𝑜𝑓 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑑𝑖𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑖𝑛𝑡𝑜 𝑖𝑜𝑛𝑠 𝑇𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 For a weak electrolyte, the molar conductance at a given concentration, is the measure of extent of dissociation of weak electrolyte. At infinite dilution, the weak electrolyte will be completely dissociated. Therefore , 𝜶 = 𝝀𝒄 𝝀∞ ---- (1) 𝝀𝒄 can be obtained by direct measurement using a conductometer and 𝝀∞ can be obtained with the help of Kohlrausch law 𝝀𝒎 ∞ = 𝝂+ 𝝀+ ∞ + 𝝂− 𝝀− ∞ Thus 𝜶 can be calculated using equation (1) 2) Determination of ionisation constant of weak electrolyte: The extent of ionization of a weak electrolyte is expressed in terms of degree of ionization 𝜶 . In solution of weak electrolyte, the ions are in dynamic equilibrium with unionised molecule. Consider an electrolyte ‘AB’ 𝑨𝑩 ↔ 𝑨+ + 𝑩− If ‘c’ is concentration of electrolyte and 𝜶 is degree of dissociation then 𝑨𝑩 ↔ 𝑨+ + 𝑩− (1- 𝜶) 𝜶 𝜶 Concentration, c (1- 𝜶) c . 𝜶 c . 𝜶 The ionisation constant of ‘AB’ is 𝑲 = [𝑨+] [𝑨−] [𝑨𝑩] = 𝜶.𝒄 𝒙 𝜶.𝒄 (𝟏−𝜶)𝒄 = 𝜶𝟐.𝒄 (𝟏−𝜶) . But 𝜶 = 𝝀𝒄 𝝀∞ ; 𝑲 = ( 𝝀𝒄 𝝀∞ ⁄ ) 𝟐 𝒙 𝒄 (𝟏− 𝝀𝒄 𝝀∞ ) Therefore , 𝐾 = 𝝀𝒄 2 . 𝐶 𝝀∞ (𝟏−𝝀∞)
- 5. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar i) Cell constant is determined by measuring conductance of 0.1N KCl and using value of specific conductance of 0.1N KCl from table. 𝐶𝑒𝑙𝑙 constant = Specific conductance of 0.1NKCl Conductance of 0.1NKCl = _____𝑐𝑚−1 ii) Using cell constant , specific conductance of different concentration of weak electrolyte is calculated using relation. Specific conductance = k = Conductance x Cell constant iii) From the value of specific conductance , molar conductance of weak electrolyte is calculated using relation 𝝀𝒄 = 𝑺𝒑𝒆𝒄𝒊𝒊𝒇𝒄 𝒄𝒐𝒏𝒅𝒖𝒄𝒕𝒂𝒏𝒄𝒆 𝑪 iv) 𝝀∞ can be calculated using Kohlrausch law . Using above values , ionisation constant can be calculated from equation 𝐾 = 𝝀𝒄 2 . 𝐶 𝝀∞ (𝟏−𝝀∞) 3) Determination of Ionic product of water : Water can be treated as a weak electrolyte and ionizes according to equation, H2O H+ + OH- The equilibrium constant for above ionization is 𝑲 = [𝑯+] [𝑶𝑯−] [𝑯𝟐𝑶] 𝒊. 𝒆 𝑲 [𝑯𝟐𝑶] = [𝑯+] [𝑶𝑯−] Since ionization is weak, concentration of water in aqueous solution will be constant 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆 , 𝑲𝒘 = [𝑯+] [𝑶𝑯−] 𝑲𝒘 is called ionic product of water . The value of 𝑲𝒘 can be calculated using Kohlrausch law and by measurement of conductance. i) Cell constant is determined by measuring conductance of 0.1N KCl and using value of specific conductance of 0.1N KCl from table.
- 6. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar 𝐶𝑒𝑙𝑙 constant = Specific conductance of 0.1NKCl Conductance of 0.1NKCl = _____𝑐𝑚−1 ii) Using cell constant , specific conductance of pure water is calculated using relation. Specific conductance = kwater = Conductance of water x Cell constant iii) Molar conductance of water is calculated using relation 𝝀𝒄 = 𝑺𝒑𝒆𝒄𝒊𝒊𝒇𝒄 𝒄𝒐𝒏𝒅𝒖𝒄𝒕𝒂𝒏𝒄𝒆 𝑪 Where C = Concentration of water = Moles of water per m3 iv) Molar conductance at infinite dilution ( limiting molar conductance) is determined using Kohlrausch’s law 𝝀𝑯𝟐𝑶 ∞ = 𝝀𝑯+ ∞ + 𝝀OH− ∞ v) The degree of dissociation can be calculated using equation , 𝛼 = 𝜆𝑐 𝜆0 𝐼𝑜𝑛𝑖𝑐 product of water = 𝐷𝑖𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠 𝑡𝑎𝑛 𝑡 𝑜𝑓 𝑤𝑒𝑎𝑘 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑙𝑦𝑡𝑒 𝐼𝑜𝑛𝑖𝑐 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑐𝑎𝑛 𝑏𝑒 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑢𝑠𝑖𝑛𝑔 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 , 𝐾𝑤 = 𝛼2 × 𝑐 (1-𝛼) 4) Determination of solubility & solubility product of sparingly soluble salt : The solubility of a sparingly soluble salt in solvent is very low. Even saturated solution of such salt is so dilute that it can be assumed to be at infinite dilution. 𝑖. 𝑒 Λ𝑐 𝑠𝑎𝑡 soln = Λ∞ 𝑠𝑎𝑡 soln 𝑀𝑜𝑙𝑎𝑟 conductivity can be obtained from Kohlrausch's law Λ𝑐 𝑠𝑎𝑡 soln = Λ∞ 𝑠𝑎𝑡 soln = Λ0 𝑠𝑎𝑡 soln = 𝜆0 + + 𝜆0 − 𝑀𝑜𝑙𝑎𝑟 conductivity of salt can be determined by 𝜆salt ∞ = 1000𝑘𝑠𝑎𝑙𝑡 𝑐 –(1) Measurement of ksalt : i) Cell constant is determined by measuring conductance of 0.1N KCl and using value of specific conductance of 0.1N KCl from table.
- 7. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar 𝐶𝑒𝑙𝑙 constant = Specific conductance of 0.1NKCl Conductance of 0.1NKCl = _____𝑐𝑚−1 ii) Using cell constant , specific conductance of different concentration of weak electrolyte is calculated using relation. Specific conductance = k = Conductance x Cell constant iii) Specific conductance of pure salt is obtained as the difference between the specific conductance of saturated solution and that of distilled water. 𝒌𝒔𝒂𝒍𝒕 = 𝒌𝒔𝒂𝒍𝒕 𝒔𝒐𝒍𝒏 − 𝒌𝒔𝒐𝒍𝒗𝒆𝒏𝒕 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑜 𝑙𝑢𝑏 𝑖 𝑙𝑖𝑡𝑦: 𝜆𝑠𝑎𝑙𝑡 ∞ = 1000𝑘𝑠𝑎𝑙𝑡 𝑐 ∴ 𝑐 = 1000𝑘𝑠𝑎𝑙𝑡 𝜆𝑠𝑎𝑙𝑡 ∞ The molar concentration ‘c’ of sparingly soluble salt is equal to the solubility of salt in mol.dm-3 ∴ S = 𝟏𝟎𝟎𝟎𝒌𝒔𝒂𝒍𝒕 𝝀𝒔𝒂𝒍𝒕 ∞ = 𝟏𝟎𝟎𝟎(𝒌𝒔𝒂𝒍𝒕 𝒔𝒐𝒍𝒏 − 𝒌𝒔𝒐𝒍𝒗𝒆𝒏𝒕) ( 𝝀+ ∞ + 𝝀− ∞ ) mol/dm𝟑 Solubility in g/dm3 = S(mol/dm3 ) x Molecular wt. 𝐷𝑒𝑝𝑒𝑛𝑑𝑖𝑛𝑔 𝑜𝑛 𝑡ℎ𝑒 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑜𝑓 𝑠𝑎𝑙𝑡, Solubility product (Ksp) can be calculated using relation 𝐾𝑠𝑝 = 𝑥𝑥 . 𝑦𝑦 . 𝑆(𝑥+𝑦) 𝐸. 𝑔. For BaCl2, x = 1 , y = 2 ∴ 𝐾𝑠𝑝 = 4𝑆3 For AlCl3, x = 1 , y = 3 ∴ 𝐾𝑠𝑝 = 27𝑆4
- 8. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar Transport number / Traansference number : The fraction of total current carried by ion is known as transport no. It is represented by the symbol t+ for cations and t- for anions. But current carried by cation is proportional to u+ and current carried by anion is proportional to u- t = t+ + t- = 1 Relation between transport no. and eq. conductance : The current carried by ion is proportional to ionic conductance. i.e current carried by cation is proportional to λ+ and current carried by anion is proportional to λ- Total current carried by ions is proportional to λ+ + λ- and Determination of transport number by Moving Boundary method: Principle : This method is based on the measurement of movement of a boundary generated and maintained between two electrolyte solutions, due to difference in the velocities of the ions of the two electrolyte. From the distance travelled by the boundary in a given time interval transport no. of the ion can be calculated. Let MA ( eg HCl) be the electrolyte whose transport no. is to be calculated. This electrolyte is known as principal/experimental electrolyte. − + − − + = u u u t 1 t 0 and 1 = t + t thus ; I + I = I I + I I = t ; I + I I = t + - + - + - + - - - + + + _ _ − + + + + = u u u t − + + + + = t − + − − + = t
- 9. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar For determination of transport no. of MA another electrolyte (NA) eg. CdCl2 is required which is known as indicator electrolyte and should satisfy the following conditions i) NA should have common anion for determination of transport no. of cation ii) Solution of indicator electrolyte NA should be denser than MA. iii) Mobility or conductance of M+ ion should be greater than N+ ion. iv) A sharp boundary must be established at the start of the experiment. Apparatus: Apparatus consists of a glass tube fitted with 2 electrodes. The top platinum electrode is cathode. The lower portion of tube contains solution of indicator electrolyte in which electrode of the same metal is dipped. The electrolyte MA whose transport no. is to be determined is added slowly over the solution of indicator electrolyte. The boundary aa’ maintained between two solution is marked with some colour. Working : When a current I is passed the Cd dissolves at anode. Cd Cd+2 + 2 e At cathode reduction of H+ ion will occur. H+ + e ½ H2 (g) As H+ ions migrates towards cathode their place is taken by Cd+2 ion. A current of ‘I’ ampere is passed for ‘t’ sec. Throughout the experiment
- 10. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar anion moves towards anode and cations moves upward towards cathode. Hence the boundary between the two solution moves in upward direction from ‘aa’ to ‘bb’. Coulometer is used to calculate the total quantity of current passed. Calculations : Let ‘l’ be the distance travelled by the boundary in time interval ‘t’ sec. If ‘A’ is area of cross section of the tube then the volume swept by the boundary after passing electric charge ‘Q’ coulombs will be . V = A x l Let the concentration of principle electrolyte be ‘c’ moles/dm3 Therefore the amount of H+ ion carried towards cathode will be , V x c = A x l x c The amount of current passed during the electrolysis is given by Q/F where Q = I x t and F = 96500 C Therefore transport no. of H+ ion will be t I F c l A Q F c l A F Q c l A passed current H of Amount = = = = + + Total cathode towards moved tH Factors affecting transport no. : 1) Concentration : Transport no. of an ion increases with decrease in the concentration of an electrolyte. The variation of transport no. with concentration c , is given by the equation. t = t0 - A√c where t0 = transport no. at infinite dilution, A = constant 2) Temperature : An increase in temperature brings the transport no. values of all the ions close to 0.5 . Thus, those transport no. values which are smaller than 0.5 increases and those which are greater than 0.5 decreases with increase in temp.
- 11. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar 3) Nature of co-ion: The transport no. of ion depends on the nature of its co-ion. Eg. Transport no. of Cl- in NaCl is 0.61 and in HCl is 0.17 𝑁aCl HCl 𝒕Cl− = 𝑢𝐶𝑙− 𝑢𝑁𝑎+ + 𝑢𝐶𝑙− tCl− = 𝑢𝐶𝑙− 𝑢𝐻+ + 𝑢𝐶𝑙− tCl− = 0.61 tCl− = 0.17 Though the speed of Cl- ion is same in each case, the speed of H+ ion is much greater than that of Na+ ion. Therefore transport no. of Cl- in HCl is much less than that in NaCl. 4) Size of the ion: Transport no. depends on the speed of the ion which in turn depends on the size of the ion. Smaller the size greater will be the velocity. In aqueous media the hydration increases the size of the ion and decreases its speed. Smaller the ionic size, maximum is hydration and transport no. value is small. Eg. Transport no. of Li+ , Na+ and K+ ions in aqueous solution are 0.33 , 0.38 and 0.48 respectively. The ionic size of these ions increases from Li+ to K+, hence it is expected that Li+ should travel fast and should have highest transport n. But due to hydration Li+ has least transport no. 5) Complex formation : Sometime transport no. of an ion decreases with increase in concentration and it becomes abnormal . Eg. Complex formation such as [CdI4]-2 , [FeCl6]-4 shows the cation migrating towards anode instead of cathode. Hence, such ions shows –ve transport no. value. Consider solution of CdI2 CdI2 Cd+2 + 2 I- CdI2 + 2 I- [CdI4]-2 If anion [CdI4]-2 moves faster than cation Cd+2 , then there will be an increase in concentration of Cd around anode instead of decrease. Therefore value of transport no. of Cd+2 ion will become abnormal at high concentration. ************