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Specific Conductance:Theoretical Considerationsand Application to AnalyticalQuality Control

United StatesGeologicalSurveyWater-SupplyPaper 2311

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Specific Conductance:

Theoretical Considerationsand Application to AnalyticalQuality Control

By RONALD L. MILLER,WESLEYL. BRADFORD, and

NORMAN E . PETERS

U.S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER 2311

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DEPARTMENT OFT H E INTERIOR

DONALD PAUL MODEL, Secretary

U.S. GEOLOGICAL SURVEY

Dallas L. Peck, Director

UNITED STATES GOVERNMENT PRINTING OFFICE: 1988

For sale by the Books and Open-File Reports Section, U.S. Geological Survey,Federal Center, Box 25425, Denver, CO 80225

Library of Congress C ataloging in Publication DataMiller,Ronald LSpecific conductance. U.S. GeologicalSurvey water-supply paper ; 2311)Bibliography: p.Supt.ofDocs.no.: I 19.13:23111 . Water quality Measurement. 2. Water Electric properties-

Measurement. 3. Electricconductivity M easurement. I. Miller,Ronald L . II . Peters, Norman E. I I I .Title. IV. Series: GeologicalSurvey water-supply paper 2311.

TD370.B69 1986 628.V61 86-600214

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CONTENTSAbstract 1Introduction 1Theory of specificconductance 1

Electrical resistance andconductance 1Definitionof conductivity 2Potassium chloridesecondary standards 2Temperature effects and instrumental temperaturecompensation 3Ionic conductance 6

Concentration relationships 7Temperaturerelationships 8

Effects of complexationand protonation 9Applicationsto analytical quality control 10

An empiricalapproach in natural waters 1 0Tests of the empiricalmodel 1 1

Adjustmentsfor effectsof complexation 1 1Calculationof the sum of conductanceand the exponentialcorrection

factor (f) 1 1Evaluationof/ 1 1

Quality control checks 1 2Comparisonof measuredwith computed specificconductancean d

anions with cations 1 2Predicting the sumof anions or cations 1 3

A special case for seawater and estuarine waters 1 3Notes on specificconductancemeasurements 1 4Instrumentation 1 4Procedures 1 4

Summary 1 5References 1 5

FIGURES

1-5. Graphsshowing:1 . Conductivity-temperaturerelationshipsfor 0 .01 N KG solution and 1 per

mil chlorinity seawater 4

2. Percentagechange in conductivitywith temperature for 0 .01 N KC1 solution and seawater in 1 °C increments 5

3. Values of the ratio of specificconductanceto conductivityfor 0 .01 N KGsolution and 1 per mil chlorinity seawater 6

4. Decreases in equivalent conductanceof selected electrolyteswith increasing concentration 8

5. Changes in limitingequivalentconductivityof selected ions withtemperature 9

Contents III

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TA B L E S

1 . Conductivityof secondary standard potassiumchloride (KC1)solutions 32. Comparisonof conductivityof 0 .01 N K C 1solutions (injiS/cm) convertedto S I

units 33. Comparisonof the ratio K /K predicted by dividing 14 10 .6 jiS/cm(at 25 °C) by

the conductance calculatedusing equation9, equation 10, and calculated

using data from Rosenthal and K idder (1969 )and Harned and Owen(1964) 74. Values of K /K for 0.01 N KG solutions in 1 °C increments calculatedby

dividing 1410.6jiS/cm (at 25 °C) by the conductancecalculated usingequation9 7

5. Limiting equivalentconductances(\°) of selected ions 106. Stabilityconstants (log K,) for ion associations betweenmajor inorganic ions in

natural waters at 25 °C 1 07. Statisticalsummaryof exponentialcorrection factor f) values 1 18. One standard-deviation rangeof estimated K using (XC,* \°/ 1 29. Relationshipof the/value and anion ratios (pequals the probabilityof accept

ing the null hypothesis,H 0; correlationcoefficientr=0) 1 210. Algorithmsfor calculatingconductivity,specificconductance,chlorinity, and

salinity of seawater andestuarine water 1 4

IV Contents

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SYMBOLS[Allunits areabsolute asdefinedby Le SystemeInternationald'Unites(SI) (Am ericanSocietyfor Testingand Materials, 1976), except as noted. The conversion of conductivity values from abase of theinternationalohm to the absolute ohm (theSI system) is made by multiplyingby 0.999505.Equations inwhich the symbol appears are in parentheses.]

A Cross-sectionalarea of a conductoror conductingsolution (cm3) (2,3,4)A,B,a,b,c Empiricalproportionality constants(13 ,14 ,15)o r Fraction of salt dissociated in solution (11)or, Fraction of the constituent/ present as the free ion (12,17,18,20)C Concentrationof a salt in solution in equivalents/liter(N) or moles/liter (M)

(7,12,13,14,15)C, Concentrationof ion i in solution in milliequivalents/liter(meq/L)

(17,18,20,27,28)C y * Concentrationof ion i after accounting for complexation(meq/L) (25,27)E Electrical potentialin volts (joules/coulomb) (1)ff Resistivityof a conductor (ohm cm) (2,3,4)7 Activitycoefficient of an ion in solution

/ Exponential correction factordefined by equation20 (20,25,26,28)Fj Fraction of major ions that are monovalent usingconcentrationsin milli-

equivalentsper liter (26)^ Viscosity of the solvent (water);also used as an empiricalconstant in some

equations (15)I Ionic strength of a solution (1/2 2 C 8) where Q is expressed in molal units

(moles/kilogramof solvent) (16)/ Electrical current in amperes (coulombs/second)(1)

K Cell constant of a measurementdevice (5,6,30)Kj Stabilityconstant fora complexation reaction (19,21,22,23,24)x Conductivityof a solution in Siemens/centimeter(S/cm) or microsiemens/ce-

ntimeter (,uS/cm)at a temperature other than 25 °C (4,8,9,10,12,30)/e ; Specific conductanceof a solution,conductivity( K )at 25 °C

(7,10,17,18,20,25,28)A ? Conductivityof a standard solution (6)xm Measured conductivityof a standard solution (6)L Length of a conductor (cm) (2,3,4)/y._ Mobilitiesof ions in solution (11)A Equivalent conductanceof a salt in solution at 25 °C; the conductanceper

chemical equivalentof a salt at concentrationC; the equivalentconductivity(A*) at 25 °C (in ftS/crn per meq/L) (14,1 5)

A* Equivalentconductivityof a salt in solution at a temperatureother than 25°C (13)A°* Limitingequivalentconductivityof a salt in solution, the equivalentconduc

tivity (A*) at infinite dilution (13)A° Limitingequivalentconductanceof a salt in solution, the limitingequivalent

conductivity(A0*) at 25 °C (14,15)AA Average equivalentconductance fora water sample (27,28)& i Equivalentconductanceof ion i ; the conductanceper chemical equivalentof

ion at concentrationQ; the equivalentconductivity(\i*) at 25 °C ( p-S/cmper meq/L) (16,17)

/ l y * Equivalentconductivityof ion i in solution; the equivalent conductance(\ )at a temperatureother than 25 °C (12)

Symbols V

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Specific Conductance: Theoretical Considerationsand Applicationto Analytical Quality Control£y Ronald L Miller,Wesley L Bradford, and Norman E . Peters

Abstract

This report considers several theoretical aspects andpractical applications of specificconductance to the study ofnatural waters.

A review of accepted measurements of conductivityofsecondary standard 0.01 N KCI solution suggests that awidely used algorithm for predicting the temperaturevariation in conductivityis in error. A new algorithm is derived andcompared with accepted measurements. Instrumental temperature compensation circuitsbased on 0.01 N KCIor NaCIare likely to give erroneous results in unusual or specialwaters, such as seawater, acid mine waters, and acid rain.

An approach for predicting the specific conductance ofa water sample from the analytically determined majorioncompositionis described and criticallyevaluated. T he modelpredicts the specificconductance to within ±8 percent onestandard deviation)in waters with specificconductances of 0to 600 /iS/cm. Application ofthis approach to analyticalqualitycontrol is discussed.

INTRODUCTION

Specificconductance is one of the most frequentlymeasured and useful water-quality parameters. Instrumentation now available,appropriatestandard solutions,and simpleprocedures allow measurementsto be madeeasily in the field or laboratorywith 95 percent or betteraccuracy. Specificconductance correlateswith the sum ofdissolvedmajor-ion concentrationsin water and often witha singledissolved-ionconcentration(Hem, 1970).Thus, itusefully supplements analytical determinationof major

ions. Specific conductance can also be used for quality-control checks on laboratory determinationsof major ionconstituents.

This report discusses several aspects of electricalconductancein aqueoussolutions,includingvariationwithtemperatureand dissolved-ionconcentrationand the ability of current theory to describe thesevariations.A newalgorithm for describingthe changes in conductivity withtemperaturein a standard solution is derived and tested.The report also presents and evaluates an empiricalmodel for estimatingthe specificconductance from ana

lytically determined concentrations of the major ions.Methods are suggested for use of measured and estimated specific conductance in analyticalquality control.Finally, the report offers suggestions and precautions onthe measurement of specific conductance in naturalwaters.

THEORY OF SPECIFIC CONDUCTANCE

ElectricalResistance and Conductance

Ohm's Law is typicallywritten

E=i R,where

(1)

E electrical potential, involts (joule/coulomb),

i= electrical current, in amperes (coulomb/second), and

R= resistance, in ohms (joule second/coulomb2).

The resistance of a conductor is directly proportional to its length (L) and inverselyproportional to itsarea (A). The proportionality constantis termed theresistivity(e) and is a fundamentalphysicalpropertyof aconductor. Thus,

n ~

an d

RA

(2 )

(3)

with units of ohm cm .Two types of electrical flow are common: metallic

and electrolytic. Metallic conductance involves valenceelectrons,which are relativelyfree to movefrom atomtoatom, rather than electrons that are bound to one atom.Metallic conductance is not of concern in this report.Electrolyticor ionic conductionoccurs mainlywith saltsin the solid, liquid, or dissolved state and involves the

Theory of Specific Conductance 1

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migration of ions rather than electrons. In that case,electrons are bound to the atoms, and changesin valencestate normally do not occur. An exception occurs inelectrolytic cells where electrons are transferred fromanode to cathode through ametallic conductor, causingchanges in the valence state of ions in solution.

When an electricalpotential is applied to anaqueous solution containing ions, positive ions (cations)

migrate toward the cathode, andnegative ions(anions)migrate toward the anode.The conductivity (abilitytoconduct an electricalcurrent) of the solution is a functionof the rate of movementof charges in the potential field,which, in turn, is a function of the speed of migrationofindividualions, the charges and concentrationsof the ions,and interactions am ongindividual ions.

Several phenomena occur in aqueous solutionsunder a potential field that do not occur in metallicconductors; that circumstance necessitates aspecificoperational definition for conductivity in aqueous solutions. Ions in solution are surrounded by a sphere ofoppositely chargedions and water. When a potential fieldis imposed on a solution, the migrationof the central iondistorts the cosphere of water and oppositely chargedions, and the cosphere itselfseeks to move inthe oppositedirection. The effect may be viewed as a drag on themigratingion. Both cations and anions experience similareffects, but in opposite directions. Under a constantpotential field, the cations and anions accumulateat theelectrodes until a solution potential is achieved that balances the applied potential;that process is called polarization.

If allowed to persist, polarization results in cessation of transfer of charge in solution,hence an absenceofelectricalcurrent. The useof alternatingpotential polarity(alternating current) prevents polarization andreducesthe drageffect on theions. Primarily forthose reasons,allstandard devices that measure resistivityor conductivityuse alternating potentialpolarity, commonly with a frequency of 1,000 cycles/second(Hz).

Definitionof Conductivity

Conductivity( K ) is defined as the reciprocalof theresistivity normalized to a 1-cm cube of a liquid at a

specified temperature.

in ohm 1 cm (4)

By common use, the reciprocal of an ohm wasformerlycalled a mho. Thus, units ofconductivityweremhos cm" 1 or, more practically in natural waters,micromhos cm" 1 (jxmho cm" 1), for one-millionthof amho (Rosenthaland K idder,1969).Present SI usage isthe jiSiemen/cm(pS/cm). The term specificconductance( / * ; )is used in this paperwhen measurementsare made at

or correctedto the standard temperature 25 °C. It is notalways convenient or practical to design a measurementcell to exact dimensions anda cubic shape; therefore, acell constant (K) relating themeasuredconductivity totheconductivityof an accepted standard is determined for acell. The cell constant is readily determined from aresistancemeasurementon a Wheatstonebridge (Danielsand Alberty, 1967).

J « V J? 5,\K ±K , \3

whereR m is the measuredresistance,and R is the knownresistance of the standard.By substituting appropriateforms of equation (4),it can be shown that

K ,n =KK°, (6)

where K nand K °are the measuredand known conductivityof the standard. The primary standard fordeterminingcell constants is mercury, but because m ercuryhas a highconductivity, aqueous potassium chloridesolutions arecommonly used as secondary standards (Harned and

Owen, 1964) .

Potassium ChlorideSecondary Standards

Early efforts to develop secondary standard solutions for conductivity measurements wereplagued byambiguity in the concentration units and methods ofmeasurement.The workof Jones and Bradshaw(193 3) asreported by Harned and Owen (1964)provided the firstunambiguousset of data on the conductivityof potassiumchloride (KG) solutions. Secondary standards now used

are based on these data (table 1). To avoid ambiguity,concentrationsof KC1 in solutions are listed in two columns. The first column gives the standard normalconcentration (N)and the less used demalconcentration(D);the second columngives the actual weight/weightconcentration. Manylater works on specific conductance,including thisreport, use thesedata as the standardof comparison.

Below 0.01molar (M) concentrations,the specificconductancein /-iS/cm of a potassiumchloride solution at25 °C is given by the following equation modifiedfromLind and others (1959):

where

* ,=149 ,940C-94 ,650C3 /2+58,740C2l ogC+198 ,460C2, (7 )

Kf = specific conductance (conductivity at25 °C) in j x , S / c m(based on the international ohm multiply K ,by 0.999505toobtain SI units based on the absoluteohm), an d

C = concentration, in moles per liter (M)(equivalent toN for KC1).

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able 1 Conductivityof secondary standard potassium chloride (KCI) solutionsModifiedfrom Harned and Owen (1964),p. 197;data from Jones and BradshawJ1

Approximateoncentration2

INID0.1 N0.1 D0.01 N0 .01 D

Weight of K C Iin grams p <kilogramof solution in vaci

71 .382871 .1352

7 .433447 .4 1 9 1 30.7465580 . 745263

jr

J0 0°C

6539865144

7150.87134.4

774.74773.26

Conductivityin pS/cm18 °C

9 8 1 5 297790111 8 6 .4111 6 1 .2

1222 .081219 .92

20 °C

1 0 1 9 7 3.

11661 .8.

1275 .09-

25 °C

111 6 7 8111 2 8 7

12879 .812849 .6

1410 .751408 .07

1 Originalvalues were based on the international ohm. The values shown havebeen corrected to SI units based on the absolute ohm bymultiplyingthe originalvalues by 0.999505.The accuracyof these measurementsin the 0.01D solution have been questioned in the fourthsignificant figureby Saulnierand Barthel (1979)and Marsh (1980).The values shownwill be used pendingfurther inquiry.

The demal (D) is definedas a solution containing onegram formulaweight of salt per cubicdecimeter(liter) of solution at0 °C. The normal(N) is definedas one gram equivalentweightper liter ofsolution. Becausethe temperatureof the solution is not part of the definition,thenormalitiesare approximate.The demalities are exact.

For a 0 .01 normal (N) solution, equation 7 gives apecificconductance thatis 0.10percent g reaterthan that

given in table 1. Franks (1973) gives an equation (nothown) of a similar form for different temperaturesthatequires a knowledge of the dielectricconstant and visosity at each temperature.

T emperature Effects and InstrumentalTemperature Compensation

The conductivityof an aqueous solution is determined by the concentration, charge, andmobility of thedissolved ions. Temperature affects the viscosity of theluid (and thus the mobilityof ions in solution),the size of

he associatedcosphere of water and oppositelychargedons around each ion, and the concentrationexpressedinvolumeunits. Each of these effectson conductivitywill bediscussed. The charges on the ions are not affected byemperature,except for changes in the stabilityconstants

of complexes,a minor effect discussed later.The conductivityof most natural waters, including

seawater, increases with temperature 2 to 3 percent perdegree Celsius above0 °C. As the temperature increasesabove 4 °C, water expands involume about 0.025percentper degree. Because quantitiesof solute in solution remainhe same, in the absence of other effects, expansion

results in a decrease in concentration expressed inunitsper volume (molar, normal) and a small decrease in

conductivity. Thus, volume changes cannot account foreither the direction or the magnitude of changes inconductivity with temperature. The viscosity of waterdecreaseswith increasingtemperatureby about 2 percentper degree Celsius (Weast, 1976),decreasing the resisance to flow, thus increasingconductivity.The direction

and magnitude of this effect approaches the increase inconductivity of about 2 percent per degree Celsiusobserved in many aqueous solutions (Hem, 1970) .

As temperatureincreases,solvationof ions (association of water m olecules) decreases, decreasing thesize ofthe associatedcosphere,and thus increasingion mobilityand conductivity(Daniels and Alberty, 1967).Rosenthal

and K idder (1969 )give a range of 0.5 to 3 percent for theincrease in conductivityper degree Celsius,but this rangewas determinedon industrial and laboratorysolutions.

Rosenthaland K idder(1969)measuredthe conductivity of a solution of approximately0.01 N KCI in 1 °Cincrements between1 5 and 30 °C in accordancewith theAmerican Society for Testing and Materials StandardD-l 125-82 (AmericanSocietyfor Testing and Materials,1985).The concentrationof this standard is verynear thatof the 0 .01D solutionof Harned and Owen (1964),whichaccounts for the apparentlow bias of about 2 /iS/cm thatappears in the Rosenthal and K idderdata (table 2). Little

informationis given on the temperature controls on themeasurements.Nevertheless,the temperaturedetail givenby Rosenthal and K idderinvites further analysis.

Rosenthal and K idder's(1969)data show a slightupward curvature in the conductivity-temperaturerelationship (fig. 1), as do those for 1 per mil (parts perthousand) chlorinity seawater(Accerboni and Mosetti,1967),plotted for comparison.Accerboni and Mosetti's

Table 2. Comparison of conductivity of0.01 N KCI solutions in /tS/cm) converted to SI units

T ° C )

01 51 82 02 53 0

J o n e s

7 7 4 . 7 4

1 2 2 2 . 0 81 2 7 5 . 0 91 4 1 0 . 7 5

R o s e n t h a l

.1 1 4 21 2 2 01 2 7 31 4 0 81 5 4 7

C a l c u l a t e d3

7 7 3 . 71 1 4 41 2 2 31 2 7 61 4 1 11 5 4 9

1 Data from Jones and Bradshaw as reported by Harned andOwen (1964).

2 Data from Rosenthal and K idder(1969).8 Calculated from equation 9.


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3600

2 6 0 0 -

§1800

^1400

60 0

20 0

Actual ral*tk>nihlp

First dtrivitivt Mop*)

S < cUJ { )

10 15 20

TEMPERATURE, INDEGREESCELSIUS

25

Figure 1 . Conductivity-temperaturerelationships for0.01 N KCIsolutionand1 per mil chlorinityseawater.

equation1 has been used in this analysis rather than theoriginal measurements obtained by Cox (1966) andBrown andAllentoft (1966) ,because the equation fitsthedata extremelywell, allowing interpolationbetween measurements.The change in conductivityper degree Celsiusas a function of temperature (the first derivative) for both0 .01 N KCI and 1 per mil Cl seawater appears to be alinear function of temperature. The plot of conductivityasa function of temperature for 0 .01N KQ fits the equationobtained by least squares regression (r 2=.825)

^=23.54+0.1536 T. 8)

1 Measurements of conductivity in seawater are based on theinternational ohm. To convert to a base of the absolute ohm (SI),multiply conductivityby 0.999505.

Integratingand evaluatingthe constantof integration at 1 8 °C (1222 .69fiS/cm of Harned and Owen'svalues), the Kvs. T relationship becomes

*=774.1+23.54 7+0.07680 T : (9 )

Equation9 agrees to within about 0.13percent with

the four measurementsby Harned and Owen (1964)at 0 ,18, 20, and 25 °C. It thus appears to be satisfactoryoverthe temperature range of interest in natural waters.

Equation9 couldbe used to tabulate another usefulparameter the temperature correction factor, or theratio of *, IKfor 0.01 NKCI.

The percentage change in conductivity withtemperature for 0 .01N KQ is comparedwith that of 1 per mil Cland 1 9 per mil Cl (undiluted)seawater in figure 2. Valuesfor 0 .01 N KCI were calculated using equation 9.

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10 15 20

TEMPERATURE.IN DEGREES CELSIUS

25 30

Figure 2. Percentage change in conductivitywith temperature for 0.01 NKCI solution and seawater in °C increments.

It is apparent that the percentagechanges in conductivity withtemperatureof the 0.01 N KCI and 1 permil Cl seawaterare significantlydifferent throughoutthetemperature range studied. Temperature-compensationcircuits onmost specific-conductanceinstrumentsin usetoday are based on the conductivity vs. temperaturefunctions of 0.01 N KCI or NaCl solutions (J. Cluzel,Beckman Instruments, oral comm., 1985). Thus, theycannot provide accurate compensation in seawatersolutions at measurement temperatures significantly higheror lower than 25 °C. The measurementof specific conductance in seawaterwill be discussed later.

It is to be expected also that temperature-compensation circuitsbased on 0.01 N KCI or NaClsolutions will not compensateaccurately in waters with afar different chemicalcomposition(a calciumsulfate-typeor an acid mine water, for example),but no systematicstudy of such effects is known to have been done.Rosenthaland K idder(1969)point out wide variationsinthe temperature function of special solutions found inindustrialapplications.The errorsthat occur in estuarine

waters are thoughtto affect the third significant figureofspecificconductance (Bradfordand Iw atsubo,1980) .

For comparison, valuesof the ratio ( KSI K )for 0.01NKCI are predictedby dividingthe specificconductance( K ,

equals 1410 . 6/nS/cm)calculatedat 25 °C using equation9by the conductance(«) calculated at other temperaturesusing equation9. These ratios are plottedin figure3 alongwith values calculateddirectly for 1 per mil Cl seawaterfrom Accerboni and Mosetti (19 67 ).The argument madeearlier that temperature-compensationcircuits basedonthe temperatureresponseof 0 .01N KCIor NaCl solutionswill lead to significant errors in specific-conductanceestimates in seawaterlike solutions is valid here as well.Errors increase to about 2.5 percent at 0 °C .

An equation for computingthe ratio is given inStandard Methods, 15th edition (American Public

Health Service, 1981 ,p. 73). Modifiedto fit terminologyin this paper, it is cited here:

(10)K~l+0.0191(r-25)'


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1 0 1 5 20

TEMPERATURE. IN DEGREES CELSIUS

30

Figure 3. Values of the ratio of specific conductance to conductivity for0.01 N KCIsolution and 1 per mil chlorinityseawater.

Ratios predictedfrom equations9 and 1 0 are comparedwith those calculated fromdata given by Rosenthal andK idder(1969)and Harned and Owen (1964) andshownin table 3.

It is apparent that the equation from StandardMethods (equation10) diverges from both actual measurements and equation 9 at temperaturesbelow 15 °Cand is in error by about 5 percent at0 °C. It also divergesat temperaturesabove 28 °C .

Becausethe temperaturedependenceof the limitingequivalent conductivity of most major ions in naturalfresh waters comes closest to that of K+ and CT, thetemperature functionof 0 .01N KCI secondary standardsis generally accepted as a model for the temperaturefunction of most natural waters. (Thiswill be discussedlater.)

For convenience in field application,the ratio K /Kfor 0 .01N KCI is tabulated (table4 ) using equation9. Forexample,if a conductance of 1 0 0 0is measured at 20 °C ,

the specific conductance is 1 0 0 0 X 1 . 1 0 6 = 11 0 6 .Theseratios are appropriate only for natural fresh waters.Special solutions likeseawater, acid mine drainage,and,possibly, acid rain are expected to have significantlydifferent temperaturefunctions, whichshould be determined caseby case. Seawater is a w ell-studiedspecial casediscussed later.

Ionic Conductance

In 1883, Arrhenius proposed that all substancesthat form highly conductingaqueous solutionsdissociateinto ions capable of transferringcharge. The body oftheory developed sincesuggeststhat theconductivityof anaqueoussolution is related to the sum of the concentrationand mobilityof the free ions. K ortum and Bockris(1951,equation 67) expressed this relation for solutions of asingle salt as

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Table 3. Comparison of the ratio K . J Kpredicted by dividing1410.6/tS/cm at 25 °C) by the conductance calculated usingequation 9, equation 10, and calculated using data fromRosenthal and Kidder 1969) and Harned and Owen 1964)

T(°C)

05

1 0

1518202528303335

Predicted byequation 9

1.8221.5781.387

1.2331.1541.1061 . 0 0 00 .9450 . 9100 .8630 .834

Predicted byequation 10

1.9141.6181 .402

1 .2361 .1541 .1061 .0000 . 9460 .9130.8670.840

Calculated

1.8211.-

1.2331.154 (1 .154)11 .106(1 .106)11.0000 .9440 .9 1 0

.-

1 CalculatedusingHamed and Owen (1964) valuesat 25 ° and at0, 1 8 ,and 20 ° C .

where(11 )

A= equivalent conductanceof the salt insolution at concentration C (equivalents/liter),

a= fractionof the salt dissociated, and+_= ionic mobilityof the ions.

By analogy, equation 11 can be generalized forsolutionsof mixed salts as follows:

awhere

C, , (12)

K = conductivityof the solution,a,= fraction of the /th constituentpresent as

the free ion,

\*= equivalentconductivityof the /th ion, andC,= concentrationof the /th species.To use equation1 2 to compute the conductivityof a

solution, the total concentrations of conducting species(C,), the fractionsof each speciespresent in ionic form(a,), and the equivalentconductivityof each free ion ( X;*)must be known. As will be shown, a, for the majorconducting speciesin natural water can be determinedwith appropriateaccuracy usingknown stabilityconstantsfor formation of complexes.The equivalentconductivity,however,varieswith the ionic strengthand temperatureofthe solution inways that theoreticalapproacheshave as yetbeen unable

todescribe accurately.

Qassically, therelative mobilityor equivalentconductivity of salts in solution has been studied by themethod of Hittorf (summarizedby K ortumand Bockris,1951) in which the rates of change in concentrationsaround electrodes in solution are determined by the

2 Original workby Hittorf dates from 1853 to 1859. Taylor(1931) gives an extensive bibliography in English of the Hittorfmethod.

Table 4. Values of K,/Kfor 0.01 N KCI in °C incrementscalculated by dividing 1410.6 /tS/cm at 25 °C) by th econductance calculated using equation9[Values at temperatures above 30 °C have not been verified bymeasurement]

Kf/K

T(°C)

01

23456789

0

1.8221.768

1 . 71 71.6691.6221.5781.5361.4961.4581.422

10

1.3871.353

1.3211.2901.2611.2331.2051 .1791.1541 .129

2 0

1 .1061.083

1.0611 .0401 .0201 .0 0 00.9810.9620 .9450.927

30

0 .9100 .894

0 .8780 .8630 .8480 .834

----

moving boundary method. The conductance of an individual ion can be determined in absolute units forsolutions of simple salts.

Concentration Relationships

The equivalentconductivity (A*)of a salt in solutiondecreases with increasing concentration. Variousstudieshave suggested that this relationship takes the formof thesquare-root law first expressed by K ohlrausch (Harnedand Owen, 1964, p.213):

A*=A°*-aVc, (13)

where A ° *is the limitingequivalentconductivity.For convenienceof notation andfurther discussion,

terms will be defined at 25 °C and equation1 3 rewrittenthus:

A=A°-a VC , (14)

whereA= equivalentconductanceof a salt in solu

tion; (A* at 25 °C),A°= limitingequivalent conductance,and

a= proportionalityconstant.The limitingequivalentconductance is the equiva

lent conductance extrapolatedto infinite dilution, whereinteractions betweenions in solution disappear and themobilityof individualions reaches a maximum.

K ohlrausch'ssquare-rootlaw successfully describesthe relationshipfor several single 1:1 salt solutions atconcentrations from infinitedilution to 0.03 N. Severalextensions of the square-root law have been used withsome successat higher concentrationsof a single salt:

A=A°-A VC +BC,

A=A°/(1+BA VC

A=A°-/1+B VC

(14a)

(14b)

(14c)


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-10

1 1

-20

-25

-300. 1 0. 2 0. 3

V C ~ < E Q U I VA L E N T S P E RL I T E R**

Figure 4. Decreases in equivalent conductance of selected electrolytes with increasingconcentration. Data from Harned and Owen, 1964, p.697.)

the general form is

A=A°-AC n (15)

where A, B, and if are empiricallydeterminedconstants(all from Harned and Owen, 1964).The square-rootlawand its extensionshave provedreasonablysuccessful onlyin predicting equivalentconductancesof dilute single-saltsolutions;even in those cases, the linearityof the relationship fails at concentrationsapproaching0.01 N (fig. 4).The equivalentconductanceof individualions in mixed-salt solutions has been shown theoreticallyby Onsagerand Fuoss (as discussedby Harned and Owen, 1964,p.114) tobe a functionof the ionic strength,as

(16)

whereX,= equivalentconductanceof ion i,

\i°= limitingequivalent conductanceof ion /,/ onic strength, and

f i) = a function containing \°, the charge onthe ion zh temperature, viscosity, thedielectric constantof the solvent, and aseries expansion.

Equation1 6 has been tested forsingle-salt solutionsonly, however,and the expansionof the seriesin the term

f i) has proved to be enormouslycomplexfor solutionsofmixed salts, as innatural waters. Becauseof this complexi t y,the relationbetween \- and / as not beendevelopedtothe point where the specific conductance of a natural

water may be calculated from the sum of equivalentconductances; equation12 is therefore rewrittenas

K = S x - X-C- 17^

In dilute naturalwaters, however,evidence suggestthat the limitingequivalentconductance o fions (table 5)is a good approximationof the equivalent conductancethus the specificconductancecan be closelyapproximatedby equation 17, in the form

K =Z a, V C - (18)

with a,- , in most cases, being unity, implying completedissociation.At total dissolved-solidsconcentrationsaboveabout 1 0 ~5N (100 /iS/cm specificconductance),however,significantreductions in equivalentconductance o findividual ions occur that invalidate equation18.

Temperature Relationships

Manymeasurementshavebeen made ofthe limitingequivalentconductivity(A0*) of single-salt solutions ovethe temperature range 0 to 100 °C. Single-ion limitin

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4

2

80

6 0

40

2 0

- 2 0

oE CO

60

1 -80

- S O

O H

N o t e s :

1 . The curve for Mfl2+ Is not distinguishable from thatof Ca2 *, end the curve for HC0 3 o not distinguishablefrom Na+,at this scale.

2. The curve for SO ii extended toward the only valueavailable above 25 °C 180»S/cm at 1 0 0 °C)and It approximate only.

-100

-12010 20 30 40 5 0 60

TEMPERATURE.IN DEGREES CELSIUS

Figure 5. Changes in limiting equivalentconductivity ofselected ions with temperature.[Data from R obinsonand Stokes 1959) p. 465, and for HCO3 from Jacobson and Langm ier1974).]

quivalentconductivity(\°*) hasbeen tabulatedby Robinon and Stokes (1959,p. 465).The variations in \°* forelected ionsover a temperaturerange commonin natural

waters are shown in figure 5. Applicationof the Onsagernd Fuoss equation(equation16) for predictionof \°* in

mixed-salt solutions is complicatedby the problems disussed earlier. For single-salt solutions, equation 1 6educes to a tractable form (seeHarned and Owen, 1964,. 113), but the theory has apparently not been thorughly tested even in simple solutions.

Robinson and Stokes (1959) note that \°*ncreases as much as fivefold from 0 ° to 1 0 0°C for someons, but that the product r{\°* (where i\ is the fluidiscosity) changes by less than 50 percent at most (for

Cl~). As noted earlier, this observation suggeststhathanges in fluid viscosityaccount for most of the variationn conductivity of aqueous solutions as a function ofemperature.

It may be surmisedfrom the relationshipsshown infigure 5 that instrument temperature-compensationcircuits based on the temperaturefunctionof a KC1solutionmay yield inaccurate measurementsof specific conductance in aqueous solutions withmajor ion compositionssubstantially different from the norm of fresh naturalwaters (high SO4 2~, highpH or low pH, for example)attemperaturesmore than 15 ° above or below 25°C .

Effects of Com plexation and Protonation

Ion associations or complexes form in naturalwaters (Stummand Morgan, 1981)particularlybetweenthe alkaline-earthcations (Ca2+, M g2 * ,and Sr2 +) and thesulfate (SO42~), carbonate(CO3 2~), and bicarbonate(HCO3~) anions. The conductivity of a solution isreduced by this effect, because the complexes are


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Table 5 . Limiting equivalentconductances \/°) of selectedions[Data from Harned and C X v e n(1964,p. 231),exceptfluoride ion datafrom Franks (1973, p.178).Values are based on theinternationalohmand should be multipliedby 0.999505to obtain SI units (juS/cm permeg/L)]

CationCaa+H+

K +Li+M g2 *

Na+

NH4,+Sr+

V+

59.50349.8

73.5238.6653.0650.1173.459.46

AnionBr~

crF~HC0 3-rNO3~O H~so4a-

\°_

78.2076.3555.3244.576.971.44

197.880.0

uncharged or less charged than the parent ions andcontribute little or nothing to the conductivity of thesolution. The extent of complexationin solution may becalculated from known stabilityconstants (K,) for thegeneral reaction

[M X0](19)

where the brackets representactivities,M representsametal cation, and X 2~ represents an anion. Complexesbetween alkaline-earthcations and thebicarbonate anion(HCO3~) predominantlyform compoundswith a singleplus charge, which contributes to solution conductivity.The reduction in free formsof the parent ions by compl

exation needs to be considered. Formost dilute naturalwaters, however, the conductivityof the complexcan beignored because therelativeamount of complexformed issmall and the mobilityof the complex is low compared tothat of the free ions. The protonatedform of the sulfateanion (HSO4~) may also be safely ignored except inhighly acidic waters containing sulfate, forexample, acidmine drainage.

Table 6 lists stability constants for complexes ofinterest, includingprotonated forms of the anions.

APPLICATIONS TO ANALYTICAL QUALITYONTROL

An EmpiricalApproach in Natural Waters

From the foregoing theoretical considerations,inparticularK ohlrausch'slaw (equation 17), it is apparentthat the sum of the products of the equivalent ionic

Table 6. Stability constants log K,) for ion associationsbetween major inorganicions in natural waters at 25 °C[Values from Plummer and others, 1 9 7 6 ]

Ion

H+

so4z-2.2382.3092.552.054

co3z-

2.9803.1532.81

10 .330

HC<V

1.0661.0151.186.351

conductances andconcentrations(C/X,)of the major ionicconstituents determined by chemical analysis shouldapproximate the specific conductance measuredin awater sample. But satisfactory modelsfor the equivalentionic conductances (\) in mixed-salt solutions have notbeen developedand tested.

M iles andYost (19 82 ) used the difference betweecalculated and measured specific conductance coupledwith the difference between measured total anion andcation concentrations in an analytical quality-control

check that allowed identification of the constituent ormeasurement mostlikely in error when agreement waslacking.Theywere constrainedwith respect to the specificconductance range of applicabilityby the need to uselimiting equivalent conductances (\°) to approximateionic equivalent conductances (\). This approximationbecomes progressivelypoorer at specific conductancesexceeding1 0 0 fiS/cm.The Miles and Yost (1982) technique couldbe extendedto a broader concentrationrangeif a suitable model for thedecrease in \ ith increasingconcentration in a mixed-electrolytesolution were developed. The objective of this section of the report is todescribe one empiricalapproach thatappears to extendthe applicablerange to at least 6 0 0 |iS/cm . This approachhas been used successfully to check analysesof waterfrom the west coast of Florida that hada specific conductance of 9 0 0 0fiS/cmor less.

Initial attempts to fit actual data to the square-rootlaw (equation14) and its generalextension (equation 15)showed a high degree of scatter, as did attempts to fit aform of equation 16 using ionic strength. The lack ofsatisfactoryfit prompted anotherapproach.

The model proposed and tested here is

K «, C, (20)

the assumptionbeing thatan exponentialcorrectionfactor(f) would faithfullydescribe curvaturein the relationshipbetween ionic conductance and concentrationin naturalwaters and, on evaluation usinga large data baseof actualanalyses, wouldprove to have a narrow range of values(approachinga constant) and a low standard deviationover a broad range of concentrations.This approach isalso discussedby Miller (written commun.).

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Table 8 . One standard-deviation range of estimated *,using 2 C X/)'[/=0.9850 and s-0.0128]

r \ ;1 5 03 0 04 5 06 0 0

M e a n 1 s

1 3 02 5 63 8 05 0 2

M e a nf

1 3 92 7 54 1 15 4 5

M e a n f 5

1 4 82 9 64 4 45 9 2

method involveda fixed-pH endpoint titration to pH 4.5,which is known to overestimate the actual value at lowalkalinities Barnes, 1964). Also, in low-ionic strengthsamplesHCO 3~ maybe less than the m easuredalkalinity.Thus, the sum of conductanceswould be biased high andthe/value biased low. The/values in this range also showa small but significant (p < 0 .001)positiverelation to KS,

the value at 150 jtS/cmbeing 0.9802, very closeto theother three mean/ values. Therefore, that mean/value isjudged to be in error and rejectedin subsequentevalua

tions. In part, the problem hasbeen corrected recently forlow-ionic strength samples by determining alkalinitythrough a strong-acid titration and Gran plot analysis(Gran, 1952).

The distributionsof/values are normal in all cases,and significantly(p < 0 .0 0 0 1 )less than unity. The sample-weighted mean and standard deviationsof the remainingthree values are/= 0.9850 and5=0.0128.Because the/

value is used as an exponential,the rangeof ±1 standard-deviationunit in the estimate of K is about ±8 percent, asshown in table 8.

The relationship betweenthe / alue and major

constituentcompositionwas examinedby calculatingcorrelation coefficientsbetween/and anion constituentratios(table 9). Absolute values of the correlation coefficientsare all less than 0.75, those for / s. SO4 2~/Q~ weresignificantly different from zero at K > 150 /tS/cm. Thedata were highly skewed to low values of the anion ratios,as can be seen by comparing ranges with medians; thecorrelationcoefficientsare probablystronglyaffectedby afew high values and are, therefore, suspect. Nevertheless,the persistent recurrence of significant negative correlation with SO4 2~/Q~ suggests that refinement in the /

value may be possible by separating high-sulfate watersfor special evaluation.The mean / alue for 28 watersamples collected in Florida and containingmore than3 0 0m g/ 1 SO4 2~ was 0.9678,for example; that suggests arelationship.

A linear regressionof/ vs. the fractionof monoval-ent ions (Fj) in 3 2 6 water samples from Florida had acorrelation coefficient (r) of 0.38 and was statisticallysignificant at the 99 percent confidence level.

Table 9. Relationship of the value and anion ratios pequals the probability of accepting thenull hypothesis, H0 ;correlation coefficient/^O)[Range and median of the constituent ratios are shown only if thecorrelation coefficient w as significantly(p < 0.05) different from zero;if not significant,values are shown by a dash ( )]

«*

0-150

150-300

300-450

450-600

Parameter

rPrP

RangeMedian

rP

RangeMedian

rP

RangeMedian

ConstituentRatiosscyci

-0.04330.08

-0.09490 .0 0 0 10 .005 -300.730

-0.12880 .0 0 0 10 .001-590.783

-0.71990 .0 0 0 10 .002 -480.815

CI/HC03

0.00410.87

0 .0 8 1 00 .0 0 0 30 .002 -470 .11 6

0 .0 1 8 80.47

0 .0 6 4 60.05

SCVHCOg

0 .0 0 1 90.94

0 .03440 .12

-0.02490.34

-0.25750 . 00010.0005-110.129

/=0.9687+ 0 .0 1 9 5 6 (26)

Although the regression equationwas determined fromdata of limited geographicalcoverage,it stronglysuggeststhat predictionsof specific conductancecan be improvedby adjusting/for water composition.

Results of this evaluation suggestthat the exponential correction factor / may be used with the limitingequivalentconductancesof individual major ions and theanalyticallydeterminedconcentrationsof major ions corrected for complexation toestimate specific conductancefor the water sample. Thiscalculatedvalue may be used ina variety of ways as a quality-controlcheck on laboratoryanalyses and field measurements.

QualityControl Checks

Comparison of Measured with Computed SpecificConductance and Anions with Cations

Use of the exponential correction factor/ ndcalculated adjustments of ion concentrations for complexation as outlined above allow extensionof the Miles

and Yost (1982) technique to sampleswith specific conductances upto at least 600 /tS/cm,the upper limit of thepresent evaluation. The technique involves plotting onorthogonal coordinates the differencebetween measuredand computedspecificconductanceon the abscissavs. thedifference between the anionand cation equivalentconcentrations measuredin the laboratoryon the ordinate.The location of a point representinga given analysis withrespect to the origin (the location of a perfect analysis)indicates, in part, which of the several measurementsinvolved may be in error. The plot may be used also as a

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control chart with warning limits in concentric circlesaround theorigin.

The technique was adapted in the U.S. GeologicalSurvey Central Laboratories during 1985 for qualitycontrol of analyses of sampleswith specificconductancesless than 1 0 0

Predicting the Sum of Anions or Cations

A method that supplements theMiles and Yost(1982)technique is to predict the sum of anion or cationequivalent concentrations in a sample and compare thepredictedvalue with the measuredvalue to judge whetherone or the other is in error.

An average limiting equivalent conductance(Ax )with adjustment for complexation is calculated for thewater sampleby

C , - *\-°

C, 1 2 (27)

where C* is the concentrationof the ion / adjusted forcomplexation andC, is the analyticallydeterminedconcentration without adjustment for complexation.Because,restating e quation2 5,

=

(25)og (2 C,' V)'

equation 27 may be written

log (2 C, /2),=(1// )log K,-log Ax , (28)

where the subscriptp designates a predicted value. The

differences

(2 C, /2),-2 Cc and (2 C, /2),-2 C., (29)

where subscriptsa and c designate analytically determined anions and cations, respectively, will suggestwhether errors in either the anion or cation determinations havebeen madeand provideguidancefor confirmatory reanalysis.

A Special Case for Seawater and EstuarineWaters

The measurement of specific conductance anditsrelation to chem ical comp ositionin seawaterand dilutionsof seawater (as in estuaries) where the seawatercomponent dominates the chemical compositionrepresents awell-studied special case. The chemical compositionofseawater worldwide is remarkably constant (Cox, 1965).Over the years, a set of algorithms to calculateconductivity, specific conductance, density, and chlorinity andsalinity (in grams/kilogramor parts per thousand) hasbeen refined to applyto this special case. During th e

1970's ,the conductivity-salinity-tem perature relationshipsin seawater wereextensivelyreevaluatedand refined.Theresults have been summarizedby the Institute of Electrical and ElectronicEngineering (1980) .

In the open ocean,variations in salinity are verysmall, but the differencesin density resulting from temperature and salinity variations determine large-scaleoceanic circulation. Thus the measurementsfrom which

salinity is determined must be made with far greateraccuracy and precision thanis common (or usually necessary) for fresh or estuarine waters, where variationsaremuch larger. Open-ocean salinities normally are determined to five significant figures (for example,35.013permil).

In estuarine waters, the relationships between m easurementsof interest can be described by a set of algorithms given in table 10. The algorithmof Accerboni andMosetti (1967) fitsactual measurements by Cox (1966)and Brown andAllentoft (19 66 ) to35 in 4 3 , 0 0 0fiS/cm,orabout 0.08percent, at worst.

The difference betweenthe algorithmof Accerboniand Mosetti (196 7) andthe algorithmof Pollak (1954),asmodifiedby D.W. Pritchard (writtencommun.,1978),wasevaluated by Bradford and Iwatsubo (1980). Theycalculated the salinity fromassumed values of conductivity andtemperature using Pollakfc algorithmand the conductivityfrom the calculated salinity and temperature usingAccerboni and Mosetti's algorithm. The differences(assumed conductivity minus calculated conductivity)were < 10 0 f iS/cmover the salinityrange 2 to 33 per miland temperature range 0 to 30 °C (roughly 2 ,0 0 0 to56 ,000fiS/cm conductivity).The algorithms areadequate

for estuarine work andmore accurate than common fieldmeasurements.

Becauseof the error likely to occur in instrumentaltemperature compensation,as discussed earlier, compensation circuits should not be used in measuring specificconductance in estuaries. Rather, the conductivity andtemperature should be measured separately, and thespecific conductance, if needed, calculatedfrom Pollack^algorithmfollowed byAccerboni and Mosetti 'salgorithm.Also, the standard solution for calibration of field instruments should be a secondarystandard seawater obtainedfrom an oceanographicinstitution laboratory. Bradfordand Iwatsubo (1980) discuss detailsof the procedure.Some common field instruments will not perform accurately at high conductivities.A four-elementconductivityprobe appears to be preferable to a two-elementplatinized-platinum(electroplatedwith platinumblack) orcarbon-ringcell.

As a quality-control check, the analytically determined chloride concentration and the sumof dissolvedsolids (expressed in per mil) should agree with thosepredictedby the algorithmsin table 10 .

Applications to Analytical Quality Control 1 3

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Table 10. Algorithms forcalculating conductivity, specificconductance, chlorinity,and salinity of seawater and estua-rine waterAlgorithmto calculate conductivity( K )of seawater and estuarine waterfrom salinity (S) andtemperature (T )[AfterAccerboni andMosetti, 1967]

where,4 = 2.19235=0.12842k= 0 .0 3 2 0< r =0 .0 0 2 9 0h =0 .12430 =0 . 0 0 0 9 7 8

7>20 °C5=0 .0000165

S =35 c

Algorithm to calculate salinity (S) of seawater and estuarine waterfrom conductivity(K )and temperature(T)[Modified fromPollak (1954) by Pritchard, D.W. (written commun.,1978)]Salinity (o/oo)=1.80655Xchlorinity(o/oo)Chlorinity o/oo)=AXK

A -0.36996

*- 1 0 7-0.7464X10- 3

whereK =conductivityin millisiemens/cmT= temperature in °C

5 0=0 .13855X1015 1=-0.46485668X10~ 1

5 2= 0 . 1 4 8 8 7 7 8 5 X 1 0 ~25 3= -0 . 6 3 0 8 3 4 3 3 X lO ~45 4=0 . 2 5 1 4 4 5 1 7 X 1 0 -55 5=-0.59600245X!0~ 7

5 6=0 .57778085X10~9

Note: The conductivityof seawater is based on the internationalohm. To convert to a base of the absolute ohm, valuesobtained from the algorithmsabove should be multipliedby0.999505.

NOTES ON SPECIFIC CONDUCTANCEMEASUREMENTS

Instrumentation

The method comm only used todetermine the conductivity of unknown solutions is to measure their resistance (R) in a cell with a known cell constant (K ).The cellconstant can be determined using equation 5 with a

standard solution of known conductivity,such as 0 .01 NKC1,at the measurement temperature. Resistance of thecell with an unknown solution is then measured on aWheatstone bridge or other balancing circuit,and conductivity is calculated as

KR 3 0)

Most commercial instruments provide measurement cells designed with constantsof 0.1,1.0, and higher,and a scale designed to show conductivitydirectly, ratherthan resistance.

Cells are commonlymade of glass or plastic, maybeof the dipor cup type, andcontain electrodesof platinizedplatinum, as described by Brown and others (1970).Theplatinizedsurface is easily damaged,and carbonor tungsten electrodes are more suitable for field instrumentation. A four-element conductivitycell has been used insome field instruments. A constant current is imposedacross the outer two elements, and the potential fielddevelopedin the solution is measuredacross the innertwo

elements, fromwhich the conductivityis obtained. Thiscell resists corrosion or fouling better than the two-element resistance-measuringtype.

In conventionaldevices using a Wheatstonebridgewith alternatingcurrent at about 1 , 0 0 0Hz, the resistanceof the sample is balanced by a variable resistor, and thenull point is indicated by an electron-raytube or a needle.Advances in electronics now permit direct-readingtechniques.

Procedures

Some operationaldetails vary from one instrumentmodel to another. In general, the following steps arerequired to measure the conductivityor specific conductance: (1) using the solution to be measured, rinse fromthe measurement cell any solution or solids remainingfrom previous sample;(2) allow the temperature of thecell and the solution to equilibrate; (3) compensate fortemperature electronically,or mathematicallyafter measurement using table 4; (4) null the instrument;and (5)record the temperature-corrected measurement(the spe

cific conductance).For natural waters, most instruments apply a 2percent/°Ctemperature compensation to readings madat temperatures other than the reference temperature of25 °C. Automatic temperature-compensation circuitsequilibrate a thermistor with a high temperature coefficient with the solution to be measured. The appropriateselection of the thermistor and three resistorswith lowtemperature coefficients permits the manufacturers tocompensate the temperature effects for a wide range ofsolutions (Rosenthal and K idder, 19 69).Other instru-

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ments require the temperature of the solution to bemeasured with a thermometer. After the temperaturetabilizes,the dialis set to the temperature of the solution,he thermometer is removed, theinstrument is nulled, andhe specificconductance recorded.

The temperature-compensation circuits of allnstruments should be checked for agreement with the0 .01 N KC1 secondary standard as describedby equation

9. This may be done by measuring thespecific conducance of the standard at several temperatures on eitheride of 25 °C and noting the variationsin readings fromhe instrument, using the temperature-compensation cir

cuit. Errors of more than 5 percent are unacceptable;inhat event, the temperature-compensation circuit should

not be used if it can be avoided.O n manualcompensation-ype meters, thetemperature dial may be kept at 25 °C.

The instrument will then measure conductivity,and speific conductance can be calculated using table4 . If the

emperature-compensation circuit cannot be eliminated,a correction graph should bedrawn and kept with thenstrument.

Before use, instrument calibration should behecked with at least three standard solutions.

SUMMARY

The specific conductanceof aqueous solutions,paricularly natural waters, has proven useful as a quantitaive indicatorof the concentrationof major ions. However,

review of current theory indicatesthat the conductivityof individual ionsin mixed-saltsolutionscannot be accu

ately predicted from physical-chemical principles.A review of accepted measurements of the conducivity of secondary standard 0 .01N KC1solutionssuggestshat the v ariationwith temperature is a complex functionrobably not duplicatedwell by instrument temperature-ompensationcircuits now available for correctingcon

ductivityto 25 °C (specificconductance)and that a widelyused equation for correcting to 25 °C is in error by asmuch as 5 percent at 0 °C. A new algorithm has beenderived and tested. Also, instrument temperature compensationis not adequate for use in seawater or estuarinewaters where the accuracy of conductivity and salinitymeasurementsmust approach 5 significant figures.

This report describes and evaluatesan approach topredicting the specific conductance of a water samplerom the analytically determined major-ion composition.

The methodcorrects for reduction in free-ionconcentraion resulting from complexation, computes a limiting

equivalent conductance for the sample by summing theproducts of the free-ionconcentrations andthe limitingequivalentconductancesof the ions, and applies anexponential correction factor to the sum of the products toestimate specificconductance.

The exponentialcorrection factor has been evaluated on the basisof about 6 ,000analysesof water samplescollectednationwide withmeasured specificconductancesof 0 to 6 0 0 jttS/cm. The correction factor is normallydistributed andsignificantlydifferent from unityand hasa mean value of 0 .9850and standard deviation of 0.0128,which predicts m easuredspecific conductances to within±8 percent (one standarddeviation).The method allows

extensionof the rangeof the quality-controlcheck (calculated specific conductancevs. measured specific condu ctance) on laboratory data beyond the current 1 0 0 /u,S/cmto 6 0 0 jttS/cm. The report describesa method for narrowing the possible numberof erroneous analyses or measurements in a quality-control check.Evaluation of theapproach at higher specific conductances is called for.Other approaches to adjustment of calculated limitingequivalent conductances to specific conductance shouldalso be critically evaluated.

REFERENCESAccerboni,Emrico, and Mosetti,F., 1967,A physical relation

ship amongsalinity, temperature,and electricalconductivity of sea water: Bollettinodi geofisci teorica ed applicata,v. 9, no. 34, p.87-96.

AmericanPublicHealthService,AmericanWater Works Association and the Water Pollution ControlFederation,1981,Standardmethodsfor the examinationof water and waste-water (15th edition): Washington,DC, AmericanPublicHealth Association, 1134p.

AmericanSocietyfor Testing and Materials,1976,Standardformetric practice, E 380-76: ASTM, Philadelphia,PA.

Barnes, Ivan, 1964,Field measurementof alkalinityand pH:U.S. GeologicalSurveyWater-SupplyPaper 1535-H,1 7p.Bradford,W.L., and Iwatsubo, R.T.,1980,Results and evalu

ationof a pilot primarymonitoringnetwork,San FranciscoBay, California:U.S. Geological Survey Water-ResourcesInvestigation80-73,115 p.

Brown, Eugene, Skougstad,M.W., and Fishman,M.J., 1970,Methods forcollection andanalysis of water samples fordissolved minerals and gases: U.S. Geological SurveyTechniques of Water-ResourcesInvestigations, book 5,chapterAl, 160p.

Brown,N.L., and Allentoft,B., 1966,Salinity, conductivityandtemperaturerelationshipof sea water over the range of 0to 50 p.p.t.:Bissett-BermanCorporation.

Cox, R.A., 1965, The physical properties of sea water, inChemical Oceanography,v . 1 , Riley, J.P., and Skirrow, G.(eds.), New York,AcademicPress, p.73-120 .

1966, nternationaloceanographictables: National Institute of Oceanographieof Great Britain and UNESCO.

Daniels,Farrington,and Alberty, R.A.,1967,Physical chem istry (3d ed.):New York, John Wiley, 767 p.

Franks, Felix, 1973,Water, a comprehensive treatise: NewYork, PlenumPress, v . 3, 472 p .

Friedman,L.C., and Erdmann, D.E.,1982,Quality assurancepractices for the chemicaland biologicalanalysesof water

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and fluvialsediments:U.S. GeologicalSurvey, Techniquesof Water-ResourcesInvestigations,book 5, chapter A6,181 p.

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Harned, H.S., and Owen,B.B., 1964,The physicalchemistryofelectrolyticsolutions (3d ed.): AmericanChemicalSocietyMonographSeries, New York,ReinholdPublishing,803 p .

Hem, J.D., 1970, Study and interpretation of the chemicalcharacteristicsof natural waters (2d ed.): U.S. GeologicalSurvey Water-SupplyPaper 1473,3 6 1 p.

Institute of Electrical and Electronic Engineering,1980,Special issue on the practical salinity scale:Journal of OceanicEngineering,v. 5, no. 1 , p. 1-65.

Jacobson, R.L., and Langmuir, Donald, 1974, Dissociationconstants for calcite and CaHCO3+ from 0 to 50 °C:Geochimicaet CosmochimicaActa, v. 38, p. 3 0 1 - 3 1 8 .

Jones, Grinnell, and Bradshaw,B.C., 1933,The measurementof the conductanceof electrolytes V. A redeterminationof the conductance of potassium chloride solutions inabsoluteunits: Journal of the AmericanChemicalSociety,v. 55, p. 1 7 8 0 - 1 8 0 0 .

K ortum, Georg,and Bockris, J.O., 1951,Textbookof electrochemistry: New York, ElsevierPublishing,v. 1 , 351 p.

Lind,J.E., Zwolenik, J.J.,and Fuoss, R.M.,1959,Calibrationofconductancecells at 25 degreeswith aqueous solutionsofpotassium chloride: Journal of the American ChemicalSociety, v. 81, p. 1557.

Marsh, K .N., 1980,On the conductivityof an 0.01 D aqueouspotassium chloride solution: Journal of Solution Chemistry, v. 9, no. 10, p. 805-807 .

Miles, LJ., and Yost, KJ., 1982, Quality analysis of USGSprecipitationchemistry data for New York: AtmosphericEnvironment,v. 16, no. 12, p. 2889-2898 .

Plummer, L.N., Jones, B.F., and Truesdale, A.H., 1976WATEQF A FORTRAN IV version of WATEQ, acomputer program forcalculatingchemical equilibriumof

natural waters: U.S. GeologicalSurvey Techniques ofWater-Resources Investigation, 76-13 , 63 p. (revised1978).

Pollak, MJ., 1954,The use of electrical conductivity measurments for chlorinity determination: Journal of MarineResearch,v. 13, no. 2, p. 228-231 .

Robinson,R.A., and Stokes, R.H., 1959,ElectrolytesolutionsLondon, Butterworths,571 p.

Rosenthal,Robert, and K idder, R.J.,1969,Solutionconductivity handbook:Cedar Grove, NJ, Beckman Instruments,26P -

Saulnier, P., and Barthel,J., 1979,Determination ofelectricaconductivity of a 0.01 D aqueous potassium chloridsolution atvarious temperaturesby an absolute methodJournal of Solution Chemistry,v. 8, no. 12, p. 847-852.

Stumm,Werner, and Morgan,J.J., 1981,Aquaticchemistry (2ded.): NewYork, John Wiley, 7 8 0p.

Taylor, H.S., 1931,A treatise onphysical chemistry: New Y orVan Nostrand,v. 1 , p. 678-683 .

Weast, R.C. (ed.), 1976,Handbookof chemistry andphysics:Cleveland,CRC Press, 2391 p .

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