CASE 0:20-cv-00358-ECT-HB Doc. 80-7 Filed 06/10/21 Page 1 of 6
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`CASE 0:20-cv-00358-ECT-HB Doc. 80-7 Filed 06/10/21 Page 1 of 6
`
`Exhibit 7
`Exhibit 7
`
`
`
`Page 1
`
`OWTEx. 2138
`Tennant Company v. OWT
`IPR2021-00625
`
`

`

`CASE 0:20-cv-00358-ECT-HB Doc. 80-7 Filed 06/10/21 Page 2 of 6
`
`Archive of SID
`
`Iranian Physical Journal, 3-2, 24-28 (2009)
`
`
`
`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-
`
`*Corresponding author: Hossein Golnabi;
` E-mail: golnabi@sharif.edu
`Tel: (+98) 21 66164652
`Fax: (+98) 21 66005118
`
`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,
`
`Plasma Physics Research Center, Science & Research Campus, Islamic Azad University
`
`www.SID.ir
`
`OWT0018617
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`

`

`CASE 0:20-cv-00358-ECT-HB Doc. 80-7 Filed 06/10/21 Page 3 of 6
`
`ultra-pure water.
`The electrical conductivity of a conductor is given
`by the relation
`
`
` (cid:2018)(cid:3404)(cid:1866)(cid:1869)(cid:1873) ,
`
`
`
`
`
`
`
` (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
`
`
` (cid:2018)(cid:3404)(cid:4666)(cid:1866)(cid:1857)(cid:2020)(cid:3032)(cid:3397)(cid:1868)(cid:1857)(cid:2020)(cid:3035)(cid:4667) ,
`
`
`
` (2)
`
`Archive of SID
`Investigation of Electrical … Iranian Physical Journal, 3-2 (2009)
`
`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
`
`
`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-
`
`and the K factor is defined by the ratio of species con-
`centrations
`
` (6)
`
` (cid:1837)(cid:3404)(cid:4670)(cid:1834)(cid:2871)(cid:1841)(cid:2878)(cid:4667)(cid:4670)(cid:1841)(cid:1834)(cid:2879)(cid:4671)
`(cid:4670)(cid:1834)(cid:2870)(cid:1841)(cid:4671)(cid:4670)(cid:1834)(cid:2870)(cid:1841)(cid:4671) , (cid:4666)7(cid:4667)
` (cid:1837)(cid:4670)(cid:1834)(cid:2870)(cid:1841)(cid:4671)(cid:2870)(cid:3404)(cid:4670)(cid:1834)(cid:2871)(cid:1841)(cid:2878)(cid:4671)(cid:4670)(cid:1841)(cid:1834)(cid:2879)(cid:4671),
` (cid:1837)(cid:3050)(cid:3404)(cid:4670)(cid:1834)(cid:2871)(cid:1841)(cid:2879)(cid:4671)(cid:4670)(cid:1841)(cid:1834)(cid:2879)(cid:4671) ,
`
`
`where one can write
`
`
`and the term in the left hand side of Eq.(8) is always
`constant defined by Kw.
`
` (8)
`
`
`
` (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]
`
` (cid:2018)(cid:3404)(cid:1857)(cid:2870)(cid:1840)(cid:3002)6(cid:2024)(cid:2025) (cid:3533)(cid:4666)(cid:1852)(cid:3036)(cid:1829)(cid:3036)(cid:4667)(cid:1870)(cid:3036)
`(cid:3036)
`
` , (cid:4666)10(cid:4667)
`
`
`where Ci is the fractional concentration. Here e is the
`electric charge, r is the ionic radius, Na is the Avoga-
`
`
`
`25
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`CASE 0:20-cv-00358-ECT-HB Doc. 80-7 Filed 06/10/21 Page 4 of 6
`
`Archive of SID
`Golnabi et al. Iranian Physical Journal 3-2 (2009)
`
`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 Kw and the
`possibility factor for the ion generation in the ion mi-
`gration process:
`
` (cid:2018)(cid:3404)(cid:1837)(cid:3050)exp(cid:3436)(cid:3398)Δ(cid:1833)(cid:1844)(cid:1846)(cid:3440), (cid:4666)11(cid:4667)
` (cid:2018)(cid:3404)(cid:1857)(cid:2870)(cid:1840)(cid:3002)6(cid:2024)(cid:2025)(cid:3533)(cid:1852)(cid:3036)(cid:1870)(cid:3036)
`exp(cid:3436)(cid:3398)Δ(cid:1834)2(cid:1844)(cid:1846)(cid:3440)exp(cid:3436)Δ(cid:1845)2(cid:1844)(cid:3440), (cid:4666)12(cid:4667)
`(cid:3036)
` Δ(cid:1833)(cid:3404)Δ(cid:1834)(cid:3398)(cid:1846)Δ(cid:1871), (13)
`
`
`which can be written as
`
`
`where the equality of
`
`
`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:
`
`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.
`
`
`Computed Electrical Conductivities for Different
`Water Liquids (T= 25 °C)
`
`200
`
`150
`
`111
`
`10
`
`0.05
`
`250
`
`200
`
`150
`
`100
`
`50
`
`0
`
`Electrical Conductivity (µs/cm)
`
`P W
`
`D W
`
`R W
`
`M W
`
`IW
`Water Type
`
`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).
`
`
`
`
`Electrical Conductivity of Distilled Water for
`Different Impurities (T= 25 °C)
`
`19.99
`
`10.00
`
`2.00
`
`0.063
`
`25
`
`20
`
`15
`
`10
`
`05
`
`Electrical Conductivity (µs/cm)
`
`DW1
`
`DW4
`
`DW3
`DW2
`Distilled Water
`
`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
`
`(cid:3440)exp(cid:4678)(cid:3398)Δ(cid:1834)2(cid:1844)(cid:1846)(cid:4679)exp(cid:4666)Δ(cid:1871)2(cid:1844)(cid:4667),
`
`
`
`
`
` (14)
`
` (cid:2018)(cid:3404)(cid:1857)(cid:2870)(cid:1840)(cid:3002)6(cid:2024)(cid:2025) (cid:3436)1(cid:1870)(cid:1834)3(cid:1841)(cid:3397)
`(cid:3415)
`
`(cid:3397)1(cid:1870)(cid:1841)(cid:1834)(cid:3398)
`(cid:3415)
`
`
`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
`
`26
`
`
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`

`CASE 0:20-cv-00358-ECT-HB Doc. 80-7 Filed 06/10/21 Page 5 of 6
`
`Archive of SID
`Investigation of Electrical … Iranian Physical Journal, 3-2 (2009)
`
`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.
`
`
`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.
`
`
`Electrical Conductivity of Municipal Water,
`Different Impurities (T=25 °C)
`
`1200
`
`Electrical Conductivity (µs/cm)
`
`1000
`
`800
`
`600
`
`400
`
`200
`
`0
`
`5
`
`1
`
`2
`
`3
`4
`Municipal Water Type
`
`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.
`
`
`Electrical Conductivities for Different Electrolytes
`(T=25°C, C=0.025 Mol/Lit)
`
`40000
`
`35000
`
`30000
`
`25000
`
`20000
`
`15000
`
`10000
`
`5000
`
`Electrical Conductivity (µs/cm)
`
`0
`B a O H
`
`B a S O 4
`
`H 2S O 4
`H 2 C O 3
`
`LiO H
`
`H Br
`
`H Cl
`
`N a O H
`
`K Br K Cl
`
`N a Cl
`
`
`
`Zn S O 4
`H ClO 4
`H N O 3
`N a2S O 4
`N H4 O H
`K O H
`Electrolyte Type
`Fig. 4. Computed electrical conductivities for different
`electrolyte solutions.
`
`
` Electrical Conductivity of H2SO4 for Different Molar
`Concentrations (T= 25 °C)
`
`7.0E+05
`
`6.0E+05
`
`5.0E+05
`
`4.0E+05
`
`3.0E+05
`
`2.0E+05
`
`1.0E+05
`
`0.0E+00
`
`Electrical Conductivity (µs/cm)
`
`0.025
`
`0.05 0.1
`
`0.15 0.2
`
`0.25 0.3
`
`0.55 0.6
`0.65 0.7
`0.45 0.5
`0.35 0.4
`Concentration (Mol/Lit)
`
`Fig. 5. Variation of electrical conductivity of H2SO4 as a
`function of molar concentration.
`
`
`0.75 0.8
`
`0.85 0.9
`
`0.95
`
`1
`
`Electrical Conductivity of NaCl for Different Concentrations
`(T= 25°C)
`
`4.0E+04
`
`3.5E+04
`
`3.0E+04
`
`2.5E+04
`
`2.0E+04
`
`1.5E+04
`
`1.0E+04
`
`5.0E+03
`
`Electrical Conductivity (µs/cm)
`
`0.0E+00
`0.025
`
`0.05 0.1
`
`0.15 0.2
`
`0.25 0.3
`
`0.75 0.8
`
`0.85 0.9
`
`0.95
`
`1
`
`0.45 0.5
`0.35 0.4
`0.55 0.6
`0.65 0.7
`
`Concentration (Mol/Lit)
`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
`
`In the second study electrical conductivity for se-
`venteen different electrolyte solutions are computed
`and the results are discussed here. Results for the elec-
`
`
`
`27
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`

`CASE 0:20-cv-00358-ECT-HB Doc. 80-7 Filed 06/10/21 Page 6 of 6
`
`Archive of SID
`Golnabi et al. Iranian Physical Journal 3-2 (2009)
`
`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).
`
`
`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.
`
`References
`
`[1] H. Golnabi, P. Azimi, J. of Applied Sciences, 8, 1699 (2008).
`[2] H. Golnabi, P. Azimi, Modern Phys. Lett. B 22, 595 (2008).
`[3] C. N. Strizzolo, J. Cinverti, IEEE Trans, On Instrumentation
`and Measurement, 42, 726 (1993).
`S. M. Huang, R. G. Green, A. B. Plaskowski, M. S. Beck, J.
`Phys. E: Sci. Instrum. 21, 539 (1988).
`E. D. Tsamis, J. N. Avaritsiotis, Sens. Actuators A 118, 202
`(2005).
`T. S. Light, S. Licht, A. C. Bevilacqua, K. R. Morash, Electro-
`chem. Solid-State Lett. 8, E16 (2005).
`[7] R. C. Weast, Handbook of Chemistry and Physics, 60 th. Ed.,
`CRC Press.1981. p. E-61.
`P. W. Atkins, Physical Chemistry, 6 th. Ed., Oxford Universi-
`ty Press. (2001).
`E. E. Washburn, International Critical Tables of Numerical
`data, Physics, Chemistry and Technology, VI, Mc Graw- Hill,
`New York, (1929).
`
`[4]
`
`[5]
`
`[6]
`
`[8]
`
`[9]
`
`
`
`
` Electrical Conductivity of Water Samples
`and NaCl Electrolyt (T= 25 °C)
`
`2807.6
`
`1000.0
`
`19.9
`
`3000
`
`2500
`
`2000
`
`1500
`
`1000
`
`500
`
`0
`
`Electrical Conductivity (µs/cm)
`
`DW
`MW
`NaCl
`
`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-
`
`28
`
`
`
`
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