Investigation of electrical conductivity of different water liquids and electrolyte solutions

Abstract

In this study one of the most important physical parameters identifying conductance of liquid solutions is investi-gated. Electrical conductivities of pure, distilled, municipal, industrial and river water liquids along with those of different electrolyte solutions are computed at room temperature (25 °C). Obtained results for ultra pure, pure dis-tilled, municipal, industrial, well and river water liquids with different impurities are compared at such a given tem-perature. A similar study is performed for different electrolytes and related results. In addition electrical conductivi-ty of water liquid is compared with that of a typical NaCl electrolyte solution and interesting results for differences in conductance values are discussed.

Full text

Iranian Physical Journal, 3-2, 24-28 (2009)
Plasma Physics Research Center, Science & Research Campus, Islamic Azad University
Investigation of electrical conductivity of different water liquids and
electrolyte solutions
H. Golnabi1,*, M. R. Matloob1, M. Bahar2, M. Sharifian3
1Institute of Water and Energy, Sharif University of Technology, Tehran, Iran
2Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran.
3Physics Department, Tehran North Branch, Islamic Azad University, Tehran, Iran
Received: 17 July 2009/Accepted: 10 August 2009/ Published: 20 September 2009
Abstract
In this study one of the most important physical parameters identifying conductance of liquid solutions is investi-
gated. Electrical conductivities of pure, distilled, municipal, industrial and river water liquids along with those of
different electrolyte solutions are computed at room temperature (25 °C). Obtained results for ultra pure, pure dis-
tilled, municipal, industrial, well and river water liquids with different impurities are compared at such a given tem-
perature. A similar study is performed for different electrolytes and related results. In addition electrical conductivi-
ty of water liquid is compared with that of a typical NaCl electrolyte solution and interesting results for differences
in conductance values are discussed.
PACs: 61.20.Gy; 61.20.Ne; 61.20.Qg; 72.15.Cz; 72.15.Eb
Keywords: Water, conductivity, impurity, electrolyte
1. Introduction
Water is one of the most important matters in the
nature and widely used for different purposes in a va-
riety of applications. One goal has been to find differ-
ent procedures to obtain high quality ultra pure water
liquids for medical or other sensitive applications.
Some researches have focused on the procedures and
mechanism in order to refine the water by ionization,
distillation, or other processes in order to obtain ultra
pure water liquid. A variety of methods has been de-
veloped to measure and test the refined products in
order to specify the purity of the produced refined
water. For example the electrical conductivity of the
solution has been one of the important physical quan-
tities in this respect and many probes and devices such
as conductive sensors have been devised [1-3]. Such
probes are used to measure conductivity or conduc-
tance of solutions at the given concentration and tem-
perature. For many applications water solution is
grouped into ultra pure, pure, and regular water de-
pending on the percentage of impurities [4-7].
Water substance can be in form of vapor, liquid,
or solid phase. Pure water is a clear, colorless, and
odorless liquid that is chemically made up one oxygen
and two hydrogen atoms. This powerful substance is a
good medium for many reactions, which is used as a
universal solvent. Physical and chemical properties of
water results from strong attraction that hydrogen
atoms have for each other in water molecules. Al-
though pure water is a poor conductor of electricity,
but natural impurities found in water can transform it
into a relatively good conductor. Salts and other con-
taminates in water can dissociate into components
called ions. In most cases, ions in water are considered
as impurities especially when referring to pure water,
while in other aqueous solutions such as hydrochloric
acid or sodium hydroxide, the ions define the actual
chemical deposition.
2. Theory of Electrical Conductance
Generally water molecules are in continuous mo-
tion, even at low temperatures and when two water
molecules collide, a hydrogen ion is transferred from
one molecule to the other. The other molecule that
losses the hydrogen ion becomes negatively charged
hydroxide ion. The molecule that gains the hydrogen
ion becomes a positively charged hydrogen ion and
this process is commonly called the self-ionization of
water. In fact at room temperature (25 °C ), each con-
centration of hydrogen ions and hydroxide ions is only
of the order of 1×10-7M, and as a result this dissocia-
tion allows a minute electrical current to flow. The
current flow is in the range of conductivity of 0.05
μS/cm at room temperature. It is important to note that
the amount of (H)+ and (OH)- ions are approximately
equal and this solution is described as a neutral solu-
tion.
In other aqueous solutions, the relative concentra-
tions of these ions are unequal and one ion is in-
creased by one order of magnitude while the other one
shows some decrease, but the relationship is constant
and the ion product is always constant given by Kw,
*Corresponding author: Hossein Golnabi;
E-mail: golnabi@sharif.edu
Tel: (+98) 21 66164652
Fax: (+98) 21 66005118
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Investigation of Electrical … Iranian Physical Journal, 3-2 (2009)
25
which is called the ion-product constant for water.
Electrical conductivity of solutions has been studied
for several reasons such as studying the process of
salvation, association and transparent properties of
ions in different solvent media. Such processes depend
on the charge, radius, and hydrate numbers of ions and
the nature of solvent. Electrolytic conductivity is a
measure of ability of a solution to conduct an electric
current and is defied by the specific conductance or
term conductibility. Conductivity is the inverse of
electrical resistivity, which defined as the measure of
the ability of a solution to resist an electric current
flow.
Water is a polar solvent with an uneven distribu-
tion of electron, and the application of electric field
causes one portion of the molecule to be somewhat
positive and another part negative (polarization ef-
fect). In an external DC electric field, the dissolved
electrolyte substances are free to move and positive
charged particles move towards negative electrode
while negative charged particles migrate toward the
positive electrode. The migration of the charged par-
ticles causes the electric current flow in liquid. Such
DC polarization can be eliminated by using AC vol-
tage at 60 Hz or higher frequencies and in practice by
increasing the cross sectional area of the electrodes.
The mechanism of electrical conduction through a
liquid is different in comparison with a solid. In solid,
when a potential is applied to a solid conductor, the
flow of current is instantaneous, and is virtually pro-
portional to the applied potential. In addition, differ-
ent types of materials conduct electrical charges with
different efficiencies. In metals, there are free elec-
trons, which are available for conduction even at a
very low temperature. One major difference of a metal
with semiconductor and isolator materials is that met-
al resistance increases as the metal heated because of
the decrease in electron mobility. Conversely, the re-
sistance of semiconductors and insulators decreases
with increasing temperature because the number of
charge carries increases. Therefore, in semiconductor
and in particular in insulators, more activation energy
is needed to excite electrons to be available to conduct
a charge.
The conductivity of a solution relates to the total
dissolved solid (TDS) and amount of the suspended
solids (SS) or insolvable solid in a water sample.
Total dissolved solid includes solid particulates such
as ions, inorganic substances, salts, and metals. Total
solid (TS) is defined as the sum of TDS and SS. In
laboratory analysis measurement of these parameters
are made by filtering and weighing to determine SS,
then drying and weighing to determine TDS. In analy-
sis of water the conductivity measurements are classi-
fied for the Ultra-pure, high-purity and pure water
samples, which show accordingly an increase in the
conductivity value (0.053 to 10 μS/cm). There are
some look up tables that can be used to convert be-
tween conductivity, resistivity and TDS in pure and
ultra-pure water.
The electrical conductivity of a conductor is given
by the relation
 , (1)
where n is the density of charge carrier, q is the spe-
cies charge , and μ is the charge particle mobility de-
fined by the ratio of the applied electric field to the
charge carrier velocity. The electrical conductivity of
a semiconductor crystal is given by
 , (2)
where n and p are the concentration of electrons and
holes, respectively. μ as defined is the mobility for
the electron and hole, accordingly.
For pure water ionization the possible colliding
reaction is
H2O+ H2O - -------H3O++OH- (6)
and the K factor is defined by the ratio of species con-
centrations

 , 7
where one can write
, (8)
and the term in the left hand side of Eq.(8) is always
constant defined by Kw.
 , (9)
which is in most practical cases a constant. The con-
ductance of electricity is a usual way to measure the
mobility of ions and conductivity meters are used for
this purpose. Conductivity is measured in unit of
(S/m) and the molar conductivity is a common expres-
sion for solutions, which is the conductivity per unit of
concentration (Sm2/mol). Conductivity meters meas-
ure and display conductivity or resistivity of a sample
solution at a given temperature. By using a standard
solution (KCl) the constant K (S/cm) for a given cell
probe is obtained.
By using the equality of the electric force and the
friction force on ions for finding the velocity of ions
for the electrolyte a general formula for the conductiv-
ity is given by [8,9]

6 

 , 10
where Ci is the fractional concentration. Here e is the
electric charge, r is the ionic radius, Na is the Avoga-
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Golnabi et al. Iranian Physical Journal 3-2 (2009)
26
dro number, Z number of involved ions and ρ is the
ion viscosity. The electrical conductivity of water
electrolyte in concentration equilibrium condition can
be obtained by the multiplication of the K
w and the
possibility factor for the ion generation in the ion mi-
gration process:
expΔ
 , 11
which can be written as

6

expΔ
2expΔ
2 , 12
where the equality of
ΔΔΔ, (13)
is plugged into Eq. 11 for G, which defines the Gibbs
free energy (kJ/mol) . Here H is the enthalpy, s entro-
py, T temperature, and R the universal gas constant.
For computations the radius used in Eq. 12 is not only
the radius of the ion but also shows the dimension of
the ion itself plus the effective radius of the polar
solvent that surrounds that particular ion. Such an ef-
fective radius is called hydrodynamic radius of ions.
By using the hydrodynamic radius of ions in (12) the
conductivity becomes:

6 13
1
expΔ
2expΔ
2,
(14)
3. Computation Results
Based on the developed theoretical formulation
different programs written in visual basics are ex-
ecuted in macro option of the Excel program. The
written program code is user friendly and can be run
easily on a PC using the usual Microsoft window op-
erating system compatible with the office program.
Based on the developed algorithms different programs
are written that easily outputs the conductance values
according to the given input parameters. Four different
water samples are considered for the first study and
the computed results for the electrical conductance are
reported. The input parameters for water samples in
written programs are the impurity; total dissolved sol-
id, density, viscosity and the temperature. For electro-
lytes in the written programs the input values are the
concentration and the temperature values.
Fig. 1 shows he computed results for different wa-
ter liquids including the pure, distilled, municipal,
industrial, rivers and well waters. Samples indicated as
PW (Pure Water), DW (Distilled Water, 5 ppm), IW
(Industrial Water,100 ppm ) RW (River Water,100
ppm) and MW (Municipal water,100 ppm). As can be
seen the electrical conductance ranging from a low
value of 0.0539 μS/cm (pure water) to 200.0 μS/cm
for the municipal water resource. The value of the
electrical conductance is given for the room tempera-
ture of 25° C for all samples.
Fig. 1. Computed electrical conductivities for different
water liquids. Samples indicated as PW (Pure Water),
DW (Distilled Water, 5 ppm), IW (Industrial Water, 100
ppm), RW (River Water, 100 ppm) and MW(Municipal
Water, 100 ppm).
Fig. 2. Variation of electrical conductivity of distilled
water as a function of impurity. Impurities for samples
are DW1 = 0.03, DW2 = 1, DW3 = 5 and DW4 = 10 ppm.
In the next study variations of electrical conductiv-
ity in respect to the impurity concentration for the
distilled water are investigated. Fig. 2. shows the var-
iation of electrical conductivity of distilled water as a
function of impurity. Impurity concentration is varied
from 0.03 ppm to 10 ppm for the distilled water. Sam-
ples indicated as DW1 = 0.03 ppm, DW2 = 1 ppm,
DW3 = 5 ppm and DW4 = 10 ppm are considered for
this computation. As can be seen the electrical con-
ductivity ranging from a low value of 0.0639 μS/cm
(DW1) to 19.99 μS/cm for the high impurity 10 ppm
Computed Electrical Conductivities for Different
Water Liquids (T= 25 °C)
200
0.05 10
111
150
0
50
100
150
200
250
PW
DW
IW
RW
MW
Water Type
Electrical Conductivity (µs/cm
)
Electrical Conductivity of Distilled Water for
Different Impurities (T= 25 °C)
19.99
0.063 2.00
10.00
0
5
10
15
20
25
DW1 DW2 DW3 DW4
Distilled Water
Electrical Conductivity (µs/cm
)
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Investigation of Electrical … Iranian Physical Journal, 3-2 (2009)
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municipal water resources(DW4). The values of the
electrical conductivities are given for the room tem-
perature of 25° C for all samples. As can be seen in
Fig. 2, electrical conductivity shows increase by in-
creasing the amount of the foreign impurity at the giv-
en temperature.
In Fig.3 variation of electrical conductivity of mu-
nicipal water as a function of impurity is shown. Here
typical concentration is increased from 100 ppm to
500 ppm for the municipal water samples. As can be
seen in Fig. 3, electrical conductivity indicated by
numbers 1, 2, 3, 4 and 5 for different samples. As
shown in Fig.3, electrical conductivity shows an in-
crease by increasing the amount of the foreign impuri-
ty. For example for the same room temperature of (25
°C), the electrical conductivity for 100 ppm is about
200 μS/cm while it is increased to about 1000 μS/cm
for the impurity concentration of 500 ppm.
Fig. 3. Variation of electrical conductivity of municipal
water as a function of impurity. Five samples indicated
by numbers 1,2,3,4, and 5 show impurities of 100, 200,
300, 400, and 500 ppm, respectively.
Fig. 4. Computed electrical conductivities for different
electrolyte solutions.
In the second study electrical conductivity for se-
venteen different electrolyte solutions are computed
and the results are discussed here. Results for the elec-
trical conductance at room temperature (25 °C, typical
concentration of 0.025 Mol/Lit) are presented in Fig.
4. As can be seen the electrical conductivity ranging
from a low value of 2807.57 μS/cm (for NaCl ) to the
highest value of 35227.12 μS/cm for the BaOH solu-
tion. All the values of the electrical conductivity are
given for the room temperature and a molar concentra-
tion of 0.025 Mol/Lit.
Fig. 5 shows the variation of electrical conductivi-
ty of H2SO4 electrolyte as a function of molar concen-
tration (Mol./Lit). In this study concentration is in-
creased from 0.025 Mol/Lit to 1 Mol/Lit for the
H2SO4 electrolyte sample. As can be seen in Fig. 5,
electrical conductivity shows an increase by increas-
ing the amount of the electrolyte concentration. For
example for the same room temperature of (25 °C),
the electrical conductivity for 0.025 Mol/Lit is about
20464.24 μS/cm, for 0.5 Mol/Lit is about 338747.68
μS/cm while it is increased to about 602230.85 μS/cm
for the electrolyte concentration of 1 Mol/Lit.
Fig. 5. Variation of electrical conductivity of H2SO4 as a
function of molar concentration.
Fig. 6. Variation of electrical conductivity of NaCl as a
function of molar concentration.
In Fig. 6 variation of electrical conductivity of
NaCl electrolyte as a function of molar concentration
(Mol./Lit) is presented. In this study concentration is
increased from 0.025 Mol/Lit to 1 Mol/Lit for NaCl
electrolyte. Similar to the previous case electrolyte
concentration is varied and as can be seen in Fig. 6,
electrical conductivity shows a notable increase by
increasing the concentration of the electrolyte. For
Electrical Conductivity of Municipal Water,
Different Impurities (T=25 °C)
0
200
400
600
800
1000
1200
1
2
3
4
5
Municipal Water Type
Electrical Conductivity (µs/cm
)
Electrical Conductivities for Different Electrolytes
(T=25°C, C=0.025 Mol/Lit)
0
5000
10000
15000
20000
25000
30000
35000
40000
BaOH
BaSO4
H2SO4
H2CO3
LiOHHBrHCl
HNO3
HClO4
KOH
NH4OH
ZnSO4
Na2SO4
NaOHKBrKCl
NaCl
Electrolyte Type
Electrical Conductivity (µs/cm
)
Electrical Conductivity of H2SO4 for Different Molar
Concentrations (T= 25 °C)
0.0E+00
1.0E+05
2.0E+05
3.0E+05
4.0E+05
5.0E+05
6.0E+05
7.0E+05
0.025
0.050.1
0.150.2
0.250.3
0.350.4
0.450.5
0.550.6
0.650.7
0.750.8
0.850.9
0.95 1
Concentratio n (Mol/Lit)
Electrical Conductivity (µs/cm
)
Electr ical Condu ctivity of NaCl for Different Con centration s
(T= 25°C)
0.0E+00
5.0E+03
1.0E+04
1.5E+04
2.0E+04
2.5E+04
3.0E+04
3.5E+04
4.0E+04
0.025
0.050.1
0.150.2
0.250.3
0.350.4
0.450.5
0.550.6
0.650.7
0.750.8
0.850.9
0.95 1
Conc entration (Mol/L it)
Electrical Conductivity (µs/cm
)
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Golnabi et al. Iranian Physical Journal 3-2 (2009)
28
example, at the same room temperature of (25 °C), the
electrical conductivity for 0.025 Mol/Lit is about
2807.57 μS/cm, for 0.5 Mol/Lit is about 31677.92
μS/cm while it is increased to about 37242.09 μS/cm
for the electrolyte concentration of 1 Mol/Lit. Com-
paring the results for the Nacl and that of H2SO4 elec-
trolyte it is noted that at the same temperature and
concentration, H2SO4 electrolyte has a much higher
electrical conductance.
In Fig. 7 comparison of the electrical conductivity
of water liquid (distilled and municipal) and a typical
electrolyte solution (NaCl,0.025 Mol/Lit) is given at
room temperature (25 °C). As can be seen the NaCl
electrolyte solution has a conductance value of
2807.57 μS/cm much higher than that of typical dis-
tilled water (19.99 μS/cm at 10 ppm) and municipal
water (1000 μS/cm at 500 ppm).
Fig. 7. Comparison of the electrical conductivity of water
and NaCl electrolyte (0.025 Mol/Lit) at room tempera-
ture (25 °C). Distilled water with 10 ppm and municipal
water with 500 ppm impurities considered.
The physical reason for such a high conductance
value can be described as following. In ionic com-
pound, entire ion may diffuse to conduct electricity,
though these ions may have very low mobility. Ap-
pling a potential to a liquid conductor causes current
to flow through solution by dissolved particles (ions)
that have electrical charges. Usually dissolved ions
move slower than electrons, depending on their geo-
metry, potential, and the temperature of solution. Gen-
erally smaller ions move through a solution more ra-
pidly than larger ones. As discussed, in water the hy-
drogen ion (H+) and the hydroxyl ion (OH-) are ex-
tremely mobile due to their geometry and size of ions
relative to each other in comparison with the Na+ and
Cl- ions in NaCl aqueous solutions. As a result, NaCl
shows a much higher conductance value in compari-
son with that of water liquid. Same argument about
higher value of electrical conductivity in comparison
with the water liquid can be given for other electro-
lytes.
As described there is a relationship between the
conductivity and concentration of electrolytes. Differ-
ent solutions with different conductivities do not al-
ways show a direct relationship proportional to con-
centration of salts or solids in solution. In dilute solu-
tions, an increase in concentration causes a linear in-
crease in conductivity provided that there are no inte-
ractions between the solution and the dissolved elec-
trolyte. When these conditions are met, the dissolved
electrolyte is said to be completely dissociated. An
example is sodium chloride. Thus, investigating con-
centration versus conductivity provides an important
physical property of solution. As shown in Fig. 5, sul-
furic acid (H2SO4) can be completely dissociated and
its conductivity is directly proportional to its concen-
tration. For this solution the H2SO4 dissociates to form
(H)+ and (HSO4)- ions and for the given low concen-
tration as shown in Fig. 5, a gradual increase of elec-
trical conductivity with the concentration is noticed.
As can be seen in Fig. 6, a similar pattern is noticed
for the NaCl electrolyte.
4. Conclusions
A theoretical model for computation of electrical
conductivity of water and electrolytes are reported in
this study. Based on the developed algorithms differ-
ent programs are written that easily outputs the con-
ductivity values according to the given input parame-
ters. The written programs offer potentials for varia-
tion study of such a quantity as a function of different
parameters. Parameters such as substance temperature
and impurity play important roles in the determination
of the electrical conductivity and results for the con-
centration variation for given substances are given in
this study.
Acknowledgments
This work was supported in part by the Sharif
University of Technology research program. The au-
thors gratefully acknowledge the grant devoted to this
research.
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Electrical Conductivity of Water Samples
and NaCl Electrolyt (T= 25 °C)
2807.6
19.9
1000.0
0
500
1000
1500
2000
2500
3000
DW MW NaCl
Electrical Conductivity (µs/cm
)
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