What is the theoretical background of conductometry?

2. BASICS OF CONDUCTOMETRY2.1 GeneralConductometry means measuring the conductivity –a conductometer measures the electrical conductivityof ionic solutions. This is done by applying an electricfield between two electrodes. The ions wander in thisfield. The anions migrate to the anode and the cationsto the cathode. In order to avoid substance conversionsand the formation of diffusion layers at theelectrodes (polarization), work is carried out with alternatingvoltage. The rule of thumb is that the frequencyof the alternating voltage must be increasedas the ion concentration increases. Modern conductometersautomatically adapt the measuring frequencyto the particular measuring conditions.Ion migration in an electric field depends on manyfactors. The temperature has a decisive influence onthe viscosity of the solution and therefore on the mobilityof the ions. As the temperature increases theviscosity decreases and the conductivity increases.Dissociation constants are also temperature-dependentquantities. This is why it is important to makemeasurements at a constant temperature or to compensatefor changes of temperature by using the socalledtemperature coefficient. The temperature coefficientof most salt solutions is approx. 2%/°C, butdepends on the temperature in very dilute solutions.The measuring unit used in conductivity measurementsis the electrical resistance of the solution. Thismeans that the conductivity is a sum parameterwhich includes all dissolved ions. Conductivity cannotbe used for the determination of a single type of ion,unless the sample is a solution of a single salt or theconcentrations of the other ions are known. The reciprocalvalue of the measured resistance of the solution,the so-called conductance L with the unitSiemens (S = Ω -1 ) is by itself less meaningful, as theshape of the measuring cell must be taken into account.The cell constant c of a conductometric measuringcellc = distance between Pt sheets (cm –1 )electrode surface areaCell constant (11)must be known. The result of the measurement istherefore always given as the specific conductivity Κwith the unit Siemens per cm (S·cm –1 ).Specific conductivity (12)κ = L * c (S cm –1 )This means that the conductometer must be calibratedbefore each measurement by determining the cellconstant in a solution of known specific conductivity.The specific conductivity for various concentrations ofmany salts is given in tables. The specific conductivityΚ is linked with the concentration c i of the individualion i via the concentration-dependent equivalent conductivityΛ i . The equivalent conductivity Λ i is similarto the activity coefficient γ (see Section 1.2.) and isalso a quantity that depends on the concentration.κ = Σ (Λ i * z i * c i )iSpecific conductivity and concentration (13)At great dilutions, i.e. c i ≤0.001 mol/L, the equivalentconductivity Λ i can be equated with the equivalentconductivity shown in the tables for an infinite dilution.89

2. BASICS OF CONDUCTOMETRYTable 14: Conductivity Κ of various substances and solutionsConductorMetallic copperPotassium hydroxidesolution (c = 1 mol/L)KCl solution(c = 0.1 mol/L)Brackish waterAcetic acid(c = 1 mol/L)Drinking waterGraphiteDistilled waterUltrapure waterPure benzeneT (K)273291293273291298273273273273Conductivity caused byElectronic conductionIonic conduction resulting fromthe complete dissociation of KOHIonic conduction resulting fromthe complete dissociation of KClIonic conduction resulting fromthe dissociation of salts and carbonic acidIonic conduction resulting fromthe partial dissociation of CH 3 CH 2 COOHIonic conduction resulting fromthe dissociation of salts and carbonic acidElectronic conductionIonic conduction resulting from contaminationby salts, dissociation of water and carbonic acidIonic conduction resulting fromlow self-dissociationIonic conduction resulting fromthe dissociation of traces of waterConductivity Κ (μS cm –1 )645’000’000’000184’00011’66020’000...1’000’0001’30010...2’0001’2000.06...100.0560.00000005Conductometry is used for direct measurements andin titration. The theory is identical for both methods.Whereas in direct measurements it is the absolutevalue that is of interest, in titrations it is the change inthe measured value. Direct measurement is oftenused for monitoring surface waters, waterworks, waterdesalination plants and in the preparation of ultrapurewater, where particular limits must not beexceeded. Conductivity detection is mostly used forprecipitation titrations, where the equivalent point isrecognized by the conductivity reaching a minimumvalue. The absolute value is of secondary importance.Selecting the right cell constantThe cell constant c is defined for conductometricmeasuring cells. A measuring cell with two parallelelectrodes at a distance of 1 cm and each with anarea of 1 cm 2 theoretically has a cell constantc = l · A -1 = 1 cm -1 . The cell constant is never exactlyl · A -1 , as the electric field is not strictly homogeneous.The rules of thumb given in Table 15 are usedfor selecting the correct measuring cell:Conductivity measurementsWhereas the instruments used for potentiometryhave been standardized (input impedance >10 12 Ω,zero point at pH 7), this is not the case with conductometers.The influence of the cable capacity, themeasuring frequency level, the conductivity rangeand the adjustable cell constant, the method used forconductivity measurements (phase-sensitive, frequency-dependent,bipolar pulse, etc.) vary and dependon the type of instrument. This means that theinstrument must be taken into account for solvingapplication problems. Important parameters are:• Platinizing quality (platinum black) ➝ high seriescapacity C S• Electrode area A ➝ high series capacity C S• Cell constant c• Measuring frequency f• Cable capacity C P• Cable resistance R C• Instrument measuring range (resistance range)Figure 13:Cell constants and recommended conductivity intervals.90

Table 15: Recommended cell constantsInterferences, carec = 0.1 cm -1c = 1 cm -1c = 10 cm -1c = 100 cm -1Conductivity measuring cells with Pt sheetsConductivity cells have a very porous black platinumcoating in order to avoid polarization effects in mediawith a high conductivity. However, the properties ofthis coating may change in time (contamination, abrasionof the platinum coating, etc.); this could alterthe cell constant. This is why it is absolutely necessaryto calibrate the conductometric measuring cell beforemaking a measurement in order to avoid measuringerrors. For the exact determination of cells with a cellconstant of 1 cm -1 ) ➝measured value displacedCarryover of residual saltswhen changing to solutionswith low conductivity ➝drift to higher valuesAir bubble located betweenelectrode plates ➝ unsteady signalMeasuresHigh measuring frequency, instrument withhigh resolution or cell constant >1 cm -1 ,short cable (low R c )Low measuring frequency, instrument withhigh resolution in upper resistance rangeor cell constant

2. BASICS OF CONDUCTOMETRY2.2. Conductivity measurement in water forpharmaceutical use according to USP andPharm. Europe (EP)There are special requirements for the conductivitymeasurement in water for pharmaceutical use («waterfor injections») according to USP 645, EP 2.2.38resp. the latest EP -4.8-07/2004:0169. Besides a precisionconductometer whose temperature compensationcan be disabled, a conductivity measuringcell and a conductivity standard are to be used thatallow to determine the cell constant with a maximummeasuring error of 2%. To prevent the uptake of carbondioxide, the measurement should be carried underexclusion of air and/or in a flow cell. The samplefulfills the specification if one of the following threeconditions is met:Stage 1:The sample is measured directly without further pretreatmentand without temperature compensation. Ifthe water fulfills the specification indicated in table17, the test is considered as passed.Stage 2:If the conditions are not fulfilled by stage 1, continueas follows: The conductivity of at least 100 mL sampleis measured under strong agitation at 25 °C ±1 °C assoon as the drift caused by the uptake of carbondioxide is smaller than 0.1 μS/cm per five minutes. Ifthe measured value is smaller than 2.1 μS/cm, the testis considered as passed.Stage 3:However, if the sample does not fulfill the specificationof stage 2, a sample of exactly 100 mL is mixedwith 0.3 mL saturated KCl solution. Then the pH valueof this solution is measured exactly to 0.1 pHunits. Only if the conductivity fulfills the conditionsspecified in table 18 the test is considered as passed.Otherwise the water cannot be used for pharmaceuticalpurposes.Table 17: First step of the conductivity measurement according to USP 645 and EP -4.8-07/2004:0169Temperature Conductivity not Temperature Conductivity notlarger than (μS/cm)larger than (μS/cm)0 0.6 55 2.15 0.8 60 2.210 0.9 65 2.415 1.0 70 2.520 1.1 75 2.725 1.3 80 2.730 1.4 85 2.735 1.5 90 2.740 1.7 95 2.945 1.8 100 3.150 1.9Table 18: pH and conductivity criteria for stage 3pH Conductivity not pH Conductivity notlarger than (μS/cm)larger than (μS/cm)5.0 4.7 6.1 2.45.1 4.1 6.2 2.55.2 3.6 6.3 2.45.3 3.3 6.4 2.35.4 3.0 6.5 2.25.5 2.8 6.6 2.15.6 2.6 6.7 2.65.7 2.5 6.8 3.15.8 2.4 6.9 3.85.9 2.4 7.0 4.66.0 2.492