CONDUCTIVITY

CONDUCTANCE OF ELECTROLYTIC SOLUTIONSWhen electricity is passed through the solution, the resistance offered by the solution is ‘R’ which measured in ohm (Ω) and in SI units is equal to (kgm2)/ (s3A2).The resistance can be measured with the help of a Wheatstone bridgeThe electrical resistance of any object is directly proportional to its length ‘l’ and inversely proportional to its area of cross section ‘A’R α l/A or R = ρ l /A ρ= R/ l/A =R x A/l( Ω xm2/m) = (Ω meter)where ρ is called the resistivity (specific resistance).Its unit in SI system is ohm meter (Ω meter) or its sub units ohm centimeter (Ω cm). (If l = 1 m and A = 1 m2, then R = ρResistivity for a substance is defined as its resistance offered when it is one meter long and its area of cross section is one m21Ωm =100 Ωcm or 1 Ωcm = 0. 01 Ω mThe reciprocal of resistance ‘R’ is called conductance represented by G (Conductance is the ability of a material to pass electrons)and is equal ohm-1 or mho or Ω-1 The inverse of resistivity called conductivity (specific conductance) represented by bykappaIts SI unit is Siemens S m-1 or S cm-1SPECIFIC CONDUCTANCE OR CONDUCTIVITYConductance G =1/R or G = A/ρl =  A/l1/ρ =Conductivity of a material in Sm-1 is conductance offered by a material of one meter long and its area of cross section 1m21Sm-1 = 100Scm-1= 1/ρ,  = kappa - the specific conductance or conductivity   The unit of specific conductance is ohm-1 cm-1.MEASUREMENTUNITSResistanceOhmConductancesiemensResistivityOhmcmConductivitysiemens/cmThe following table gives the conductivity at 298K.The value of conductivity depends on the nature of the material and also on temperature.CONDUCTORS, INSULATORS AND SEMICONDUCTORS.Materials are classified into conductors, insulators and semiconductorsDepending on their magnitude of conductivity.METALLIC OR ELECTRONIC CONDUCTORS Conductors which transfer electric current by transfer of electrons, without transfer of any matter, are known as metallic or electronic conductors. Metals such as copper, silver, aluminum, etc., non-metals like carbon (graphite - an allotropic form of carbon) and various alloys belong to this class.They are good conductorsGlass, ceramics have low conductivity are insulators.Substances like silicon, doped silicon or gallium etc are having conductance in between conductors and insulators are called semiconductorsELECTROLYTIC CONDUCTORS: Conductors like aqueous solutions of acids, bases and salts in which the flow of electric current is accompanied by chemical decomposition are known as electrolytic conductors.DIFFERENCE BETWEEN ELECTRONIC CONDUCTORS AND ELECTROLYTIC CONDUCTORSElectronic or metallic conductorsElectrolytic conductorsConduction is through the movement of electronsEg conduction of electricity through a copper wireConduction is through the movement of ionsConduction of electricity through molten NaClDepends on the nature of the materialDepends on the nature of the electrolyte usedThe number of electrons per atomDepends on the size of the ions and solvationDecreases with increase of temperatureIncreases with increase of temperatureMEASUREMENT OF CONDUCTANCE OF IONIC SOLUTIONSFor the determination conductance of a solution we are taking the solution in a conductivity cell. The cell consists of two Pt electrode coated with Pt black (finally divided metallic pt is deposited on electrodes)These two electrodes have area of cross section ‘A’ and the electrodes are separated by distance ‘l.’Therefore the solution is confined between these electrodes is a column of length ll and area of cross section A.The resistance of such a solution is R = ρ l /A = l/A. l /A = R/ ρ=R x The quantity l/A is called cell constant represented by G* unit is length-1It can be calculated if we know the value l and ACell constant G* = Resistance X conductivity DETERMINATION OF CELL CONSTANTMeasurement of cell constant is inconvenient and also unreliable. Therefore the cell constant is usually determined by measuring the resistance of a cell containing a solution whose conductivity is accurately known at different temperatures.The cell constant G* isl/A = R After the determination of the cell constant we can use it for the determination the résistance or conductivity of any solution .The arrangement is given belowIt consists of two resistances R3 and R4 and a variable resistance R1and the conductivity cell having the solution at R2 and the Wheatstone bridge is fed by an oscillator O and P is suitable detector like a head phone and bridge is balance when no current flows through the detector. Now at this timeThe unknown resistance (resistance of the solution)R1/R2=R3/R4R2 = R1 R4/R3So if the cell constant is known and the resistance of the solution is determined we can calculates the conductivity of the solutionCell constant G*= x RG*Conductivity X ResistanceConductivity=Cell constant/ResistanceSPECIFIC CONDUCTANCE OR CONDUCTIVITYConductivity depend on the number of ions present in unit volume (1 ml ) solution In the case of electrolytic solutions, the specific conductance (conductivity)is defined as the conductance of a solution of definite dilution enclosed in a cell having two electrodes of unit area separated y one centimeter apart asConductivity and molar conductivity of KCl at 298KEQUIVALENT CONDUCTANCE ()Equivalent conductance is defined as the conductance of all the ions produced by one gram equivalent of an electrolyte in a given solutionTo understand the meaning of equivalent conductance, imagine a rectangular trough with two opposite sides made of metallic conductor (acting as electrodes) exactly 1 cm apart, If 1 cm3 (1 mL) solution containing 1 gram equivalent of an electrolyte is placed in this container is measured. = V In case, if the concentration of the solution is c g equivalent per litre, then the volume containing 1 g equivalent of the electrolyte will be 1000/C.1000 x IN= Vxc :V=1000/c So equivalent conductance eq =  1000/c =  × 1000/N Where N = normality The unit of equivalent conductance is ohm-1 cm-2 equi-1.One of the factors on which the conductance of an electrolytic solution depends is the concentration of the solution. In order to obtain comparable results for different electrolytes, it is necessary to take equivalent conductance. . MOLAR CONDUCTIVITYThe molar conductance is defined as the conductance of all the ions produced by ionization of 1 g mole of an electrolyte when present in V mL of solution. It is denoted by. Molar conductancem =  ×V   Where V is the volume in mL containing 1 g mole of the electrolyte. If c is the concentration of the solution in g mole per litre, then m =  × 1000/c It units are ohm-1 cm2 mol-1. Equivalent conductance =  (Molar conductance)/n Where       n = (Molecular mass) / (Equivalent mass)Cell constant G* = Conductivity X Resistance=100 Ω x 1.29 S/m=129 m-1=1.29cm-1Conductivity of 0.02molL-1 KCl= 129 m-1/520Ω = 0.248Sm-1=0.248x10-2Scm-2Molar conductivity m =  × 1000/c =0.248 x1000/0.02=0.248x 0.248x10-2Scm-2x1000cm-3L-1x/0.02molL-1= 124Scm2molEFFECT OF DILUTION ON EQUIVALENT CONDUCTANCEThe value of equivalent conductance increases with dilution. This is due to the fact that degree of ionization increases with dilution thereby increasing the total number of ions in solution. Solution which contains large number of ions compared to another solution of the same concentration at the same temperature has more conductances and is said to be stronger electrolyte. The one which has relatively small number of ions is called a weak electrolyte. The number of ions from an electrolyte depends on the degree of dissociation. The curve (Fig.12.6) shows the variation of the equivalent conductance of some electrolytes with dilution. It shows that electrolytes behave in two ways o dilution.Equivalent conductance at infinite dilutionElectrolytes like KCl have high value of conductance even at low concentration and there is no rapid increase in their equivalent conductance on dilution. Such electrolytes are termed strong electrolytes. In the case of strong electrolytes, there is a tendency for equivalent conductance to approach a limiting value when the concentration approaches zero. When the whole of the electrolyte has ionized, further addition of the water does not bring any change in the value of equivalent conductance. This stage is called infinite dilution. The equivalent conductance has a limiting value at infinite dilution and is represented by Electrolytes like acetic acid have a low value at high concentration and there is a rapid increase in the value of equivalent conductance with dilution. Such electrolytes are termed weak electrolytes. There is no indication that a limiting value of equivalent conductance can be attained even when the concentration approaches zero. Thus, graphically, of weak electrolytes cannot be obtained.KOHLRUSCH LAWAt time infinite dilution (m) , the molar conductivity of an electrolyte can be expressed as the sum of the contributions from its individual ions v+ and v- are the number of cations and anions per formula unit of electrolyte respectively and, λ∞+ and  λ∞- are the molar conductivities of the cation and anion at infinite dilution respectively APPLICATIONS OF KOHLRAUSCH'S LAWDetermination of Λ∞m for weak electrolytes Determination of the degree of ionization of a weak electrolyte Determination of the ionization constant of a weak electrolyte Determination of the solubility of a sparingly soluble salt It is thus concluded that equivalent conductance of electrolytes whether strong or weak increases with dilution and reaches to a maximum or limiting value which is termed  (equivalent conductance at infinite dilution.) in the case of strong electrolytes cannot be obtained by extrapolation of the graph of equivalent conductance to zero concentration but in the case of weak electrolytes it cannot be obtained accurately. An indirect method for obtaining   for weak electrolyte has been given by Kohlrusch.