Journal of Chemical Reviews, 2020, Volume 2, Issue 3, Pages 182-188 Short Review Article Estimation of the Diffusion Coefficient and Hydrodynamic Radius (Stokes Radius) for Inorganic Ions in Solution Depending on Molar Conductivity as Electro-Analytical Technique-A Review Muhammed J. Kadhim *, Maher Ibraheem Gamaj * Department of Power Mechanical Techniques, Institute of Technology-Baghdad, Middle Technical University, Baghdad, Iraq Receive Date: 18 January 2020, Revise Date: 04 March 2020, Accept Date: 07 April 2020 Abstract: Diffusion coefficient (D) and radiuses of inorganic charge ions (R) in different environments is of importance in scientific fields, explaining certain features of ions. D values were obtained using the Einstein- Smoluchowski equation depending on limiting molar conductivity (λo) of inorganic charge ions. Inorganic ions have D values at the range of 1−3×10−9 m2.s-1, except hydroxyl and hydrogen ion (5.2×10−9 and 9.1×10−9 m2.s-1, respectively). The hydrodynamic radius R for diffusing ions was calculated using the Stokes–Einstein equation based on D values. Inorganic ions have R, values at the range of 1−3×10−10 m, except hydroxyl and hydrogen ion (R=0.47×10−10 and 0.27×10−10 m, respectively). DOI: 10.33945/SAMI/JCR.2020.3.5 Keywords: Diffusion coefficient; Hydrated radius; Molar conductance; Movement of ions Graphical Abstract: Graphical abstract illustration the conductance of ions (A), and the diffusion of ions (B), in solution. Biography: Muhammed J. Kadhim Assistant lecturer obtained B.Sc. in chemistry in 1997 and M.Sc. in 2001 from Chemistry Department, Science College, Baghdad University, Iraq. Currently Muhammed J. Kadhim serves as teaching remember in Power Mechanical Techniques, Institute of Technology, Baghdad, Middle Technical University. Muhammed J. Kadhim has numerous scientific searches published and acceptance to publish in Iraqi Journal of science and IOP Conference Series Materials Science and Engineering. Maher Ibraheem Gamaj Lecturer obtained B.Sc. in an electric engineer in 1983 and M.Sc. in 1985 from an electric engineer department, an engineer College, Belgrade University, Serbia. Currently Maher Ibraheem Gamaj serves as teaching remember in Power Mechanical Techniques, Institute of Technology, Baghdad, Middle Technical University. Maher Ibraheem Gamaj has numerous scientific searches published in Iraqi and word scientific researches journals. *Corresponding authors: M. J. Kadhim & M. I. Gamaj, Email: [email protected], [email protected] page 182 of 188 Journal of Chemical Reviews Short Review 1. Introduction the hydrated radius by Einstein-Smoluchowski Diffusion is the motion result of atoms or molecules equation and Stokes–Einstein equation respectively from a higher concentration area (chemical potential for inorganic charge ions in water solution depending is higher) to a lower concentration area (chemical on molar conductivity . potential is lower). In chemical potential, diffusion is 2. Electrical Mobility and Conductivity a gradient driven by diffusing atoms, molecules or Electrical mobility is the capability of charged ions. At the unit concentration gradient of materials in particles to motion through an environment relative to a mixture, the diffusion coefficient D, provides a an electric field that is pulling the charged ions. The number of moles of a given ions, atoms or molecules split-up of ions resulting to their mobility in (gas which passes through unit area per unit time. phase) is termed to ion mobility spectrometry, in Conductance and diffusion are including motion of (liquid phase) it is termed to electrophoresis. When a ions, so a joining between them is present [1]. charged species in a liquid or gas is acted upon Conductance and diffusion can be attributed to uniform electric field, it will be speeded until it velocity property at infinite dilution, because, the reaches a constant drift velocity according to Ohm's interionic forces are disappear, which repels law formula that can be explained in terms of drift movement of ions in the solvent [2]. The movement of velocity [14] as Equation 1: ions through the solvent molecules as an environment υd = μE (1) is very important. There are two sides of these -1 Where, υd is drift velocity, (m.s ), E is magnitude of movements. One of them is ionic motions with the applied electric field, (V. m-1), µ is mobility, random in direction and speed basically. Secondly, (m2.V-1.s-1). movements have a collection side that is of particular In physics the average of velocity achieved by impact when more ions are movement in certain sides charged species is a drift velocity, like ions, in a than in others and product drift of ions. The ions drift solution accustom to an electric field. In other words, has important results because an ion has a mass and the electrical mobility of the ion is well-defined as the bears a charge [3]. Electrolyte substances are ratio of the drift velocity to the amount of the electric constituents of ions, those anions and cations in field Equation 2: dissolved state or liquid exist in dissociation form. μ = υ ⁄E (2) They are capable to conduct the electric current, as the d Conductivity can be measured by applying an charge cations and anions carriers are free to motion alternating electrical current to two electrodes between the cathode (-) and the anode (+) by diffusion immersed in a solution and measuring the resulting [4]. Measurement of molar conductance of solutions is voltage. Kohlrausch’s law states that the equivalent a classical electro-analytical practice that had conductivity of a material at infinite dilution is equal application in different chemical and biochemical to the anions conductance plus cations conductance. If studies. For example, conductivity can be used to electrolyte dissolved in water, the conductivity of the evaluate the solvent purity, follow kinetics of solution is the sum of anions and cations conductance, dissolution, determine relative solution ionic strengths so Kohlrausch's law can be expressed as Equation 3 (including functioning as a detector for ion [15]: chromatography), the attitude to partially soluble salts Λo = v λo + v λo (3) equilibrium, monitor of some enzymatic reactions m + + − − Where,Λo is the limiting molar conductivity, course, determine critical concentrations of micelle, m (S.m2.mol-1), v : is the number of ions i in the formula and to provide thermodynamic electrolyte solutions unit of the electrolyte, λo is the limiting molar data ]5[. Conductivity measurements have been used conductivity of ion, i., (S.m2.mol-1). in many environmental and industrial applications as a In solution the limiting molar conductivity of ion fast and trustworthy method of measuring the ionic species can be represented by Equation 4 [16]: content in solutions [6]. Many techniques are μ = λ⁄zF (4) available for the determination of diffusion Where, λ is molar limiting conductivity of ion, coefficients of ions in aqueous solutions; one of them (S.m2.mol-1), z is the charge number of ion, μ is is the ionic conductivity method. Diffusion coefficient mobility of ion, (m2.V-1.s-1), F Faraday’s constant, of different species in different media is an important (Coulomb.mol-1). property in scientific and practice research ]7[ , like As the values of mobility by different expression in petroleum engineering ]8[ , biochemistry ]9], and (Equation 2 and Equation 4) are equal, the units after nanotechnology ]10[. The radiuses of inorganic deriving is the same as shown in Equation 5: charge ions are important to use in explain a certain λ S m2 C s−1 m2 m2 μ = = = = (5) features of the ion, like bonding, shielding and zF C V C Vs numerous biological properties in solution ]11-13[. In Where m is meter, V is volt, s is second, S is Siemens, this review, we estimated the diffusion coefficient and C Coulomb. page 183 of 188 Journal of Chemical Reviews Short Review Table 1. Molar Ionic conductivity, λo /S cm2 mol-1, in water at 298 K [18]. Ion λo D Ion λo D Ion λo D K+ 073.5 1.957 IO3- 040.5 1.078 Na+ 050.1 1.334 - - 2+ I 076.8 2.045 H2PO4 036.0 0.959 Ni 099.2 0.661 + - 2+ H 349.6 9.311 NO2 071.8 1.912 Co 110.0 0.732 - 2- 2- Cl 076.4 2.032 CO3 138.6 0.923 HPO4 114.0 0.759 Table 2. Molar Ionic conductivity, λo /S cm2 mol-1 and Ions mobility, µ/ 10-8m2 s-1 V-1, in water at 298 K [19]. Ion λo µ Ion λo µ Ion λo µ + + 2+ H 34.96 36.23 NH4 07.35 07.62 Mg 10.60 05.50 Li+ 03.87 04.01 OH− 19.91 20.64 Ca2+ 11.90 06.17 Na+ 05.01 05.19 F− 05.54 05.74 Sr2+ 11.89 06.16 + − 2− K 07.35 07.62 Cl 07.64 07.92 CO3 13.86 07.18 + − − Rb 07.78 08.06 Br 07.81 08.09 NO3 07.15 07.41 + − 2− Cs 07.72 08.00 I 07.68 07.96 SO4 16.00 08.29 The molar conductance, the mobility (by used 3. MIP-Based Sensors for Determination Equation 4) and the diffusion coefficient (by used The relation between diffusion coefficient D, and the Equation 6) of different inorganic ions are listed in mobility of ion μ, described by Einstein– Table 3 and 4. Smoluchowski equation (6) [17]. Table 3. The molar conductance λo/ (×10-4 S m2 mole−1), the D = KBT μ⁄q (6) mobility µ/ (×10−8 m2 s−1 V−1), and the diffusion coefficient D/ 2 -1 -9 2 −1 Where D: is the diffusion coefficient, (m .s ), µ: is (×10 m s ) of different inorganic cations.