White Paper
ELECTRICAL CONDUCTIVITY, TEMPERATURE DEPENDENCE, & GE M9 ANALYZER
Though the Conductivity is a relatively fundamental measurement both online and in the laboratory,
the theory and practice of its measurement can be quite technical. This article serves to describe basic
theory of Conductivity and the variables that can affect its measurement. Particular attention is given
to Temperature, which is often modeled to yield a Temperature-Compensated Conductivity reading.
Finally, a discussion of the specific methodology found in the GE Sievers* M9 Total Organic Carbon
(TOC) Analyzer is presented.
Introduction
The following white paper discusses the concept of electrical conductivity in aqueous
solutions, the effects of temperature on conductivity, and the methodology of conductivity
measurements in the GE Sievers M9 TOC Analyzer.
Electrical conductivity is a measure of a substance’s ability to transmit electric charge. For
purposes of water quality, conductivity is a result of dissolved ionic material. This is typically
indicative of some sort of contamination but can also be a gauge of composition, chemistry,
and consistency. Because of the relative speed and ease of measuring conductivity, it has
long been a regulated measurement in many applications and is used as a first indicator of
water quality changes in many others.
While the measurement of conductivity, itself, is typically a stable, accurate, and reliable one,
it is important to consider the effects that the environment can have. These effects can
change the measured conductivity, even though the composition of the solution has not
changed.
Of the many variables that can affect a solution’s conductivity, temperature is the most
studied and modeled. To better compare the conductivity measurements of aqueous
samples, the concept of Temperature-Compensated Conductivity was created. This allows for
the comparison of conductivity measurements by using a reference temperature (typically 25
°C). To properly compensate for temperature, the ionic species must be known or
approximated. In the latter case, the compensated value of conductivity to the reference
temperature would also represent an approximated value.
Different conductivity measuring apparatus handle compensation differently. In all cases,
however, the temperature compensating algorithm is only as accurate as the constant used.
In the GE Sievers M9 TOC Analyzer, the constants are fixed, which requires the operator to
choose appropriate standards, control the samples to 25 °C, or use raw conductivity and
temperature data to manually calculate an accurate temperature-compensated conductivity
value.
Cell Constants and Measuring Conductivity
Electrical conductance is the inverse of electrical resistance, which is, in turn, defined by
Ohm’s Law:
𝑅=
𝑉
𝐼
* Trademark of General Electric Company; may be registered in one or more countries.
©2016, General Electric Company. All rights reserved
300 00322 EN Rev. B
Where R is resistance, V is an applied potential, and I is a measured current. Whereas
resistance is measured in Ohms (), the SI unit for conductance is Siemens (S). Again, the
reciprocal nature exists; if a sample has a resistance of 5.0 , it will have conductance of 0.2
S.
To measure conductivity, a probe or cell is used to measure the dynamics of current and
potential. Though there are many designs, most employ two or more electrodes of known
dimensions across which a known potential is applied. The current is measured and
conductance (resistance) is calculated per Ohm’s Law.
In order to convert conductance to sample conductivity (or specific conductivity), the
conductance must be normalized by the cell constant, K,
𝐾 = 𝑑/𝑎
where d is the distance between the electrodes and a is the area of the electrodes. Note that
the units of K are [length]-1, typically given in cm-1. Therefore, whereas conductance is given
as S, sample conductivity is generally expressed as S/cm.
Conductivity Measurement Theory & Ions
In the context of aqueous solutions, the concept of electrical conductance is simply the ability
of the water to transmit an electrical charge. Empirically, it is understood that as the purity of
water increases, the ability to conduct electricity is reduced. Furthermore, it is generally well
understood that the presence (or absence) of ions (charged molecules) affects a solution’s
conductivity.
This dependence on ions for conductivity is most commonly observed with salts.1 For
example, sodium chloride is a common salt that is frequently found in aqueous solutions.
The behavior of sodium chloride in water is fairly easy to describe:
𝑁𝑎𝐶𝑙 ↔ 𝑁𝑎+ + 𝐶𝑙 −
This clearly shows how a salt dissociates into ions which, in turn, are free to carry electrical
charge. The degree to which these ions carry charges is highly variable, however. It is the
nature of these variables that is fundamental to understanding a sample’s conductivity. For
example, magnesium sulphate (MgSO4) is a salt that is highly soluble in water but will impart
different conductivity behaviors due to the anions and cations produced upon dissociation.
Without delving into the atomic and sub-atomic theories of physics and physical chemistry,
the role ions play in electrical conductivity can be summarized as one of mobile facilitators.
That is, the presence of ions facilitates the transfer of electrical charge through their mobility
in solution. Ions are carriers of electrical charge; when a potential is applied to solution, ions
increase the speed at which the electrical charge is carried. This is what we measure as
conductivity.
1
A salt is an ionic substance that results from the neutralization reaction of an acid and base. Because salts are
ionic solids (typically), most have some degree of solubility in water.
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300 00322 EN Rev. B
Once it is understood that ions, through their mobility, facilitate the carrying of electrical
charge in the solution, it is imperative to acknowledge that not all ions are created equal with
respect to carrying a charge.
Mathematically, this can be demonstrated with the following equation:
S  1c1 1  2 c2 2  3 c3 3  4 c4 4  ....
where
S  conductivity
i  specific conductance of the ion
c i  concentrat ion of ion
  charge of the ion
The specific conductance are studied and determined empirically, rather than by theoretic
modeling. The values can often be found in the literature to complete an appropriate model.
Affinity, Solubility, Concentration, Mobility, Viscosity, and Temperature
There are a significant number of variables that can affect a solution’s conductivity. Detailed
analyses of these variables can be found in the literature and are the subject of many peer
reviewed journal articles written by esteemed researchers at major universities. The
objectives here are not academic; therefore, a summarized approach is given.
Though, perhaps obvious, it is important to understand that ions can be quite different from
one another. 𝐶𝑙 − , 𝑆𝑂42− , 𝑁𝑎+ , 𝑁𝐻4+ , and others all have different properties that affect their
respective abilities to carry charge and, therefore, influence sample conductivity. Different
molecules have different affinities, or attraction to electrons. How tightly a molecule governs
its electrons affects its influence on conductivity.
Solubility and concentration also are important to conductivity. For example, sodium-based
salts are typically readily soluble in water and lead to larger concentrations of ions than less
soluble substances, e.g., carbonate (𝐶𝑂32− ) salts. As concentration increases, there are more
ions in solution to facilitate the carrying of charge and conductivity increases.
As a general rule the smaller the ion, the greater the electrostatic field around the ion, and
the slower the ionic mobility of that ion becomes. This is called the Hydration Effect and
influences sample conductivity. Note that the hydration effect can be minimized by the
conjugate ions a substance contributes. Potassium salts (e.g., KCl) have a much different
conductivity behavior than potassium hydroxide (KOH).
Sample viscosity has an inverse relationship with sample conductivity. As viscosity increases,
conductivity decreases. To the extent that a substance increases the water’s viscosity, this
will decrease the conductivity that might otherwise have been expected due to that
substance’s contribution of charge-carrying ions.
Temperature has a dynamic effect. Generally speaking, as temperature increases, viscosity
decreases, solubility and concentration increase, and mobility increases. Nearly all of these
dynamics have an overall net increase on sample conductivity.
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300 00322 EN Rev. B
Because temperature is most likely to change significantly, it has the greatest effect on
sample conductivity measurements. For this reason, it is the most commonly studied,
modeled, and discussed variable on conductivity.
Temperature Correction Methodologies
Modeling the temperature dependence of conductivity requires careful studies of ion-specific
behaviors across a range of temperatures and concentrations. Common conductivity values
for various types of water can be classified as follows:
Solution Type
Theoretical Limit
Online DI & WFI
Distilled Water
Drinking Water
Sea Water
Typical Conductivity Value
µS/cm
mS/cm
0.055
0.1 - 1.0
0.5 - 3.0
500 - 2,000
0.5 - 2.0
50,000
50
Temperature affects conductivity of samples, changing by 2% per C.2 For example, a 0.05
C fluctuation will cause a ±0.1% change in conductivity. To account for this variation, most
laboratory-based measurements are performed on samples that have been equilibrated to
25 C in a water bath, or equivalent. Similarly, other instruments, including the M9, have the
ability to apply an algorithm to calculate a “temperature-corrected” or “temperaturecompensated” conductivity value.3 Typical conductivity instruments will show three
measurements:
 Raw conductivity – the actual measured conductivity value
 Temperature
 Temperature-compensated conductivity – the actual measured conductivity value
normalized to the reference temperature, usually 25 C
An additional dynamic is observed with the self-ionization of water, governed by the
following equilibrium:
2𝐻2 𝑂 ↔ 𝐻3 𝑂+ + 𝑂𝐻 −
The conductivity of pure water is given by:
S ( H  OH ) K w
where
K w  ionizationproduct water
While the specific conductance of H and OH are fairly linear with temperature, the ionization
product is very nonlinear with temperature. This is the main reason the conductivity of water
as a function of temperature is so nonlinear.
2
Ibid.
Virtually all conductivity standards are specified at 25 C. For example, a calibration standard won’t be listed as
1,409 µS/cm, such a standard will be described, marketed, and sold as 1,409 µS/cm at 25 C.
3
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300 00322 EN Rev. B
It also represents a temperature-dependent phenomenon that becomes significant at
ultrapure levels. ASTM D11254 shows one study to demonstrate the nonlinear conductivity of
pure water. The chart below shows a subset of Table 3 from the ASTM standard:
ASTM D1125 Table 3:
Conductivity Value of Pure Water
Conductivity, µS/cm
0.20
0.15
0.10
0.05
0.00
0
10
20
30
40
50
60
Temperature, C
In aggregate, the dynamics discussed above (and others that are not discussed5) lead to a
nonlinear relationship between temperature and conductivity. But, it can also be seen that
most of the discussed dynamics are significant at relatively low conductivity values. For
example, if drinking water is being analyzed at 1,000 µS/cm, then the self-ionization of water
is probably not of any concern.
And, like many scientific laws and governing equations, there is a linear approximation for
temperature compensation. While there is no definitive criteria in the literature to guide
when it is appropriate to use a linear approximation to model the temperature dependence
of conductivity, the general guideline employed by GE Analytical Instruments is 10 µS/cm.
However, when the substance is known (such as a calibration or verification standard) and
the nonlinear compensation algorithm is available, it is always recommended to use the
nonlinear model.
Each model is examined in further detail below.
Linear Temperature Correction and Conductivity Standards
As discussed above, conductivity is dependent on temperature, which can make it difficult to
compare readings of the same sample on different instruments. It complicates the
calibration and verification of conductivity probes, meters, and instruments. It also explains
4
ASTM D1125 – 14 (2014), Standard Test Methods for Electrical Conductivity and Resistivity of Water, Table 3
Conductivity Values of Pure Water and Increases Due to Sodium Chloride, “2015 Annual Book of ASTM Standards,
Section 11: Water and Environmental Technology, Volume 11.01: Water (I)”, pg 108.
5
For example, slightly acidic or basic salts (e.g., ammonium chloride) create a dynamic relationship between the
conductivity of the water and the conductivity of the contaminating salt. NaCl is a good example of a neutral salt.
This leads to a model that assumes the water conductivity and the salt’s contribution to conductivity are
completely independent of one another. This assumption begins to fail with non-neutral salts and contaminants.
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300 00322 EN Rev. B
the temperature rating on commercially available conductivity standards. A given standard
isn’t simply expressed as a conductivity value, such as 1.409 mS/cm. Rather, it is given as a
specific substance at a specific temperature: 1.409 mS/cm KCl at 25.0 C.
The concern naturally comes from the need to verify instruments against a standard of
known concentration. In practice, laboratories, instruments, and the standards themselves
are typically at some temperature other than 25.0 C. Unfortunately, that 1.409 mS/cm
standard will read ~1.460 mS/cm at 26.8 C (using an average of 2% per C). This is not due
to contamination or some other alteration of the standard, but due to the increase in
temperature.
Fortunately, the behaviors of common ions have been studied enough to be modeled.6
Though the relationship between conductivity and temperature is typically nonlinear, it may
be acceptable to use a linear approximation given by the following equation:
𝐶𝑡 =
𝐶𝜃
1 + 𝛼𝜃 (𝜃 − 𝑡)
Where:
𝜃 = 𝑡ℎ𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑠𝑎𝑚𝑝𝑙𝑒
𝑡 = 𝑡ℎ𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒, 𝑡𝑦𝑝𝑖𝑐𝑎𝑙𝑙𝑦 25 ℃
𝐶𝜃 = 𝑡ℎ𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑟𝑎𝑤 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑎𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝜃
𝛼𝜃 = 𝑡ℎ𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝐶𝑡 = 𝑡ℎ𝑒 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑒𝑑 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑡
Note that the temperature compensation coefficient 𝛼𝜃 (the constant) is an empirically
measured value that is available in literature, user manuals, and other sources. It is also
important to understand that, for myriad reasons explained above, this constant is unique to
every substance. Thus, there is no compensating algorithm that would be appropriate for all
samples of various ions.
For calibrations and verifications, the substances are known. Typically KCl is used as the
calibration media, for reasons discussed in the next section. The relative purity of this
standard allows the user to choose the appropriate constant for KCl and use the appropriate
equation to account for temperature variations.
Similarly, as instruments are challenged with known substances to calibrate or verify the
instrument’s performance, it is imperative that the proper constant be used to model the
temperature dependence.
For unknown samples, it becomes a problem to find an appropriate algorithm to model the
temperature dependence of the compounds and ions in solution. Typically, the constant for
sodium chloride is used to approximate the temperature dependence of the unknown
sample’s conductivity. Sodium chloride is a representative salt that mimics an average
constant value; the constant for sodium chloride falls near the middle point of the range of
common ionic constants, 𝛼𝜃 .
6
Barron, J. J. and C. Ashton, The Effect of Temperature on Conductivity Measurement, Reagecon Diagnostics, Ltd.
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300 00322 EN Rev. B
It is due to the temperature dependence of conductivity and the ion-specific nature of this
dependence that compendial methods (USP, EP, JP, etc.) typically require raw conductivity
values be used or that the sample be maintained to 25.0 C (thereby eliminating the need to
compensate for temperature). In either case, the compendia eliminate the potential
inaccuracies of the temperature compensating constants and equations by instead using the
raw conductivity measured by the instrument.
Nonlinear Temperature Correction
Complimentary to the above chart based on ASTM D1125 is the following taken from Light et
al.7:
This again shows the nonlinear relationship between temperature and conductivity.
Similarly, it demonstrates that below 30 C, the percent change of the conductivity reading is
between 5-7% per C of change. Thus, a sample with 1.0 µS/cm conductivity reading at 30
C will read ≥0.75 µS/cm at 25 C. This is significant and the nonlinear behavior becomes
important to accurately model in ultrapure water.
The following chart for sodium chloride demonstrates that this general behavior is consistent
for other ionic species, but that the specific model varies:
7
Light, T.S., Licht, S., Bevilacqua, A.C., and Morash, K.R., “The Fundamental Conductivity and Resistivity of Water,”
Electrochemical and Solid-State Letters, 8 (1), E16-E19, 2005.
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300 00322 EN Rev. B
The discussion to this point clearly demonstrates the nonlinear relationship between
temperature and conductivity. Furthermore, the ion-specific nature of this relationship can
clearly be seen. Thus, it is incumbent upon the user to ensure that he appropriately models
the solution. For samples near the reference temperature and whose expected values are
larger than 10 µS/cm, the linear relationships may be an appropriate approximation. If a
nonlinear equation is necessary, this can be determined experimentally using the following
methodology.
For a dilute solution of a salt, the relationship between temperature, T, and conductivity, C,
may be modeled as such:
𝐶 = (𝜆𝑎 (𝑇) + 𝜆𝑏 (𝑇))𝑚 + 𝐶𝐻2 𝑂 ,
where
𝜆𝑎 and 𝜆𝑏 are limiting ionic conductance of the individual ions
m is the moles of salt in solution
𝐶𝐻2 𝑂 is the conductivity of pure water
By substituting 25 C as the reference temperature of interest and solving the equation for
conductivity at this point, the governing equation is used to define the temperaturecompensated conductivity:
𝐶25 =
where:
𝜆𝑎 (25)+𝜆𝑏 (25)
(𝐶𝑇
𝜆𝑎 (𝑇)+𝜆𝑏 (𝑇)
− 𝐶𝐻2 𝑂(𝑇) ) + 𝐶𝐻2 𝑂(25),
25 represents that temperature is the reference 25 C
T is the actual temperature of the measurement
Additional detail on how to set up and conduct experiments to model a specific substance’s
temperature dependence can be found in the literature and various guides. For the purposes
of this discussion and the methodology found in the GE Sievers M9 TOC Analyzer, the
following were used:
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300 00322 EN Rev. B




Pure water: ASTM D1125-14. Other common guides include ISO 7888.
Sodium chloride (NaCl): Data included in Lange’s Handbook of Chemistry8 and Light et
al.9
Potassium chloride (KCl): Data included in the NIST guidance10. Note that the model
here is not for dilute solutions.
Hydrochloric Acid (HCl): Data included in Strong’s research.11
Conductivity Calibration, Verification, & USP <645>
Per pharmacopoeia standards the cell constant of the cell must be known to within 2%.12
This is typically achieved by calibrating the instrument and then verifying against a known
standard.
The first step is to choose a suitable calibration point. This is the first area that can cause
confusion as there are two seemingly contradictory guidelines13:
1. Calibrate at a nominal value of 1.409 mS/cm for “general use”
2. Choose a calibration point near the point of interest
To understand the nature of the seemingly odd 1.409 mS/cm standard, an analysis of the
NIST primary standard is required.14 Potassium chloride (KCl) is the standard solute for
conductivity standards due to its stability and ease of purification. Standard concentrations
are generated in terms of molality15, wherein 1.0, 0.1, and 0.01 m solutions are generally
used. The 0.01 m standard yields a 1.40933 mS/cm response. By adhering to the guidance in
NIST, calibration standards at 1.409 mS/cm (or 1,409 µS/cm) provide traceability.16
As noted above, the regulatory limits are in the 1.0 – 5.0 µS/cm range and the points of
interest for most life science customers are in the 0.5 – 3.0 µS/cm range. This is three orders
of magnitude lower than the 1.409 mS/cm calibration point discussed in the previous
paragraph.
Common sense prevents us from reconciling those two guidelines, unless one takes a liberal
view of “near”; most would conclude that three orders of magnitude represents a wide gap
8
Lange’s Hanbook of Chemistry, 16th Edition, “Conductance.”
Light, T.S., S. Licht, A.C. Bevilacqua, and K.R. Morash, “The Fundamental Conductivity and Resistivity of Water,”
Electrochemical and Solid-State Letters, 8 (1), E16-E19, 2005.
10
NIST Special Publication 260-142, 2004 Ed. Standard Reference Materials: Primary Standards and Standard
Reference Materials for Electrolytic Conductivity, Shreiner, R. H. and Pratt, K. W.
11
Strong, L.E., “Aqueous Hydrochloric Acid Conductance from 0 to 100 C,” J. Chem. Eng. Data, 1980, 25, pg 104106.
12
Per USP and EP. Other pharmacopoeias may have different criteria, such as CP at 5%.
13
Guidelines are suggestions and appear in myriad publications, including regulatory documents such as USP.
Guidelines are not prescriptive, but, rather, suggest generally accepted good practices. Adherence is typically not
mandatory or enforced.
14
Ibid. 3, pg 13-24.
15
Molality is defined by the number of moles of a solute divided by the mass of the solvent. In this case, the moles
of KCl divided by the mass of the water in which the KCl was dissolved.
16
Some offer standards that are 1.408 mS/cm, but this value discounts the conductivity contribution from the
solvent (water). 1.409 mS/cm is a better descriptor of the conductivity of a 0.01 m KCl in water solution, per Table
6 in the NIST document.
9
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300 00322 EN Rev. B
between two points. Rather, it is necessary to revisit the effects of creating calibration
standards near these low points of interest.
NIST specifically addresses this in §6.3 Low Conductivity Standards.17 In this section, NIST
addresses inherent variation in a 5.0 µS/cm standard produced with KCl and water. Its
solution is to create a solvent that is 30% n- propanol. This alcohol-water solution lowers the
effect of CO2 on the stability such that a ±0.1 µS/cm (2%) variability is observed
theoretically.18
However, before using a 5.0 µS/cm calibration standard, it’s important to understand the
effectof the standard’s variability on the resulting calibration curve. Whereas 5 µS/cm
standards have uncertainties in the 2 – 10% range, typically the 1.409 mS/cm have variability
in the 0.01 – 0.25% range.
Gingerella and Jacanin19 explore the real-world performance of “low-conductivity standards,”
defined as 10 µS/cm. While advances have been made in the years since this study, the
conclusions are still generally valid today. Specifically, the authors cite several sources of
variability:
 Atmospheric CO2 via the following reaction describing the dissociation of the carbon
dioxide molecule:
𝐶𝑂2 + 𝐻2 𝑂 ↔ 𝐻2 𝐶𝑂3 ↔ 𝐻 + + 𝐻𝐶𝑂3−
The presence of the proton and bicarbonate ions raises sample conductivity by as
much as 1.05 µS/cm.20






Container surface contamination (both the vessel in which the standard is packaged
and the vessel from which the measurement is made)
Sample handling
Manufacturer quality control
Container head-space
Tolerances that exceed scientific theoretical limits
Tolerances that exceed the ability of the instruments purported to measure them
Ultimately, many of these standards show the theoretical tolerances at the time of
manufacture and do not correlate to tolerances the user can expect to see when actually
measuring them. This leads to difficult-to-use and difficult-to-validate standards.
17
Ibid. 3, pg.21.
Ibid.
19
Gingerella, M. and Jacanin, J.A., Is There an Accurate Low-Conductivity Standard Solution? The International
Journal of Metrology, July-August 2000, pg 29-36.
20
Ibid.
18
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300 00322 EN Rev. B
From authors of papers, to conductivity measurement equipment manufacturers21, to
regulatory bodies22, there is overwhelming caution against using low-level standards.
With that said, and as mentioned above, there continue to be advances made in all
technological fields, including low-level conductivity standards. There are a number of
manufacturers who develop novel and oft-patented systems that purport to maintain the
integrity of low-level standards. Though not endorsed or used by GE Analytical Instruments,
Aurical Company is one such manufacturer.
The table below shows how a 1.409 mS/cm standard compares to three standards by the
Aurical standards and the theoretical NIST reference material of 5 µS/cm ± 2%.
Standard
Nominal
1409
10.0
5.0
1.0
5.0
Tolerance per
Actual Values
Reading at 1.0 mS/cm
CoA
Lower
Upper
Lower
Upper
0.25%
1405.478 1412.523
0.9975
1.0025
5%
9.5
10.5
0.9500
1.0500
10%
4.5
5.5
0.9000
1.1000
20%
0.8
1.2
0.8000
1.2000
2%
4.9
5.1
0.9800
1.0200 23,24
As is easily seen in the table, using an accurate calibration standard three orders of
magnitude above the point of interest yields a much more accurate measurement than do
the best low-conductivity standards. This may seem counterintuitive, but it illustrates two
points that govern nearly all analytical instruments:
 Calibration errors propagate to every additional measurement; the accuracy,
stability, and precision of calibration standards is critical in defining instrument
performance.
 Calibrating near the point of interest is not necessarily as important as maximizing
the calibration stability itself.
This second bullet-point must be explored a bit further, as it assumes linear behavior.
In some instruments, the linearity of the measurement technology would not support
interpolation between the origin and a point three orders of magnitude above the point of
interest. Thus, the language was chosen to provide provisions where calibrating at or near
the point of interest might be of paramount importance. The operator can quickly ascertain
whether a given instrument is linear in nature by verifying that instruments performance. It
21
E.g., Thornton (Mettler Toledo) “Therefore more accurate results are normally achieved through verification
and/or calibration using 25 or 100 μS/cm standards than could be obtained using standards with lower values.”
22
E.g., ASTM Standard Test Method D5391 – 14 (2014), Standard Test Method for Electrical Conductivity and
Resistivity of a Flowing High Purity Water Sample, section 10.4, states that “cell calibration with standard solutions
below 100 µS/cm is not recommended.”
23
The “Tolerance per CoA” is the stated variation or uncertainty on a standard’s certificate of analysis. The “Actual
Values” define the expected range of values based on the standard’s nominal value and the tolerance
specification.
24
The bottom shaded row is the theoretical NIST standard described in the literature.
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will be demonstrated below that, by employing patented technology,25 the M9 possesses
such linearity, lending validity to the conclusions made above.
Conductivity Verification & Linearity
While the above section concludes that a calibration with highly stable and accurate 1.409
mS/cm can be advantageous, this is only true if the linearity of the instrument can be
demonstrated.
For the purposes of verification, lower level standards are often sought. Verification
standards can accommodate more variability because that variability is specific to the
measurement of that a single sample. Thus, the variability does not propagate through
successive measurements the way a calibration standard’s error will.
Perhaps the most common verification standard is the 25 µS/cm HCl standard. By creating
an acidic standard, the pH is lowered and the chemical reaction below demonstrating the
dissociation of CO2 to bicarbonate and hydronium ions is affected.
𝐶𝑂2 + 𝐻2 𝑂 ↔ 𝐻2 𝐶𝑂3 ↔ 𝐻 + + 𝐻𝐶𝑂3−
pH < 4
pH > 4
This invokes Le Chatelier’s principle and shifts the equilibrium in favor of gaseous or dissolved
CO2 molecules. Without this dissociation, atmospheric CO2 no longer poses a contaminant
and the relative accuracy of the 25 µS/cm HCl standard is maintained.
Unfortunately, at lower concentrations, the acidity of the standard and the resulting pH
reduction are not enough to prevent the dissociation of CO2 and the contamination of the
standard. Thus, the reliability of low HCl standards (≤ 10 µS/cm) is no better than KCl-based
standards.
Nevertheless, the 25 µS/cm HCl standard is quite effective in demonstrating linearity of the
calibration to two orders of magnitude lower than the calibration point of 1.409 mS/cm. This
accommodates the need to show linearity and the natural conclusion is to expect that,
provided the calibration is linear for the first two order of magnitude (1,409 to 25 µS/cm), then
it should maintain this linear behavior for the final order of magnitude (25 to 1 µS/cm).
The table below shows the verification results against GE Analytical Instruments’ 25 µS/cm
verification standard, as well as three Aurical standards. These data were collected at a
customer facility in an open environment.
The Theoretical Range is defined as the specified variability of the standard itself plus the 2%
tolerance in the calibration, per USP and EP. There are no allowances in the Theoretical
Range for sources of contamination discussed above or any additional influences in the
measurement.
25
Patent US 9116099 B2 “Wide Dynamic Range Conductivity Measurement in Water”
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Theoretical Measured
Standard
Range
Value
25
24.5 - 25.5
24.62
10
9.31 - 10.71
10.72
5
4.41 - 5.61
5.45
1
0.784 - 1.53
0.92
The data clearly show that the measurement response of the M9 with a 1.409 mS/cm
calibration is quite linear through the point of interest, 1.0 µS/cm.26
Complementing the above data is a controlled study performed by GE Analytical Instruments.
Using commercially available 100 µS/cm sodium chloride (NaCl) standards with carefully
controlled serial dilutions, the following data were collected:
Non-Blank Adjusted, Non-Temperature
Corrected
Actual Measurement, µS/cm
120
100
80
60
y = 1.0911x + 0.6508
R² = 1.0000
40
20
0
0
20
40
60
80
100
120
Theoretical Standard Value, µS/cm
This shows a high degree of linearity down to 1.00 µS/cm based on a calibration point of
1.409 mS/cm. Note that the slope of this curve suggests that the data are not accurate,
showing in excess of 9% variation between theoretical and actual. This can easily be
explained by the serial dilutions and the temperature effects. The dilution water used
contributed some amount of conductivity to the measured standard. Furthermore, the
standard is certified to a reference temperature of 25 C and the temperature of
measurement was elevated.
If the data are corrected for the dilution water contribution and the nonlinear temperature
compensation for NaCl, the chart becomes more reflective of the accuracy capability of the
M9:
26
Note that response associated with the 10.0 µS/cm standard was 0.01 µS/cm out of the Theoretical Range, but
this can be explained by any number of contamination sources described above.
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300 00322 EN Rev. B
Blank Adjusted, Temperature Compensated
Actual Measurement, µS/cm
120
100
80
60
y = 1.0102x + 0.0475
R² = 1.0000
40
20
0
0
20
40
60
80
100
120
Theoretical Standard Value, µS/cm
The primary purpose of these data is to demonstrate linearity between the calibration point
and the expected point of use for ultrapure water analysis. This linearity is demonstrated in
both plots. Furthermore, the accuracy of the GE Sievers M9 Analyzer is also demonstrated
after correcting for the dilution water (blank) and the temperature.
Temperature Compensation in the GE Sievers M9
For many instruments in the commercial marketplace, the user must select and enter an
appropriate constant. These constants are sometimes provided by the manufacturer, but
can also be also be found in the literature and using online search tools. The M9 currently
does not have a user-selectable temperature compensation feature. The reference
temperature is fixed to 25 C and the temperature-compensating algorithms are nonlinear
and fixed to the following substance type:
Operating Mode
Sample Conductivity Calibration
Sample Conductivity Verification
Measurement Mode
Constant Used
KCl
HCl
NaCl
For this reason, the M9 cannot be used to verify samples with known quantities of alternative
ions. When the M9 is in normal measurement mode, it will apply a temperature
compensation algorithm appropriate for NaCl. If, for example, an HCl standard were being
used and the temperature were not 25 C, the correction algorithm applied would not yield
an accurate result.
A graphical representation of the linear temperature-compensated conductivity readings are
shown below:
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300 00322 EN Rev. B
As noted, as the actual temperature moves away from the reference temperature, the
measured value of conductivity will be quite different. Therefore, if a conductivity value is
measured and an improper constant used to compensate that value to a reference
temperature, it is easy to see how this will lead to an inaccurate compensated value.
USP <645> and Equivalent Standards
Though there are many global standards (such as USP, EP, JP, other pharmacopoeias, ASTM,
etc.), many have standardized on the methodology documented in USP <645> Water
Conductivity. Many of these standards and compendia have been harmonized, an effort to
ensure the same procedures and criteria are present in each document. While this has
helped reduce complexity for customers, some of these standards and compendia may have
slight differences between them. A focus on USP <645> follows, so be certain to check with
your local regulations before proceeding with your testing regime.
USP <645> contains three types of conductivity testing: Stage 1, Stage 2, and Stage 3.
Stage 1 is the simplest method, but contains the tightest pass/fail levels. The user need only
to measure temperature and conductivity online or in “a suitable container.” Note that the
definition of “suitable container” is left unspecified and, therefore, may be defined by the
customer.
There are no other requirements or prescribed actions for Stage 1 measurement, save that
the reported value of conductivity be the raw measurement and not a temperaturecompensated value. The pass/fail criteria are then dictated by the abridged table below:
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300 00322 EN Rev. B
(The table continues to temperatures of 100 C in the USP monograph.)
The pass/fail criteria for nominal sample temperatures are in the 1.0 – 1.4 µS/cm range,
which again underscores the importance of minimizing contamination, including
atmospheric CO2.
If the customer fails Stage 1 conductivity, he must proceed to Stage 2. Stage 2 is much more
prescriptive about the testing protocol. The sample must be ≥ 100 mL, be kept at 25 ± 1 C,
be agitated, and the conductivity measurement must be stable within 0.1 µS/cm over a five
minute period. None of these requirements or restrictions existed in any form for Stage 1.
The pass/fail limit for Stage 2 is 2.1 µS/cm. Note that this is nearly double the pass/fail limit at
25 C for Stage 1. The customer must devote quite a bit more time and effort to measure
with Stage 2, but there is a wider acceptance criterion.
If Stage 2 conductivity fails, the customer adds KCl to the sample, measures pH, and
compares conductivity to a new pH vs. conductivity table, per Stage 3. Pass/fail criteria are
as high as 4.7 µS/cm.
Note that while conductivity calibration standards are specified (and discussed below),
temperature must only be verified and, as a limit test, there is no required operational and
performance qualifications required.
Mechanics of Measurement in the M9
The measurement cell in the M9 comprises gold electrodes mounted in a quartz cell with a
thermistor at the exit end of the cell. There are a number of proprietary electronic algorithms
and methodologies applied to the measurement module that yield the linear behavior
characterized above.
The conductivity measurement is performed upstream of the TOC measurement and prior to
the addition of any reagents for TOC measurement; the conductivity cell is the first
component in the sample flow path.
During the normal mode, a measurement cycle lasts two minutes. For the first 30 seconds, a
conductivity measurement is made ten times per second; thus, 300 measurements are
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300 00322 EN Rev. B
made.27 The reported value is the average, or mean, of these data. After careful analysis of
many data sets, the mean was selected as the best indicator of the central tendency.
Suitable Sampling Vessels
The primary value proposition behind the sample conductivity option is the ability measure
both TOC and conductivity simultaneously. This creates a unique challenge in that TOC
needs to be measured from a glass container, but glass containers typically leach ions into
water and are unsuitable for conductivity measurement.
To overcome this challenge, GE Analytical Instruments has developed Dual Use Conductivity
and TOC (DUCT) Vials. These vials have a proprietary coating that seals the glass and
protects the integrity of the water samples with respect to both TOC and conductivity. 28
When using the M9 for sample conductivity, the DUCT Vials must be used.
Summary and Conclusions
Conductivity is a complex measurement that is dependent on a number of variables. Though
its relationship with temperature is understood, it is a unique relationship for each ionic
species. For compendial reporting purposes, temperature-compensated conductivity is
either prohibited or effectively eliminated by controlling the samples to the reference
temperature of 25°C.
For calibration and verification, the standards contain a known, purified substance that can
be adequately modeled to provide accurate and precise results. However, it is imperative
that the proper constants be used when modeling these substances.
The GE Sievers M9 TOC Analyzer does not yet allow the user to enter his own constant and
instead relies on fixed constants that vary per operating mode. Users must either conform to
the proper ionic species that match the constants, control their samples to the reference
temperature, or conduct manual calculations based on the given equation and the
appropriate constants.
27
In the Turbo mode, the measurements are made over a three second period; 30 measurements are taken, but
the remainder of the methodology is unchanged.
28
See GE AI application note on Dual Use Conductivity and TOC Vials for more information.
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