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Transcript

TRANSPORT OF IONS IN SOLUTION Conductivity of electrolyte solutions Strong and weak electrolyte Ion Mobility Ion mobility and conductivity, Transport number Diffusion Jaslin Ikhsan, Ph.D. Chemistry Ed. Department State University of Yogyakarta Conductivity of Electrolyte Solution Ions in solution can be set in motion by applying a potential difference between two electrodes. The conductance (G) of a solution is defined as the inverse of the resistance (R): 1 G , in units of 1 R For parallel plate electrodes with area A, it follows: A G Where, L Κ: the conductivity, L : the distance separating the plates Units: G → S (siemens) R→Ω κ → S m-1 Conductivity of Electrolyte Solution The conductivity of a solution depends on the number of ions present. Consequently, the molar conductivity Λm is used m C C is molar concentration of electrolyte and unit of Λm is S m2 mol-1 In real solutions, Λm depends on the concentration of the electrolyte. This could be due to: Ion-ion interactions γ 1 The concentration dependence of conductance indicates that there are 2 classes of electrolyte Strong electrolyte: molar conductivity depends slightly on the molar concentration Weak electrolyte: molar concentration falls sharply as the concentration increases Conductivity of Electrolyte Solution In real solutions, Λm depends on the concentration of the electrolyte. This could be due to: 1. Ion-ion interactions γ 1 2. Incomplete dissociation of electrolyte strong electrolyte, weak dependence of Λm on C weak electrolyte, strong dependence of Λm on C Strong Electrolyte Fully ionized in solution Kohlrausch’s law m 0 m KC1/ 2 Λ0m is the limiting molar conductivity K is a constant which typically depends on the stoichiometry of the electrolyte C1/2 arises from ion-ion interactions as estimated by the Debye-Hückel theory. Strong Electrolyte Law of the independent migration of ions: limiting molar conductivity can be expressed as a sum of ions contribution 0 m ions migrate independently in the zero concentration limi Weak Electrolyte Not fully ionized in solution H3O (aq) A (aq) HA(aq) H2 O(l ) (1 ) c c 2c Ka , 1 1 1 2 c K a K a c Ka Ka 0 2 Ka Ka 4 Ka c 2 Ka 2c 2c Ka 4 Ka c 2 2c c Ka c is degree of ionisation K a K a 4c 1 2c 2c K a 1/ 2 1/ 2 Ka 4c 1 1 2c Ka Weak Electrolyte The molar Conductivity (at higher concentrations) can be expressed as: m 0 m At infinite dilution, the weak acid is fully dissociated (α = 100%) It can be proven by the Ostwald dilution law which allows estimating limiting molar conductance: c m 1 1 0 m m Ka ( 0 m ) 2 m 0 m 1 1 m 0 m 1 1 1 0 x m m 1 1 0 m m c x 1 Ka m 1 1 c 0 x 0 0 m m Ka m m Weak Electrolyte The limiting molar conductance: c m 1 1 0 m m Ka ( 0 m ) 2 Graph to determine the limiting value of the molar conductivity of a solution by extrapolation to zero concentration The Mobility of Ions Ion movement in solution is random. However, a migrating flow can be onset upon applying an electric field , E L F zeE ze L is the potential difference between 2 electrodes separated by a distance L F accelerates cations to the negatively charged electrode and anions in the opposite direction. Through this motion, ions experience a frictional force in the opposite direction. Taking the expression derived by Stoke relating friction and the viscosity of the solvent (), it follows: Ffric 6rs, ( for ions with raidus r and velocity v) The Mobility of Ions When the accelerating and retarding forces balance each other, s is defined by: zeE ze s E , where 6 r 6 r u is mobility of ions, and r is hydrodynamic radius, that might be different from the ionic radius, small ions are more solvated than the bulk ones. Mobility in water at 298 K. Viscosity of liquids at 298 K The Mobility of Ions and Conductivity Finally, it can be shown that: zF , where F N A e Fully dissociated electrolyte: stA. vcN A J (ions) svcN A At J (ch arg e) zervcN A zrvcF zEvcF I J . A zEvcFA zvcFA L I G R L zvcF The Mobility of Ions and Conductivity In solution: zF 0 m ( z v z v ) F Example: 1. if =5x10-8 m2/Vs and z=1, Λ=10mS m2 mol-1. 2. From the mobility of Cl- in aqueous solution, calculate the molar ionic conductivity. zF = 7.91 x 10-8 m2 s-1V-1 x 96485 Cmol-1 = 7.63x10-3 sm2 mol-1 The Mobility of Ions and Conductivity • Taking a conductimetre cell with electrodes separated by 1 cm and an applied voltage of 1 V, calculate the drift speed in water at 298 K. rCs = 170 pm H2O = 0.891x10-3 kg m-1 s-1 1602 . x10 19 C 6 r 6 x 31416 . x 0.891 x 10 3 kgm 1 s 1 x 170 x 10 12 m ze 5 x 10 8 m2V 1 s 1 1V E L 0.01m 100Vm 1 s E 5 x 10 8 m 2V 1 s 1 x 100Vm 1 5 x 10 6 ms 1 It will take a Cs+ ion 2000 s to go from one electrode to another. For H+ ion, H+=36.23 x10-8 m2 s-1 V-1, it will take 276 s. Transport Numbers Diffusion Diffusion Diffusion Diffusion Diffusion Diffusion Solution of Diffusion Equation Diffusion Probablities Random Walk Problems Summary Migration: Transport of ions induced by an electric field. The concentration dependence of the molar conductivity strongly differs for strong and weak electrolytes. Diffusion: Mass transport generated by a gradient of concentration. 2 F 0 m ( z v D z v D ) RT m 0 m KC 1/ 2 D RT zF kBT D 6r Thank You