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Conductometry – Conductivity MeasurementPeter Bruttel

Monograph

PFIZER, INC., IPR2017-01358, Ex. 1017, p. 1 of 52

Conductometry – Conductivity Measurement 1

Conductometry – Conductivity Measurement

Peter A. Bruttel

All rights reserved, including those of translation.

Printed by Metrohm Ltd., CH-9101 Herisau, Switzerland

8.028.5003 – 2004-11


2 Metrohm Monograph 8.028.5003 Conductometry – Conductivity Measurement 3PFIZER, INC., IPR2017-01358, Ex. 1017, p. 3 of 52

2 Metrohm Monograph 8.028.5003 Conductometry – Conductivity Measurement 3

Table of Contents

4 Foreword

4 Terms / definitions

21 Measuring instruments

22 Conductivity measuring cells

23 Calibration

26 Practical applications

41 Literature

42 Tables



ForewordThe measurement of the electrical (electrolytic) conductivity – conductometry – can look back on a long tradition. Conductivity measurements were already being made about 125 years ago. For approximately 50 years Metrohm has provided measuring instruments and accessories for its customers. This monograph is concerned only with the measurement of conductivity in solutions.

Although conductivity measurements are carried out frequently, they have never achieved the wide range of application of potentiometry (e.g. pH, ion, redox measurements). The reason for this may be that in conductometry there is no generally valid equation (such as, for example, the Nernst equation) that permits the appropriate calculations. On the contrary, in conductometry experience, experiments and comparative measurements come to the fore instead of calculations.

This monograph is intended to provide a basic familiarization course in conductometry in a short time. Help is provided by the alphabetically arranged terms and definitions as well as the practical examples.

Terms / DefinitionsActivity a

In water and polar solvents ionic compounds dissociate into their single ions (e.g. NaCl → Na+ + Cl–). At normal concentrations, strong electrolytes (e.g. HCl, K2SO4) are completely dissociated, but weak electrolytes (e.g. NH3, CH3COOH) are always incompletely dissociated. However, strong electrolytes behave as if an incomplete dissociation were present. This is caused by the fact that interactions (associations) occur between the oppositely charged ions and these reduce the chemical potential. For this reason the electrical conductivity is not a linear function of the concentration. The effective concentration (c) is known as the activity a. (Of course, these interactions also occur with weak electrolytes, but can normally be neglected because of the low ionic concentration.)

Activity coefficient

In real ionic solutions the interaction (association tendency) causes the «mass action» of the ions to be smaller than would be expected from the weight present. The stoichiometric concentration c must therefore be multiplied with a correction factor so that the mass action law continues to remain valid. This concentration-independent factor is known as the activity coefficient fi, the effective concentration as the activity a (see above).

Amount-of-substance concentration

c(X) = amount-of-substance concentration of substance X in mol/L, e.g. c(KCl) = 0.01 mol/L.

Ash

The ash content of sugars can be determined by measuring the electrical conductivity. This method is much more rapid than the ashing process itself and provides usable results. The theoretical basis is that the majority of the ash components consist of electrolytes, whereas the sugar itself is a non-electrolyte. This means that the electrical conductivity of sugar solutions is practically only determined by their ash content.



5.0 g sugar is dissolved in dist. H2O, the solution made up to 100 mL and mixed. The electrical conductivity is measured at 20 ±0.1 °C → K5The electrical conductivity of the water used is measured at the same temperature → KWK5 = electrical conductivity in µS/cm of the 5% sugar solution

% ash = K5 – (0.9 x KW) x 0.0018

Calibrated Reference (767)

With the 2.767.0010 Calibrated Reference, Metrohm can provide users of conductivity meters with a handy solar-cell-powered device for checking their instruments. The built-in resistors are certified. This means that it is possible to check the conductometer displays for electrical conductivity as well as the temperature (Pt 100 or Pt 1000 temperature sensor) and validate the instruments in this way.

The same instrument is also suitable for checking pH/mV meters, potentiometric and Karl Fischer titrators.See also the Calibration section.

Calibration

See the Calibration section.

Calibration solutions

These solutions are used for calibrating conductivity cells, i.e. for determining the cell constant. See also the Calibration section.

Calibration solutions are solutions whose electrical conductivity γ is known exactly. It is best to use so-called secondary standards. These are certified and can be directly traced to standard reference materials (e.g. National Institute of Standards and Technology – NIST, USA – www.nist.gov).

Of course, you can also make up your own calibration solutions by dissolving the corresponding salts in ultrapure water or by diluting concentrated solutions (e.g. c(KCl) = 0.1000 mol/L – Metrohm no. 6.2301.060). However, for electrical conductivities


The relationship to the electrical conductivity γ, the real subject of interest, is provided by the cell constant c, which depends on the geometrical dimensions of the measuring cell:

γ = c/RX = c x GX (S/cm)

In a two-plate measuring cell the cell constant c is obtained from the area F and the distance d between the plates:

c = d/F (cm/cm2)[c] = cm–1

Because the distribution of the lines of current is not ideal, this calculated value does not agree exactly with the effective cell constant of the measuring cell. The effective value of c can only be determined by calibration; see below in the «Calibration» section.

Charge number

The charge number zi gives the charge of the particular ion including its sign.

Examples:

NaCl → Na+ + Cl– z+ = +1; z– = –1

CaCl2 → Ca2+ + 2 Cl– z+ = +2; z– = –1

K3PO4 → 3 K+ + PO43– z+ = +1; z– = –3

Conductance

The conductance G is the reciprocal of the electrical resistance (1/R) and has the unit Siemens (S) = Ω–1. The electrical conductivity is obtained by multiplying it with the cell constant. Conductivity titrations only require the conductance G.

Conductivity cells

See section on Measuring cells/conductivity cells.

Conductivity standards

See Calibration solutions.

Conductivity titration

See conductometric titration

Conductivity water

Term (introduced by W. Ostwald) for highly pure water with a very small self-conductivity. It expresses the fact that such a water is suitable for even demanding studies in the field of electrical conductivity (e.g. preparation of Conductivity standards). The term also applies to the ultrapure water used in the pharmaceutical industry. USP Monograph 645 defines the specifications for such a water as


As at each point in the titration, all the ions present contribute to the conductivity, typical V-shaped titration curves are obtained.

Example: Titration of HCl with NaOH

H+ + Cl– + Na+ + OH– = H2O + Cl– + Na+

Thin lines contributions of the individual ions to the conductivity

Bold lines total conductivity (produces titration curve)

Contact-free methods

As the name says, in these methods (for measuring the electrical conductivity) there is no contact between the measuring cell electrodes and the sample. These methods are frequently called «electrode-free» which is, of course, incorrect. Two basic methods are used:

1. Capacitive method

See under the term High-frequency measurement.

2. Inductive method

In this case the sample forms a coupling loop between two windings of a transformer that are magnetically shielded from each other. Measuring frequencies of 50 Hz...500 Hz are used in this case. There is a relationship between the electrical conductivity of the sample and the voltage transferred from the primary to the secondary winding throughout a very wide range. This means that it is possible to evaluate the measured values by using the cell constant.

Contact-free methods have the advantage that the measured values can never be falsified by polarization. There are also no corrosion or contamination problems with the electrodes. However, the cost and complexity of the necessary apparatus is considerably higher when compared with those for «normal» instruments.

For this reason such methods are used, if at all, for industrial applications.

Convection

One of the three mechanisms (convection, migration, diffusion) by which ion transport can take place is convection – ions travel as a result of liquid flow, e.g. thermal convection (temperature gradient).

Degree of dissociation

Quantity that describes the extent to which dissociation occurs. It represents the ratio be-tween the free ions and the total molecules present in the solution and is given either rela-tively or as a percentage (1 or 100% means complete dissociation, 0.5 or 50% means that only half the molecules are dissociated).



Strong electrolytes such as HCl, HNO3, H2SO4, NaOH, KOH and their salts are always completely dissociated in aqueous solution.

Dependency of electrical conductivity

The electrical conductivity of a solution depends on:

• The number of ions: The more ions a solution contains, the higher its electrical conduc-tivity.

• In general on the ionic mobility, which in turn depends on:

– The type of ion: The smaller the ion, the more mobile it is and the better it conducts. H3O+, OH–, K+ and Cl– are good conductors. If hydration occurs (the ion surrounds itself with water molecules that make it larger) then the conductivity is reduced.

– The solvent: The more polar a solvent is, the better the dissolved compounds it con-tains can ionize. Water is an ideal solvent for ionic compounds. In alcohols ionization decreases as the chain length increases (methanol > ethanol > propanol). In non-polar organic solvents (e.g. chlorinated and non-chlorinated hydrocarbons) practi-cally no ionization occurs.

– The temperature: In contrast to solids, in solutions the electrical conductivity increas-es as the temperature increases by 1...9% per K, depending on the ion.

– The viscosity: As the viscosity increases, the ionic mobility and therefore the electrical conductivity decreases.

Dielectric constant D

In electrochemistry the dielectric constant is important wherever opposite charges act on each other. Examples are dissociation or ionic interaction. The larger the relative dielectric constant (Dvacuum = 1), the better the ionic compounds dissociate in the particular solvent. A few examples:

Solvent D (20 °C)

Formamide 110

Water 80

Methanol 34

Ethanol 25

Acetone 21

Propanol 19

Chloroform 4.8

Hexane 1.9

Diffusion

One of the three mechanisms (convection, migration, diffusion) by which ion transport can take place is diffusion – ions travel as a result of differences in chemical potential (concentration gradients).

Diffusion is described quantitatively by Fick’s law.



Dissociation

In solvents with a high dielectric constant (polar solvents) ionic compounds break down into freely mobile single ions, e.g.

KCl → K+ + Cl–

A different type of dissociation occurs when a chemical compound with a heteropolar bond is dissolved in a protic solvent, e.g.

CH3COOH + H2O → CH3COO– + H3O+

The most important solvent for dissociation is water. It has a high dielectric constant and is polar.

Ionic solutions are electrically conductive and decompose when a direct current is applied (electrolysis).

Ionic solutions are also known as electrolytes. Both strong and weak electrolytes occur; these are differentiated by their degree of dissociation.

Dissociation constant

This quantity is used to describe the ionic equilibrium in aqueous solutions of weak electrolytes and is defined by the following equation:

K = (CA x CC) / CCA

CA and CC are the concentrations of the anions and cations formed by dissociation, CCA is the concentration of the molecules that remain undissociated.

K increases as the degree of dissociation increases and therefore represents a usable quantity for describing the strength of a weak acid or weak base.

The negative common logarithm of K is also known as the pK value; pK = –log K. As all dissociation equilibria are temperature-dependent this also applies to K and pK.

Dosimat

Metrohm term for motor-powered piston burets. Dosimats are high-precision universal dosing devices that can be controlled manually or remotely. Dosimats are equipped with so-called Exchange Units.

Dosino

Metrohm term for a stepper-motor-controlled drive for precise dosing in small spaces. Dosing Units are attached to the dosing drive by a quick-action coupling and screwed directly onto the reagent bottle.

Electrical conductivity

The electrical conductivity γ is equal to the reciprocal of the electrical resistance (conduc-tance G) multiplied by the cell constant c:

γ = conductivity unit: S cm–1 (S m–1)R = resistance unit: ΩG = 1/R conductance unit: S (Siemens) = Ω–1l = length of measuring path unit: cm (m)A = cross sectional area unit: cm2 (m2)c = l/A cell constant unit: cm–1 (m–1)



The electrical conductivity is normally given in µS/cm or mS/cm (12.88 mS/cm = 1288 mS/m; 5 µS/cm = 500 µS/m). In American usage the terms mhos and µhos are frequently encountered.

Definitions according to EN 27888 (1993) or ISO 7888.

Electrolytes

Electrolytes are substances that, in solutions or melts, undergo heterolytic dissociation into ions that conduct the electrical current. Electrolytes include acids, bases and salts.

Strong electrolytes dissociate completely, weak electrolytes only partially.

Emulsions

Emulsions («water in oil» or «oil in water») normally belong to the group of non-electrolytes. Migration of ions in an electric field and the resulting electrical conductivity do not occur. However, a technical effect can be used for measurement – this is charge transport in an electric field. According to Coehn’s law, two phases that are immiscible are characterized by the occurrence of surface charges. The phase with the higher dielectric constant (water) assumes a positive charge, that with the lower one (oil) a negative charge. At maximum viscosity the stability of the emulsion is also at its maximum, but also has the lowest «electrical conductivity». This means that under defined measuring conditions conclusions can be drawn about the stability of emulsions.Reference:Dahms, G.H., Jung, A., Seidel, H.Predicting emulsion stability with focus on conductivity analysisCosmetics & Toiletries Manufacture Worldwide 2003, p. 223–228

Equivalent conductivity

The equivalent conductivity Λ* is a quantity that is primarily used in theoretical studies. It can be obtained from the molar conductivity Λ and the electrochemical valency ne:

Λ* = Λ / neThe electrochemical valency ne can be calculated for a molecule that dissociates into ν– anions and ν+ cations with the corresponding valencies z– und z+ as follows:

ne = ν– x z– = ν+ x z+Examples:

NaCl → Na+ + Cl– ν+ = ν– ne = 1

AlCl3 → Al3+ + 3 Cl– ν+ = 1 and z+ = 3 ne = 3

Four-electrode measuring technique

In particular when materials other than platinized platinum (e.g. steel) are used for electrodes, interference occurs and incorrect measured values are obtained because of polarization.

The four-electrode measuring technique was introduced to prevent this. It is somewhere in the middle between the classical two-electrode method and contact-free methods.

It uses two current and two voltage electrodes. The resistance RX between the two voltage electrodes, which is proportional to the conductance G, and the voltage drop resulting from RX are measured (high-impedance), amplified and compared against a reference voltage Uref in a controller. If there is a difference between the two voltages then this is



compensated by the controller altering the oscillator potential Uvar. The current J flowing in the sensor area is then a measure of the required resistance RX or the conductance G, respectively:

J = Uref/RX = Uref x GX

Thanks to advances made in the fields of measuring and electrode technology we have been able to establish that, despite its advantages, this method with its extra costs for apparatus cannot replace the classical two-electrode measuring technique and that the extra costs involved for laboratory applications are not justified.

High-frequency measurement

This term is used in connection with capacitive, contact-free methods for measuring the electrical conductivity. It refers in particular to the relatively high frequencies (3 MHz...100 MHz) used for this type of measurement.

The special measuring cells are constructed so that two ring-shaped metal electrodes are attached to the outer sides of a non-metallic cell body (e.g. glass beaker).

The electric field penetrates the cell body and is influenced by the properties of the sample that it contains.

A major component of all instruments used for measuring the high-frequency conductivity is an oscillating circuit. The contact-free measuring cell is located parallel to the rotary condenser of the oscillating circuit. If resonance tuning is carried out during the measurement (maximum value of voltage U), then evaluation is carried out by the reactive component method. In contrast, if after resonance tuning has been carried out the value of U is divided by the conductance G, the evaluation takes place according to the active component method. Both types of evaluation require calibration with different conductance standards and also produce different calibration curves.

In comparison to the classical method, high-frequency measurement has practically no advantages – this is why it has never been able to establish itself on the market.

Hydration

In an aqueous solution all the ions are surrounded by a sheath of oriented water dipoles (hydration sheath). This phenomenon is known as hydration.

Interionic interaction

In infinitely dilute solutions no electrostatic attraction can occur between the oppositely charged anions and cations of a dissolved electrolyte. This condition would occur for an ion i at the hypothetical concentration ci = 0, which can only be achieved by extrapolation.

As the concentration increases the ions move closer together. This causes an interaction between the ions in which each cation is surrounded by a cloud of oppositely charged anions. In the same way each anion is surrounded by a cloud of cations. Interionic interaction is particularly important for strong electrolytes.

Ionic mobility IiThe product of the migration speed ui and the Faraday constant F is the ionic mobility. ui refers to a uniform field with a field strength of 1 V/cm. The distance covered by an ion i is given in cm. The ionic mobility depends on the temperature and the concentration. It usually



refers to 25 °C and an infinite dilution (measurement series extrapolated to ci = 0). Some examples:

Cation I+(cm2 / Ω)

Anion I–(cm2 / Ω)

H+ 350 OH– 199

Li+ 39 Cl– 76

Na+ 50 NO3– 71

K+ 74 CH3COO– 41

1⁄2 Mg2+ 53 1⁄2 SO42– 80

1⁄2 Ca2+ 60 1⁄2 CO32– 69

Ionic product of water

Water undergoes a self-dissociation known as autoprotolysis:

2 H2O → H3O+ + OH–

As a result of this self-dissociation, pure water has an electrical conductivity of 0.055 µS/cm at 25 °C or 0.039 µS/cm at 20 °C. Please note the high temperature coefficient of 5.8% per °C!

Ionic strength

The ionic strength is a measure of the interionic interaction occurring in the solution of an electrolyte. It is determined solely by the concentration ci and charge zi of the ions, and not by their characteristic features. The following applies for the ionic strength:

J = (1/2) Σci x zi2

The calculation of the ionic strength J of a known molar concentration ci of a particular electrolyte is simplified by the fact that there is a multiplication factor for each type of electrolyte. It is calculated for 1-molar solutions and can then be used generally:

Type of salt Example Factor1,1 KCl 11,2 K2SO4 32,2 MgSO4 41,3 K3PO4 6

The ionic strength is obtained by multiplying the particular molar salt concentration by this factor. Example:c(MgSO4) = 0.0025 mol/L

J = 4 x 0.0025 mol/L = 0.01 mol/L

Ions

are positively or negatively charged atoms or molecules that are formed by dissociation from compounds with ionogenic or heteropolar bonds. In an electric field the positively charged ions (cations) migrate to the cathode (negative pole), negatively charged ions (anions) to the anode (positive pole).



In dilute solutions anions and cations migrate independently without any interactions in an electric field.

Kohlrausch cells

See section on Measuring cells/conductivity cells.

Kohlrausch’s square-root law

This law for strong electrolytes links the molar conductivity ΛC with the square root of the concentration c according to:

ΛC = Λ0 – A

The equation states that the molar conductivity extrapolated to infinite dilution decreases as the square root of the concentration. The constant A depends on the type of electrolyte.

Limiting conductivity

Λ0 is the limiting equivalent conductivity or limiting conductivity for short. Λ0 is the sum of the limiting conductivities of the cations (λ0+) and anions (λ0–) (law of independent ionic migration).

For Λ see the definition under equivalent conductivity.Limiting conductivities of some ions in water at 25 °C

Cations Limiting conductivity

(S x cm2 x mol–1)

Anions Limiting conductivity

(S x cm2 x mol–1)

H3O+ 349.8 OH– 197.0

NH4+ 73.7 SO42– 80.8

K+ 73.5 Br– 78.4

Ba2+ 63.2 I– 76.5

Ag+ 62.2 Cl– 76.4

Ca2+ 59.8 NO3– 71.5

Mg2+ 53.1 ClO4– 68.0

Na+ 50.1 F– 55.4

Li+ 38.6 CH3COO– 40.9

Mass fraction

w(X) mass fraction of the substance X in %, e.g. w(NaOH) = 25%

Mass concentration

ρ(X) mass concentration of the substance X in g/L, e.g. ρ(NaCl) = 2.5 g/L

Measuring cell See section on Measuring cells/conductivity cells.

Measuring frequency

For conductivities the measuring frequency has a decisive influence on the correctness of the measured conductance G. Interfering polarization effects can be eliminated by



increasing the measuring frequency. At the same time the usable measuring range is extended. On the other hand, it must also be taken into consideration that at high frequencies a «cable error» could occur as a result of capacitive «shunting». The following time-proven compromises apply:

– At low conductances (not electrical conductivity) measurements are made at a frequen-cy of 300 Hz.

– At high conductances measurements are made at a frequency of 2.4 kHz (712 Conduc-tometer).

Measuring range

The usable measuring range depends on the type of conductivity cell (platinized/non-platinized), the cell constant and the measuring frequency. Unfortunately no universal measuring cell exists for the whole usable range. This is why Metrohm offers measuring cells with different cell constants. The following tables should make your choice easier:

Cell constant Measuring range

0.1 cm–1 0.1 µS/cm...20 µS/cm

1 cm–1 1 µS/cm...10 mS/cm

10 cm–1 10 µS/cm...100 mS/cm

100 cm–1 100 µS/cm...10 S/cm

Solution Measuring cell Cell constant Measuring frequency


Typical values for ui are about 10–4 cm/s.

If ui is multiplied by the Faraday constant F we obtain the ionic mobility Ii.

The sum of the ionic mobilities of the anions and cations of an electrolyte produces the molar conductivity Λ.

Molar conductivity

The molar conductivity Λ is defined as the quotient of the specific conductivity γ and the concentration c (mol/L) of the dissolved substance:

Non-electrolyte

In contrast to electrolytes, non-electrolytes release no freely mobile anions and cations and therefore make no contribution to the electrical conductivity in aqueous solutions.

Typical representatives of this group are e.g. alcohols, urea, sugar (raw sugar), nonionic surfactants and emulsions.

Electrolytic contaminations may contribute to the electrical conductivity – see Ash.

However, higher concentrations of non-electrolytes may influence the viscosity of the solution, which also affects the ionic mobility.

Oscillometry

See under high-frequency measurement.

Ostwald’s dilution law

This law applies for strong electrolytes and links the molar conductivity ΛC with the square root of the concentration c as follows:

ΛC = Λ0 – A

The equation states that the molar conductivity extrapolated to infinite dilution decreases as the square root of the concentration.

The constant A depends on the type of electrolyte. See also Kohlrausch’s square-root law.

Platinization

Platinization is the deposition of finely dispersed platinum (platinum black) on smooth platinum electrodes. It is an important feature of all classical conductivity cells and is used to avoid polarization effects (and the measuring errors they cause), particularly at high electrical conductivities. Platinized measuring cells are not suitable for industrial applications. Application Bulletin no. 64 provides information about the pretreatment and platinization of measuring cells (the 712 Conductometer has a built-in 20 mA DC source).

Polarization

In the measurement of the electrical conductivity a number of technical measurement effects that produce incorrect measured values are grouped together under polarization. Their source lies at the electrode/solution boundary. Of chief interest here are the



polarization resistance, which is in series with RX (resistance of the solution), and the polarization capacity, which is also in series. Interference by polarization usually results in too low electrical conductivities being measured.

Polarization depends mainly on the current density at the electrode. This current density can be kept negligibly small if platinized measuring cells are used together with a suitable, not too low measuring frequency.

Reference temperature

The electrical conductivity measured at a given temperature is converted to a reference temperature. The conversion is carried out (usually automatically) by using the temperature coefficient.

The normal reference temperatures are 20 °C and 25 °C.

Salinity

Applications exist in which it is not the electrical conductivity that is of interest, but rather the total content of the dissolved salts. Separation into the individual ions cannot be achieved by measuring the conductivity, as each type of ion makes a different contribution to the total conductivity. This is why when the salinity is measured it is the electrical conductivity of the sample solution which is compared with those of pure NaCl solutions and the corresponding NaCl concentration is given. The salinity is given in mg/L or g/L NaCl as the TDS (Total Dissolved Solids).

Solvents, non-polar

Non-polar (also known as aprotic) solvents have no self-dissociation. Molecules with ionic bonding only decompose in them to form ions on rare occasions.

Examples of acidic non-polar solvents are:

pyridine, dimethylformamide (DMF), dimethylsulfoxide (DMSO)

Examples of neutral polar solvents are:

acetone, methyl isobutyl ketone (MIBK), acetonitrile, nitrobenzene, ethers, hydrocarbons and chlorinated hydrocarbons.

«Normal» conductometers are not suitable for non-polar solvents such as chlorinated and non-chlorinated hydrocarbons, insulation oils or petrochemical products. In order to measure the electrical conductivity (insulation properties) of such products, special instruments are required. These work with voltages in the kV range and with special measuring cells.

Solvents, polar

Polar (also known as amphiprotic) solvents have an appreciable self-dissociation. In such solvents molecules with ionic bonding decompose by dissociation to form ions (the higher the dielectric constant, the better). The most polar solvent is water:

2 H2O H3O+ + OH–

Alcohols also belong to the protic solvents,

e.g. 2 CH3OH CH3OH2+ + CH3O–



Examples of acidic polar solvents are:

formic acid, glacial acetic acid, cresols, phenol

Examples of basic polar solvents are:

ethylenediamine, benzylamine, butylamine

Examples of neutral polar solvents are:

methanol, ethanol, isopropanol, ethylene glycol, ethylene glycol monomethyl ether

Specific conductivity

Earlier term for the electrical conductivity γ (EN and ISO standard). It was known as κ and had the same units, i.e. S/cm (from conductance G x cell constant c).

Specific resistance

The specific resistance ρ is the reciprocal of the specific conductivity κ – electrical conductivity γ – with the unit Ω x cm.

In earlier days it was usual in water purification plants to give the water quality in these units. 1 µS/cm corresponds to a specific resistance of 1 MΩ x cm.

Temperature coefficient

25 and °C are temperatures at which the electrical conductivities have been measured.

The temperature coefficient can be given as reciprocal Kelvin or % per °C.

The temperature coefficient depends primarily on the ions contained in the solution and shows seldom a linear behavior. We recommend that it is determined automatically by the 712 Conductometer.

Temperature compensation

See under the term Reference temperature.

Temperature dependency

The temperature dependency of the electrical conductivity can be explained by observations concerning the migration speed of the ions in an electric field. See also Walden’s rule. This can be used to explain at least the positive temperature coefficient.

However, the quantitative relationships are complicated and calculations are therefore practically impossible.

Even with uniform substances (e.g. KCl solutions) the temperature coefficient changes with the concentration. In mixtures all the ions contribute to a new, mixed temperature coefficient.

If high accuracy is required the temperature coefficient must therefore be determined experimentally.

See also under the terms Reference temperature, Temperature coefficient and Temperature compensation.



Titrando

Metrohm name for the most modern titration system on the market. The Titrando provides flexibility at the user interface and dosing system. The basic unit can be extended to form a fully automated «supertitrator».

Titrino

Metrohm name for a whole range of titrators. The range of titrators covers everything from a simple endpoint titrator up to potentiometric and Karl Fischer titrators for universal use.

Transference number

The transference numbers n+ und n– describe the current fraction transported by the cation and anion respectively.

n+ = λ+/Λ = u+ / (u+ + u–)

n– = λ–/Λ = u– / (u+ + u–)

Experimental determination of the transference numbers allows the calculation of the ionic conductivities and ionic mobilities.

Validation

Validation is the systematic checking of analysis procedures and/or measuring devices with the aim of ensuring that if defined SOPs (= Standard Operating Procedures) are observed then reliable and reproducible measurements and results will be obtained.

See also the Calibration section.

Viscosity

The (dynamic) viscosity η is the property of a liquid to resist (by internal friction) the mutual laminar displacement of two neighboring layers. For Newtonian liquids at a given temperature, η is a material constant with the SI unit Pascal per second (Pa s–1).

In connection with the measurement of conductivity there is the fact that, as the viscosity increases, the ionic mobility and therefore the electrical conductivity decreases and vice versa. See also Walden’s rule.

Walden’s rule

In its general form this rule states that the product of the ionic mobility Ii of an ion and the viscosity η of a solvent is constant:

Ii x η = K

An increase in the viscosity results in a reduction of the ionic mobility (and therefore the electrical conductivity) and vice versa.

Water, self-conductivity

Kohlrausch already recognized about 150 years ago that even the most overdone purification of the water by distillation resulted in a self-conductivity that could not be lowered any further. The cause is the self-dissociation of the water, which is also known as autoprotolysis:

2 H2O H3O+ + OH–



This self-dissociation depends very strongly on the temperature. Examples are shown in the following table:

°C µS/cm

0 0.010

18 0.038

25 0.060

34 0.090

50 0.170

The very large temperature coefficient is conspicuous. Between 18 °C and 25 °C it is 8.3% per °C!



InstrumentsInstruments for measuring the electrical conductivity are called conductometers. They are instruments for measuring complex resistances with changing potentials. (In contrast to the measurement of purely ohmic resistances of metallic conductors, in liquids together with the measuring cell a whole network of resistances and capacitances exist.) It makes sense to have at least two frequencies available for the applied alternating potentials (see under Measuring frequency and Polarization). However, by the correct choice of the measuring frequency, the cell constant and the material of the measuring cell, purely ohmic relationships can be achieved. Under these conditions the electrical conductivity can be determined from the measured resistance.

This means that an instrument for measuring the conductivity must be able to measure the electrical conductivity of liquids. The demands placed on such instruments for laboratory use have increased year by year. With the 712 Conductometer Metrohm provides the user with an instrument of the highest performance class that leaves nothing to be desired. The possibilities of this instrument are listed below:

Types of measurement

– Electrical conductivity– Standard (calibration solutions)– TDS (Total Dissolved Solids), expressed

as mg/L NaCl or g/L NaCl – salinity– Titration (conductivity titration)– Temperature (of solution)

Sensor connections

One input each for conductivity measuring cell and temperature sensor (Pt 100 or Pt 1000)

Measuring ranges

– Electrical conductivity (automatic range switching):

0...2000 µS/cm and 0...20’000 mS/cm. Resolution: max. 41⁄2 digits are shown.– Temperature: –170.0...500.0 °C.

Resolution: 0.1 °C.

Compensation ranges, e.g. for titrations, back-ground suppression

– Electrical conductivity: 0...2000 µS/cm and 0...2000 mS/cm (0...2 S/cm)

– Temperature: –170.0…500.0 °C

Measuring frequencies

300 Hz or 2.4 kHz; automatic switching to the most suitable frequency or manual setting.

Temperature coefficient

Automatic determination with connected temperature sensor; TC = f(T) is calculated as a polynomial. Can also be entered manu-ally. Range 0.00...9.99% per °C.

Reference temperature

For automatic temperature compensation. Freely selectable, 20 °C or 25 °C are normal.

Cell constant

Automatic via determination – dialog-guided with automatic calculation, or manual input. Range 0.001...500/cm.

Platinization

DC output for platinizing conductivity cells. I = 20 mA.

Interface RS 232

For connection to printer or PC.

«Remote» I/O lines

For connecting a sample changer or labora-tory robot or for triggering any type of alarm.

Analog output for electrical conductivity

Connection of a lab recorder or titrator. Out-put signal 0...2000 mV with a resolution of 0.5 mV (12 bit).

Analog output for temperature

E.g. for connection of a lab recorder. Output signal 0...2000 mV with a resolution of 0.5 mV (12 bit).

Instrument diagnosis

The instruments carries out a self-diagnosis when switched on. The built-in diagnosis pro-gram allows the user to localize or exclude in-strument faults.



Conductivity measuring cellsThese measuring cells, which are also known as Kohlrausch cells, normally have two platinized platinum electrodes. By selecting the area of and the distance between the two electrodes it is possible to vary the cell constant of such electrodes throughout a wide range. Platinizing the electrodes greatly reduces the risk of obtaining incorrect measured values because of polarization. This also has a favorable effect on the usable measuring range. This means that a conductivity cell with a cell constant of c = 1 cm–1 can be used at a measuring frequency of 1 kHz from 10 µS/cm to 100 mS/cm. Smooth, i.e. non-platinized measuring cells should only be used for low electrical conductivities (


CalibrationGLP (Good Laboratory Practice) requires, among other things, that the accuracy and precision of analytical instruments are checked regularly by using SOPs (Standard Operating Procedures).

Calibration is used to validate the whole system that is used for making the measurements. In our case this means that instrument and the measuring cell(s) used must be calibrated from time to time.

The following test procedures should be considered as guidelines. The limits they contain are merely examples. Depending on the accuracy required for the measuring system it may be necessary to redefine these limits in your own SOPs.

Literature: Application Bulletin no. 272

A) Checking the instrument (using the 712 Conductometer as an example)

Required accessories:

– 2.767.0010 Calibrated Reference– 2 x 6.2106.020 cable (2 x plug B)– 1 x 6.2104.080 electrode cable (with plug B)

Parameter settings at the Conductometer (712) for the two following tests:

> cond/parameters

cell constant 1.000 / cm

meas. temp. 25.0 °C

ref. temp. 25.0 °C

TC selection: const.

TC const. 0.00% / °C

frequency: auto

meas. type: standard

The following equation applies:γ = G x cγ = electrical conductivity (µS cm–1)G = conductance (µS)c = cell constant (cm–1)

At the 767 Calibrated Reference the cover over the solar cells is closed. The two banana plugs of the electrode cable are inserted into the input sockets (measuring cell) of the conductometer and the electrode plug screwed onto socket 5 or socket 6 of the 767. The two 6.2106.020 cables are now used to connect the two input sockets of the 712 with sockets 1 and 2, or 2 and 3, respectively, of the 767.



Examples of measured value

Socket(s) Actual value µS/cm

Theoretical value µS/cm

Difference µS/cm

Error tolerance(±0.5%)µS/cm

5 70.07 70.01 0.06 ±0.35

6 2.168 2.17 –0.002 ±0.011

1 & 2 10010 10008 2 ±50

2 & 3 999.2 999 0.2 ±5

Evaluation: The checked instrument is OK.

In order to check the temperature display, the two 6.2106.020 cables are used to connect both red input sockets of the des 712 with sockets 1 and 2 (Pt 100) or 2 and 3 (Pt 1000) of the 767.

Examples of measured value

Socket(s) Actual value °C

Theoretical value °C

Difference °C

Error tolerance°C

1 & 2 –0.2 –0.20 00 ±0.1

2 & 3 00.1 00.17 –0.07 ±0.1

Evaluation: The checked instrument is OK.

B) Checking the conductivity cell with calibration solution

It is assumed that the conductivity cell is in a well-conditioned state.

The measuring vessel is thoroughly rinsed, first with ultrapure water and then with the calibration solution. It is then filled with the calibration standard and thermostatted at 25 °C.

The measuring cell is first immersed several times in the calibration solution and then positioned so that the upper openings at the sides are completely immersed in the liquid. Any air bubbles that are present inside the measuring cell can be removed by swirling and tapping.

The Conductometer is switched on and the corresponding value for the cell constant (printed on the measuring cell) is entered in the 712. The measuring and reference temperatures are also entered in the 712.

712 parameters:

> cond/parameters cell constant value printed on electrode (e.g. 0.78 / cm) meas. temp. 25.0 °C ref. temp. 25.0 °C TC selection: const. TC const. 0.00% / °C frequency: auto meas. type: standard



Wait until the temperature is constant and then read off the measured value. If the KCl calibration solution from Metrohm (6.2301.060) is used then the electrical conductivity must be 12.90 ±0.15 mS/cm.

New cell constant = theoretical conductivity / measured conductance

Example c(KCl) = 0.1000 mol/L, 25 °C

Electrical conductivity γ = 12.90 mS/cm

Displayed conductance G = 16.13 mS

New cell constant c = 12.90 mS/cm / 16.13 mS = 0.80 cm–1



Practical applications

1. Determination of the cell constant c

Metrohm conductivity cells are supplied with the cell constant printed on them. The use of the cells may cause the cell constant to change. This is why, if high-precision measurements are to be made, the cell constant must be checked or redetermined from time to time. KCl solutions of a known concentration are used for these determinations. For reasons of precision (weighing errors) a stock solution with c(KCl) = 0.1000 mol/L is either prepared or purchased and lower concentrations are prepared from it by dilution with conductivity water.

The electrical conductivity of conductivity water is ≤1 µS/cm.

c(KCl) = 0.1000 mol/L (Metrohm no. 6.2301.060)

KCl reagent grade (e.g. Merck no. 104936) is dried at 105 °C for 2 h and allowed to cool down in a desiccator. 7.456 g is dissolved in conductivity water and made up to 1000 mL.

The conductivity of this solution is:

– at 20 °C: 11.67 mS/cm

– at 25 °C: 12.88 mS/cm

c(KCl) = 0.010 mol/L

10.0 mL c(KCl) = 0.1 mol/L is diluted to 100 mL with conductivity water.


– at 20 °C: 1.28 mS/cm

– at 25 °C: 1.41 mS/cm

c(KCl) = 0.001 mol/L

This solution should only be prepared immediately before use. It cannot be stored. The conductivity water must be freed from carbon dioxide before use by passing nitrogen through it. 10.0 mL c(KCl) = 0.01 mol/L is diluted to 100 mL with degassed conductivity water.


– at 20 °C: 133 µS/cm

– at 25 °C: 147 µS/cm

Certified conductivity standards with a wide range (1 µS/cm...100 mS/cm) are sold, e.g., by Messrs Reagecon, Chemical Measurement Specialists, in Shannon Free Zone, Shannon, Co. Clare, Ireland; www.reagecon.com



Example of a determination at 20 °C, 712 Conductometer

Instruments and accessories:

– 2.712.0010 Conductometer, 2.728.002X Magnetic Stirrer– Conductivity cell, e.g. 6.0907.110– Printer and printer cable, thermostat, nitrogen from gas cylinder– 6.1414.010 titration vessel lid, 6.1418.250 titration vessel with thermostat jacket and

6.1440.010 gas inlet and overflow tube

Reagents:

– c(KCl) = 0.0100 mol/L– Acetone and conductivity water

Procedure

The measuring cell is placed in acetone for 30 min. It is rinsed with conductivity water and then allowed to stand in it for at least 2 h, preferably overnight. The titration vessel is first rinsed with c(KCl) = 0.01 mol/L and then filled with this solution. The measuring cell is also rinsed with c(KCl) = 0.01 mol/L and inserted in the titration vessel. The thermostat is used to bring the liquid in the titration vessel to 20.0 °C under stirring while nitrogen is bubbled through the solution for at least 10 min. The nitrogen is then allowed to blanket the solution. Care must be taken that there are no gas bubbles inside the measuring cell. The following settings are made on the 712 Conductometer (see also parameter report):

Cell constant 1.0 / cmMeasuring temperature 20.0 °CReference temperature 20.0 °CTC selection: const.TC const. 0.0% / °CFrequency autoMeas. type: StandardRange limit: offStandard 1.278 mS/cm

The automatic determination is now started at the 712.

If no thermostat is available then the following procedure can be used:

The measuring cell and the solutions are prepared in exactly the same way. The use of nitrogen in the closed measuring cell and titration vessel is also identical. However, instead of a thermostat a Pt 1000 or Pt 100 temperature sensor (6.1110.100 and 6.1103.000 respectively) is connected. All the 712 Conductometer settings remain the same with the exception of the temperature coefficient, which is entered as 2.11% / °C.

Calculation:

New cell constant = theoretical conductivity / measured conductance

Example:

Theoretical conductivity = 1.28 mS/cm (0.010 mol/L KCl, 20 °C)Measured conductance = 1.533 mS1.28 mS/cm / 1.533 mS = c = 0.835 cm–1

Example with 6.0907.110 conductivity cell:

c = 0.8195 ±0.007 cm–1 (n = 10)PFIZER, INC., IPR2017-01358, Ex. 1017, p. 27 of 52


2. Determination of the temperature coefficient α of c(Na2SO4) = 0.05 mol/L

As explained in the theoretical section, the conductivity of ionic solutions is extremely temperature-dependent and this dependency is rarely linear. This is why we recommend that the TC in the temperature range of interest is recorded automatically at the Conductometer.


– 2.712.0010 Conductometer and 2.728.002X Magnetic Stirrer

– e.g. 6.0912.110 conductivity cell with built-in temperature sensor (Pt 1000)

– Printer and printer cable, thermostat

– 6.1414.010 titration vessel lid, 6.1418.250 titration vessel with thermostat jacket

Reagents:

– c(Na2SO4) = 0.05 mol/L. 7.10 g Na2SO4 or 16.11 g Na2SO4 x 10 H2O is dissolved in con-ductivity water and made up to 1000 mL.

– Conductivity water

Procedure

The conditioned measuring cell is rinsed with conductivity water and then with Na2SO4 solution. Sufficient Na2SO4 solution is filled into the measuring vessel and the measuring cell inserted and made bubble-free.

The following settings are made on the 712 Conductometer (see also parameter report):

Start temperature 40.0 °CStop temperature 15.0 °CReference temperature 20.0 °CFrequency autoTemperature coefficient 0.00%Cell constant actual value

The stirrer is switched on and the solution is brought to approx. 45 °C by using the thermostat. The automatic determination is started and the solution is allowed to cool down slowly (not faster than 1 °C / min).

Example:

Measured value; TC = 2.35 ±0.09% / °C (n = 8)

3. General remarks concerning conductivity measurements

The measuring cell

– The cell constant should match the liquid to be measured. Low conductivities require the use of a small cell constant, high conductivities a high one:

c ≈ 0.1 cm–1 for poorly conducting solutions such as fully or partially deionized wa-ter

c ≈ 1 cm–1 for moderately conducting solutions such as drinking water, surface water, ground water and wastewater

c ≈ 10 cm–1 for solutions with good conductivity such as seawater, rinsing water, physiological solutions, etc.



c ≈ 100 cm–1 for solutions with very good conductivity such as brine, acids, alkalis, electroplating baths, etc.

– The measuring cell must be well conditioned/prepared. Measuring cells stored dry must be placed in acetone for 30 min. They are then rinsed in conductivity water and allowed to stand in it for at least 2 h, preferably overnight. Frequently used measuring cells are stored in conductivity water or 20% ethanol (to prevent the growth of microor-ganisms). Measuring cells that are only used occasionally should be stored dry.

– Contaminated measuring cells cannot be used for conductivity measurements and must be cleaned. After cleaning they should be thoroughly rinsed with conductivity wa-ter. Possible sources of contamination:

• Deposits of calcium carbonate or barium sulfate: Rinse with HCl. For BaSO4 immerse the cell overnight in a solution of w(Na2EDTA) = 10% in c(NaOH) = 0.1 mol/L under stirring.

• Fat and oil residues: Rinse with acetone. If this does not help, saponify with ethanolic c(NaOH) = 1 mol/L at approx. 40 °C.

• Algae or bacterial growth: Place in hot chromosulfuric acid.

• Protein: Place in w(pepsin) = 5% in c(HCl) = 0.1 mol/L for 1...2 h.

The instrument

– Set the measuring frequency to «auto» – this ensures that the measurement is made at the optimal measuring frequency. Generally: Measure low conductivity at a low measur-ing frequency and high conductivity at a high one.

– Temperature coefficient: If known then set on instrument, otherwise determine it. A fur-ther possibility is to use a thermostat and to perform the measurement at the reference temperature, which means that this setting is not necessary.

– Temperature: It is best to use a measuring cell with a built-in temperature sensor. Other-wise connect a separate temperature sensor or use a thermometer – in the latter case the measuring temperature must be entered at the instrument.

– Cell constant: Enter the cell constant marked on the measuring cell or determine the cell constant again.

– Reference temperature: This is normally 20.0 °C; for some applications 25.0 °C is stipu-lated or preferred (water samples or, e.g., measurements in tropical countries). Any ref-erence temperature can be entered at the 712 Conductometer.

The measurement

Only use well-conditioned measuring cells. It is best to rinse them with the solution to be measured before the measurement. Immerse the measuring cell in the measuring solution to an adequate depth and make sure it is bubble-free. The lateral openings must be fully immersed. Remove and re-immerse the measuring cell a few times. Wait until the temperature of the measuring cell and solution become constant.



4. Conductivity measurements in water

A) Wastewater, ground, mineral, surface and drinking water

The reference temperature is normally 25.0 °C. In order to avoid errors by incorrectly selecting the temperature coefficient (TC) it is either recommended or stipulated that the sample solution is thermostatted at 25.0 °C. If this is not required then a TC can be entered as given in the table below, or TC Ident: «DIN» can be selected. The latter setting is suitable for water that contains mainly calcium and bicarbonate ions as well as small amounts of magnesium, sulfate, chloride and nitrate ions.

Sample temperature TC in % / °C

5...10 °C 2.62

10...15 °C 2.41

15...20 °C 2.23

20...25 °C 2.08

25...30 °C 1.94

30...35 °C 1.79

Examples:

Tap water in Herisau, 25 °C γ = 512.5 ±8.3 µS/cm (n= 10)

Mineral water, 25 °C γ = 1.813 ±0.013 mS/cm (n= 10)

B) Deionized water

Because of possible interferences, a special procedure must be selected for water with a conductivity of


5. Salinity

Applications exist in which it is not the electrical conductivity that is of interest, but rather the total content of the dissolved salts. Separation into the individual ions cannot be achieved by measuring the conductivity, as each type of ion makes a different contribution to the total conductivity. For this reason, when the salinity is measured it is the electrical conductivity of the sample solution that is compared with that of pure NaCl solutions and the corresponding NaCl concentration is given. The 712 Conductometer carries out this conversion automatically if the measuring mode TDS (Total Dissolved Solids) is selected. TDS appears on the 712 as mg/L or g/L NaCl in the dialog display instead of the cell constant.

Examples:

Tap water Herisau, 25 °C TDS = 245.6 ±4.2 mg/L NaCl (n = 10)

Mineral water, 25 °C TDS = 894.8 ±6.7 mg/L NaCl (n = 10)

6. Conductometric titrations

For conductometric titrations the cell constant does not normally need to be known. A double platinum sheet electrode is used for the measuring electrode as the titration is usually carried out in a beaker. This electrode is easy to clean. Thermostatting is not required for simple titrations – room temperature is adequate. Alterations in conductivity caused by temperature variations are of virtually no consequence.


– 2.712.0010 Conductometer

– Titrino with 2.728.0040 Magnetic Stirrer

– 6.3026.220 Exchange Unit

– 6.0309.100 double Pt-sheet electrode with 6.2104.080 electrode cable

– 6.2116.000 connecting cable 712 – Titrino

– PC with connecting cable for Titrino, printer and printer cable

– E.g. Metrodata «VESUV 3.0 Light» for the manual evaluation of L- or V-shaped titration curves (VESUV = Metrodata Application software; Verification Support for Validation).

Reagents:

– c(AgNO3) = 0.01 mol/L as titrant (in Exchange Unit)

– c(KCl) = 0.1000 mol/L, e.g. Metrohm no. 6.2301.060

– Conductivity water and acetone

Procedure

The instruments are connected together as described in the 712 Instructions for Use. 0.25 mL c(KCl) = 0.1 mol/L and 30 mL each of acetone and conductivity water are placed in a beaker. The electrode and buret tip are immersed and the titration with c(AgNO3) = 0.01 mol/L is started after the following instrument parameters have been set:



712 Conductometer 799 Titrino>cond/parameters MET U Cond. titr.cell constant 1.0/cm >titration parametersmeas. temp. 20.0 °C V step 0.10 mLref. temp. 20.0 °C dos. rate max. mL/minTC selection: const. signal drift 50 mV/minTC const. 0.0% / °C equilibr. time 26 sfrequency: auto start V: offmeas. type: Titration pause 0 slimits: off >stop conditions>cond/analog output stop V: abs.status: on stop V 4.0 mLpolarity + filling rate max. mL/min1 V range: 1 mS/cm >evaluation0 V at: 0 µS/cm EP criterion 30 mVoffset: 0 mV EP recognition all>cond/limitsstatus: off>cond/plot marginsleft: 0 µS/cmright: 1000 µS/cm

Example of a titration (VESUV 3.0):

Evaluation

L- and V-shaped titration curves are evaluated as follows:

Tangents are applied to the two legs of the curve. The titration endpoint is defined as the intercept of the tangents. In the Metrodata VESUV 3.0 program this is carried out as follows:

Move Tangent 1 along the curve with the key and the left-hand mouse key, Tangent 2 with the key and the left-hand mouse key.



7. Conductivity measurements in deionized water according to USP guidelines

Summary

The electrical conductivity of ultrapure water is measured according to USP Method 645 (US Pharmacopeia; USP 23, Vol. 5) in a flow-through cell with a cell constant of c = 0.1 cm–1.

Sample

Ultrapure water from a «Barnstead Nanopure» unit, Application Lab, Herisau.

Reagents

Hamilton conductivity standard. 5 µS/cm ±5%; WO 1197985, P/N 238926

Instruments and accessories

712 Conductometer 2.712.0010Conductivity cell PP, c = 0.091 cm–1 Conductivity cell glass, c = 0.082 cm–1 Flow-through cell 6.1420.100767 Calibrated Reference 2.767.0010728 Magnetic Stirrer 2.728.0010Titration vessel 6.1418.250Titration vessel lid 6.1414.010683 Pump 2.683.0010Thermostat bath Cable 712 – PC (RS 232) 6.2125.060Cable 712 – PC (RS 232) 6.2125.010Metrodata VESUV 3.0 6.6008.140

The schematic shows the connections.



Fig. 2 Parameter settings at the 712

712 Conductometer OP1/106 712.0015date 2001-03-07 time 15:28:11 conductivity >cond/parameters cell constant 0.091 / cm meas.temp. 25.0 °C ref.temp. 25.0 °C TC selection: const. TC const. 0.0 %/°C frequency: auto meas.type: standard range limit: OFF> cond/analog output status: OFF> cond/limits status: OFF> cond/plot margins left: 0 µS / cm right: 0 µS / cm ----------------------------------------config > config / print id. 1 id. 2 print header: always date & time ON send to: IBM> config / print meas. values print crit.: time time interval 300.0 s stop time 12000 s date & time ON> config / report type orig. cal. Report: OFF cal. Report format: short> config / Pt sensor

Pt id

Pt correction 0.0 °C



> config / auxiliaries

run number

date 2002-03-07

time 15:28:15

dialog: english

device label

program 712.0015

> config / RS 232 settings

baud rate: 9600

data bit: 8

stop bit: 1

parity: none

handshake: HWs

RS control: ON

----------------------------------------

Sample preparation

Water is taken from the «Nanopure» unit. The first 500 mL is rejected. 1 Liter is then filled into an amber glass bottle (thoroughly rinsed) and the bottle placed in a thermostat bath for 1 h at 25 °C.

Preparing the measuring setup

The 712 Conductometer is validated with the 767 Calibrated Reference as described in Application Bulletin No. 272. The protocols shown below provide an overview:

712 Conductometer: protocol of measuring amplifier check

Instrument: 1.712.0010 Serial/Fabr.-No: 16162 ID-No (if available): ...................

Test agent: 2.767.0010 Serial/Fabr.-No: 01102 ID-No (if available): ...................

Cal. date: 12/2001 checked by: S. Jung ..........................................

Calibrator (master) Type .......................................................

SCS Cal. Serv. Reg. No. Certificate No 8.767.3003 ......................

Check carried out on: 2002.02.25 Name: Christian Haider Signature: ..........................................................

Checked instrument meets

requirements:

Place Calibrated Reference on bench near sensor. The cover remains always closed and therefore the light is not of importance.

The electrode cap must not necessarily be firmly screwed onto sockets (4), (5), (6) of the 767; plugging it in is

sufficient.

Yes x

no Decision:



Prepare the 712 Conductometer:Remove all cables except the mains cable. Switch on instrument.

, LCD display: conductivity

>cond/parameters

:

Note down the following parameters (see LCD display) in list below and then enter the following standard values:

cell constant ............... /cm → 1.0 /cm

meas. temp. ............... °C → 20°C

ref. temp. ............... °C → 20°C

TC selection: ............... → const.

TC const ............... %/°C → 1.0 %/°C

frequency: ............... → auto

meas.type: ............... → standard

range limit ............... → OFF

, , LCD display: 20.0 °C 1.000 /cm 1.00%/°C

Conductivity

Carry out on 712 or on sensor Remarks Carry out on 767

Enter theo-retical value from 767 cover

Enter actual value from 712 display1

Difference2 Permitted Difference

OK

ü

1. Screw off cable at the plug-in head of the sensor (if no sensor or sensor without plug-in head is connected: use 6.2150.020 cable from accessories in 767 case, insert into ‘Cond. Cell’ socket)

Close cover Sensor cable to socket (6)

2. Main display: µS/cmLCD display: conductivity

(Cover remains closed)

µS value 6:2.167µS 2.169 µS –0.2 µS ±0.04 µS

ü

3. Sensor cable to socket (5)

µS value 5:69.86 µS 69.881 µS –0.0281 µS ±0.77 µS

ü

4. Remove sensor cable from Cond Cell input and use 2x 6.2150.000 instead

Sensor cable to sockets (2) and (3) (Pt 1000)

µS value 2)/(3):

999.80 µS 999.842 µS –0.042 µS ±11 µS

ü

5. Sensor cable to sockets (2) and (1) (Pt 100)

µS value 1)/(2):

9990.1µS 9995.202 µS –2.202 µS ±70 µS

ü

6. Display 0 →

ü

7. Display as before →

ü



Temperature (Pt 100 / Pt 1000)

Carry out on 712 or on sensor

Remarks Carry out on 767 Enter theo-retical value from 767 cover

Enter actual alue from 712 display

Difference2 Permitted difference

OK

ü

1. Remove banana cables from the sockets ‘Cond Cell’ and connect them to the temperature measuring input of 712.

Leave banana cables at the sockets (1) - (2) (Cover does not matter whether open or closed)

2. Measuring (mode) °C on the main display there appears: X.X °C

3. Insert banana cables to the sockets of 2.767.0010 according to the table at the right and always depress .

Temp. value sockets (1) and (3) see certificate

On 767.0010:

Sockets (1) and (2) (Pt 100) →

Sockets (2) and (3) (Pt 1000) →

Sockets (1) and (3) (Pt 1000) →

°C value:

0.1 °C

0.0 °C

25.7 °C

0.2 °C

0.0 °C

25.8 °C

0.1 °C

0.0 °C

0.1 °C

±0.4 °C

±0.4 °C

±0.4 °C

ü

ü

ü

Remove cable and re-enter the parameters noted above.

During pH checks the two Pt 100/Pt 1000 resistances at sockets (1)...(3) can be used at the same time. However, it must be clear that the measuring temperature assumed by the 712 Conductometer being tested will then be approx. 0 °C, while the information in the table refers to 25 °C. This must be taken into account.

1 Wait until display remains stable2 The given permitted difference applies for normal room temperatures (20…30 °C) and warmed-up instruments.

Otherwise this should be determined from the technical specifications of the 767 and 712 Conductometer.

The cell constants of the conductivity cells are measured at 25 °C with 100 mL conductivity standard (Hamilton 5 µS/cm) in a closed, thermostatted titration vessel. When the conductivity standard has reached the stipulated temperature of 25.0 °C the cell constant is determined as described in Method 1 above. The temperature compensation is switched off at the 712 during the measurement. The newly determined cell constant is entered at the 712 Conductometer or taken over by it. Result reports for two conductivity cells are shown below:

Conductivity cell PP

Subject Requirement Achieved

Conductometer validation yes yes

Cell constant ±2% ±0%

c displayed: 0.091 cm–1 0.091 cm–1

γ, limit at 25 °C


Conductivity cell glass

Subject Requirement Achieved

Conductometer validation yes yes

Cell constant ±2% ±0%

c displayed: 0.082 cm–1 0.082 cm–1

γ, limit at 25 °C


Summary / Procedure

In practice the electrical conductivity of water from ultrapure water units is determined according to the USP Guidelines 645 for conductivity measurements as follows:

1. The conductometer (712) is calibrated using the 767 Calibrated Reference.

2. The cell constant of the conductivity cell is determined at 20 °C according to Application Bulletin no. 272. The value given on the conductivity cell should be in agreement with the value measured to ±2%.

3. The 6.1420.100 flow-through cell is connected to the outlet valve of the ultrapure water unit (inlet at bottom, outlet on top) and the conductivity cell is inserted.

4. The water now flows through the cell into the outlet (a pump can also be used to trans-port it through the cell).

5. Temperature compensation is switched off at the conductometer (712).

6. The measuring setup is rinsed with 200...500 mL water (from the unit).

7. The electrical conductivity of the water is now measured at the temperature at which it leaves the unit (to ±1 °C) and the value is accepted after a flow-through time of 15 min.

8. The value is compared with the following table (USP requirements):

USP 645 Requirements – Ultrapure water (without temperature compensation)

Temp. °C µS / cm Temp. °C µS / cm

0 0.6 55 2.1

5 0.8 60 2.2

10 0.9 65 2.4

15 1.0 70 2.5

20 1.1 75 2.7

25 1.3 80 2.7

30 1.4 85 2.7

35 1.5 90 2.7

40 1.7 95 2.9

45 1.8 100 3.1

50 1.9

9. If the electrical conductivity (at the corresponding temperature) is not greater than the value given in the table then the USP requirements have been fulfilled. However, if the measured electrical conductivity is larger than the corresponding table value then step two given under «Remarks» is carried out.



Literature

– Metrohm Application Bulletin no. 102

Conductometry

– Metrohm Application Bulletin no. 272

Validation of Metrohm conductometers

– United States Pharmacopeia Convention, Inc.

USP 26 / NF 21 (2003) Water conductivity (645)

– Kunze, U.R., Schwedt, G.

Grundlagen der quantitativen und qualitativen Analyse

Wiley-VCH, Weinheim 2002. ISBN 3-527-30858-X

– Donald T. Sawyer et al.

Electrochemistry for chemists

John Wiley & Sons, New York 1995 ISBN 0-471-59468-7

– Öhme, F., Bänninger, R.

ABC der Konduktometrie

Reprint «Chemische Rundschau», 1979 (out of print)

– EN 27888: 1993

Water quality – Determination of electrical conductivity

– AOAC, Method 973.40 (1990)

Specific conductance of water

– DIN 38404, Part 8 (1982)

German standard methods for the examination of water, waste water and sludge; physi-cal and physicochemical parameters. Determination of the electrical conductivity



Tables

Electrical conductivity of organic acids at 25 °C

% formic acid mS/cm % acetic acid mS/cm

5 6.22 5 1.36

10 8.26 10 1.76

15 9.86 15 1.82

20 11.1 20 1.82

25 11.4 25 1.71

30 11.8 30 1.58

40 11.1 40 1.23

50 9.78 50 0.840

60 7.92 60 0.521

70 5.92 70 0.270

80 3.92 80 0.093

90 1.95

100 0.32

M(HCOOH) = 46.026 g/mol

M(CH3COOH) = 60.052 g/mol

Electrical conductivity of hydrogen bromide and hydrogen chloride at 25 °C

% HBr mS/cm % HCl mS/cm

5.09 239 2.03 202

9.16 409 6.00 506

15.3 603 10.0 698

20.4 706 15.2 821

25.3 787 19.0 849

30.5 828 20.3 844

32.5 833 24.8 809

35.5 833 29.9 737

37.5 825 33.0 688

40.7 801 36.0 638

M(HBr) = 80.912 g/mol

M(HCl) = 36.461 g/mol



Electrical conductivity of nitric acid at 25 °C

% HNO3 mS/cm % HNO3 mS/cm

3.06 176 45.1 7754.89 270 49.9 7198.99 454 55.0 65914.0 631 60.0 59718.1 741 70.1 44224.0 830 80.1 23928.0 852 88.5 80.033.1 859 92.6 70.636.3 844 99.5 48.840.0 819

M(HNO3) = 63.013 g/mol

Electrical conductivity of phosphoric acid at 25 °C

% H3PO4 mS/cm % H3PO4 mS/cm5 31 40 22210 61 45 23215 91 50 23320 122 55 22425 152 60 21030 180 70 16935 204 80 98

M(H3PO4) = 97.995 g/mol

Electrical conductivity of sulfuric acid (and oleum) at 25 °C

% H2SO4 mS/cm % H2SO4 (SO3) mS/cm3.93 177 53.5 5557.00 308 58.4 47110.0 426 63.1 38014.6 586 72.3 22319.8 717 85.9 12425.3 798 95.4 12429.4 825 98.0 94.734.3 819 100.0 10.4639.1 781 101.5 32.0543.9 714 103.8 34.5048.7 640 105.1 28.84

M(H2SO4) = 98.07 g/molM(SO3) = 80.06 g/mol



Electrical conductivity of potassium and sodium hydroxide at 25 °C

% KOH mS/cm % NaOH mS/cm

5 225 5 197

10 360 10 353

15 407 15 478

20 395 20 567

25 342 25 618

30 266 30 624

35 209 35 595

40 169 40 525

M(KOH) = 56.106 g/molM(NaOH) = 39.997 g/mol

Electrical conductivity of ammonia solutions at 25 °C

% NH3 mS/cm % NH3 mS/cm

1.04 0.821 15.2 0.810

3.73 1.176 18.6 0.625

5.26 1.275 23.2 0.419

7.46 1.236 27.3 0.286

9.52 1.142 31.0 0.197

11.5 1.035

M(NH3) = 17.030 g/mol

Electrical conductivity of lithium chloride at 25 °C

% LiCl in H2O mS/cm % LiCl in ethanol mS/cm

2.5 45.4 2.5 3.648

5.0 82.6 5.0 4.565

7.5 112.5 7.5 6.565

10.0 135.6 10.0 4.035

12.5 142.6 12.5 3.139

15.0 148.6 15.0 2.541

M(LiCl) = 42.394 g/mol



Electrical conductivity of potassium and sodium chloride at 25 °C (own measurements)

% KCl mS/cm % NaCl mS/cm

5 68.9 5 70.3

10 134.0 10 118.8

15 197.8 15 164.2

20 250.2 20 196.8

25 299.6 25 220.2

M(KCl) = 74.551 g/molM(NaCl) = 58.443 g/mol

Electrical conductivity of potassium and sodium nitrate at 20 °C

g/L KNO3 mS/cm g/L NaNO3 mS/cm

1.01 1.236 0.85 1.025

2.02 2.405 1.70 2.00

5.05 5.745 4.25 4.775

10.1 10.94 8.50 9.11

20.2 20.62 17.0 17.19

50.5 46.6 42.5 38.7

M(KNO3) = 101.103 g/molM(NaNO3) = 84.995 g/mol

Electrical conductivity of calcium and magnesium chloride at 20 °C

g/L CaCl2 mS/cm g/L MgCl2 mS/cm

0.555 1.085 0.476 1.030

1.11 2.088 0.952 1.982

2.77 4.90 2.38 4.64

5.55 9.26 4.76 8.76

11.1 17.39 9.52 16.38

27.7 39.35 23.8 36.55

M(CaCl2) = 110.99 g/molM(MgCl2) = 95.211 g/mol



Electrical conductivity of magnesium and sodium sulfate at 20 °C

g/L MgSO4 mS/cm g/L Na2SO4 mS/cm

0.602 0.798 0.71 1.015

1.204 1.42 1.42 1.925

3.010 2.98 3.55 4.39

6.020 5.20 7.10 8.22

12.04 12.04 14.2 14.97

35.5 31.3

M(MgSO4) = 120.36 g/molM(Na2SO4) = 142.04 g/mol

Electrical conductivity of ammonium chloride and sodium carbonate at 20 °C

g/L NH4Cl mS/cm g/L Na2CO3 mS/cm

0.535 1.275 0.53 1.010

1.07 2.50 1.06 1.883

2.675 6.02 2.65 4.220

5.35 11.57 5.30 7.670

10.7 22.25 10.6 13.81

26.75 52.9 26.5 28.70

M(NH4Cl) = 53.491 g/molM(Na2CO3) = 105.989 g/mol

Electrical conductivity of NaCl and H3PO4 solutions at 20 °C

% G/V NaCl γ in mS/cm c(H3PO4) in mol/L γ in mS/cm

5 65 0.05 7.5

10 113 0.10 10.2

15 148 0.50 32

20 175 1.00 57

25 191 2.00 110

3.00 165

4.00 190

5.00 210

M(NaCl) = 58.443 g/molM(H3PO4) = 97.995 g/mol



Electrical conductivity of potassium chloride solutions at 20 °C and 25 °C

c(KCl) in mol/L µS/cm at 20 °C µS/cm at 25 °C

0.0005 67 74

0.001 133 147

0.005 654 720

0.010 1280 1410

0.020 2510 2770

0.050 6060 6700

0.100 11670 12900

0.200 22440 24800

M(KCl) = 74.551 g/mol1 mS/cm = 1000 µS/cm1 µS/cm = 0.001 mS/cm

Electrical conductivity and temperature coefficient (TC) of potassium chloride solutions at various temperatures

°C mS/cm0.1 mol/L

TK (α) in % per °C0.1 mol/L

mS/cm0.01 mol/L

TK (α) in % per °C0.01 mol/L

18 11.19 2.06 1.225 2.07

19 11.34 2.06 1.251 2.11

20 11.67 ---- 1.278 ----

21 11.91 2.06 1.305 2.11

22 12.15 2.06 1.332 2.11

23 12.39 2.06 1.359 2.11

24 12.64 2.07 1.386 2.11

25 12.88 2.07 1.413 2.11

M(KCl) = 74.551 g/mol

Electrical conductivity of water – temperature coefficient (TC) as a function of sample temperature

Sample temperature in °C TK (α) in % per °C

05...10 2.62

10...15 2.41

15...20 2.23

20...25 2.08

25...30 1.94

30...35 1.79

– The reference temperature for water samples is normally 25 °C.– The above values refer to water samples containing mainly calcium hydrogen carbon-

ate ions and small amounts of magnesium, sulfate, chloride and nitrate ions.PFIZER, INC., IPR2017-01358, Ex. 1017, p. 46 of 52


Electrical conductivity of salt solutions – temperature coefficient (TC) as a function of the salt content

Salt TC at 5% TC at 10% TC at 15% TC at 20% TC at 25%

NH4Cl 1.98 1.86 1.71 1.61 1.54

NH4NO3 2.03 1.94 ---- 1.79 ----

(NH4)2SO4 2.15 2.03 ---- 1.93 ----

BaCl2 2.14 2.06 2.00 1.95 ----

CaCl2 2.13 2.06 2.02 2.00 2.04

Ca(NO3)2 2.18 2.17 ---- ---- 2.18

KBr 2.06 1.94 ---- 1.77 ----

KCl 2.01 1.88 1.68 1.66 ----

KNO3 2.08 2.05 2.02 1.97 ----

K2SO4 2.16 2.03 ---- ---- ----

LiCl 2.23 2.18 ---- 2.20 ----

MgCl2 2.22 2.20 ---- 2.37 ----

MgSO4 2.26 2.41 2.52 2.69 2.88

Na acetate 2.51 2.59 ---- 2.93 ----

Na2CO3 2.52 2.71 2.94 ---- ----

NaCl 2.17 2.14 2.12 2.16 2.27

NaNO3 2.21 2.17 ---- 2.15 ----

Na2SO4 2.36 2.49 2.56 ---- ----

AgNO3 2.18 2.17 ---- 2.12 ----

ZnSO4 2.25 2.23 2.28 2.41 2.58

TC (α) in % per °C, at 18 °C



Requirements of USP 645 for ultrapure water(without temperature compensation)

Temp. °C µS/cm Temp. °C µS/cm

0 0.6 55 2.1

5 0.8 60 2.2

10 0.9 65 2.4

15 1.0 70 2.5

20 1.1 75 2.7

25 1.3 80 2.7

30 1.4 85 2.7

35 1.5 90 2.7

40 1.7 95 2.9

45 1.8 100 3.1

50 1.9

TC (% per °C) calculated from the above values:

0...20 °C 2.73%

20...40 °C 3.24%

40...60 °C 3.86%

60...80 °C 4.07%

80...100 °C 4.35%

Dependency of the electrical conductivity of dist. H2O and KCl solutions on the measuring frequency (at 25 °C and c = approx. 1 cm–1)

(own measurements)

Solution 300 Hz 2.4 kHz

dist. H2O 1.12 µS/cm 1.59 µS/cm

KCl, c = 0.001 mol/L 147 µS/cm 151 µS/cm

KCl, c = 0.01 mol/L 1.35 mS/cm 1.41 mS/cm

KCl, c = 0.1 mol/L 11.03 mS/cm 12.90 mS/cm

KCl, c = 1 mol/L 45.37 mS/cm 96.18 mS/cm


48 Metrohm Monograph 8.028.5003PFIZER, INC., IPR2017-01358, Ex. 1017, p. 49 of 52

mono konduktometrie e · 2017. 5. 22. · 4 metrohm monograph 8.028.5003 conductometry –...

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