Zwanzig Theory Application for Bromide and Iodide Ions in Pure Solvents at 25 ° C

The Zwanzig theory of dielectric friction has been applied to trimethylsulfonium ion, bromide and iodide ions in different solvents at 25°C. The radius values which obtained from the slope (hydrated radius) and that one which obtained from the intercept (hydrodynamic radius) were calculated and the reason for such difference discussed on the basis of the assumptions of Zwanzig theory.


I. INTRODUCTION
Fuoss [1] has introduced a relationship between the ionic conductivity of an ion in different solvents and solvent properties.Boyd [2] and Zwanzig [3] have upgraded it and It was considered interesting to examine the applicability of Fuoss-Boyd-Zwanzig (F.B.Z) theory to present data.Equation (1) can be applied in the linear form proposed by Atkinson and Mori [4] where results in a number of solvents are to be compared.When equation ( 1) is inverted and rearranged with insertion of the numerical constant and radii in a 0 , we obtain For convenience in plotting, this can be written as where So that a plot of L* versus R* should be linear and ri can be obtained from both intercept and slope.The aim of this work, is applying the Zwanzig theory to illustrate the values of the slope and the intercept for different ions in pure solvents at 25°C.The obtained new results were interpreted.

II. EXPERIMENTAL PART
All salts were highly purified reagent grade and used without further purification.where trimethylsulfonium bromide (Me3S.Br) and trimethylsulfonium iodide (Me3S.I) are Analar analytical reagent "BDH".

A. Conductivity water
It was obtained by passing ordinary distilled water from a tin still over a 60 cm long Elgstat deionizer and guarded against contamination with atmospheric CO2 by sodalime tubes.Its specific conductance ೫° amounted to (2-7 x 10 -7 ) ohm -1 cm -1 .
All the solutions were used by weight.Salts are weighted on a microbalance which reads to ± 0.1 mg.Dilution was done into the cell by siphoning the solvent by a weighing pipette.The model of the conductivity bridge was Crison GLP31+ and a cell with bright platinum electrodes was used.The cell constant was 0.1 cm -1 for dilute solutions.

III. RESULTS AND DISCUSSION
Table (1) shows the ionic conductances of various ions in some pure solvents, water, ethanol, n-propanol and nbutanol, while Table (2) summerizes the solvent parameters used for the F.B.Z calculations.Tables (3)(4)(5) show the parameters obtained from F.B.Z calculations.Figures ( 1-3) explain a plot of L* versus (R* x 10 11 ), where the least square method was used to calculate the values.The points of the ions under this study were noticed to be scattered around the straight lines and this is attributed to the uncertainty in the values of the time ( ).Table (6) includes values of radii (ri)calculated from the intercepts and slopes of the straight line graph according to equation (3) as shown in Figures (1)(2)(3).A quantitative test for equation ( 3) is to deduce the values of (ri) obtained from the slope and intercept of the straight lines of each ion.It is noticed that the two values from each other but they are increasing with the increase of the size of the ions in different solvents.The increase in the value of hydrated radii (ri slope) for  Br ,  I and trimethylsulfonium + ion with increase in ion size may be attributed to the ion solvent interaction.The increasing in the values of hydrated radii obtained from slope more than hydrodynamic radii from intercept refers to occurrence of solvation.Nightingale [5] and kay et al. [6], have calculated the hydrated radii and hydrodynamic radii for tetra-alkyl ammonuim ions.They noticed that the hydrated radius increases with increasing ion size.The intercept value reflects factor closely related to the ion solvent interaction for a particular ion.Evan and Gardam [7]  ClO and s-alkylisothiouronuim ions (s-Meis + , s-n-Buis + , sn-Amis + and s-n-Heptis + ) in water, methanol, n-propanol and CH3CN at 25°C.They found that the radii obtained from the slope increase with increase in size for both cation and anions.The increase in the value of hydrodynamic radii (ri intercept) for s-Meis + , s-n-Buis + , s-n-Amis + and s-n-Heptis + with increase in ion size may also be due to ionic solvation interaction of ions.
El-Hammamy et al. [9], have applied Zwanzig theory of dielectric friction for chloride ion in different solvents at 25 o C.They compared the values of radius (ri) obtained from the slope and that one obtained from the intercept of the straight line for  Cl and it was found that the radius from both of slope and intercept slightly decreases with increasing the ionic size from  Cl to  I .This may be attributed to the decrease in solvation.
El-Hammamy et al. [10], have obtained the values of the radius from slope (hydrated radius) and intercept (hydrodynamic radius) for  Br ,  I and  4

ClO
in water, methanol and acetonitrile at 30 o C using Zwanzig theory.They found that the radius from slope and intercept increases with increasing the size of ions.This was due to theionic solvation.
El-Hammamy et al. [11],calculated the hydrated radii and hydrodynamic radii for sodium diethyldithiocarbamate and alkali metal ions in aqueous and non-aqueous solvents at 25 o C.They found that the two values are different; the value of (ri) obtained from the slope increases with increasing of the size from Na + ion to diethyldithiocarbamate ion (DDC -), but the value of (r i ) obtained from the intercept decreases with increasing the size from Na + ion to (DDC -) ion.The increasing in the values of hydrated radii obtained from slope more than hydrodynamic radii from intercept refers to occurrence of solvation.

IV. CONCLUSION
It may be found that the Zwanzig equation has been applied to give correct overall trends in the effect of solvent dielectric relaxation on ion mobility.This is true both in pure solvents and also in solvent mixtures of different character.The difference between (ri intercept) and (ri slope) is not too distributing.The intercept value still reflects factors closely related to the ion-solvent interaction for a particular ion.The slope value-the real concern of the Zwanzig theory-is identical for the Li+, Na+, K+, Cs+ metal ions.This could be interpreted as a distance beyond which the solvent is no longer affected by the ion field.In short, the Zwanzig theory may be reminding us that the concept of an ion radius in a structured solvent is not an easily defined parameter.In addition, it has been pointed out that the "wetted" sphere of the stokes law is to some extend inconsistent with the zwanzig treatment which ignores the existence of stream lines in the medium.It should be noticed that Zwanzig examined only the special case where the rate of dielectric relaxation is slower than the rate of solvent exchange.The relative constancy for solvent-exchange rate on simple mono-valent ions probably helps us to obtain the relatively good qualitative agreement.However, a more general treatment must probably consider the relationship between solvent-exchange rates and ion-mobilities in a more detailed way.

:
Static (low frequency) dielectric constant of pure solvent at 25°C   : Optical (infinite frequency) dielectric constant of pure solvent at 25°C  : Dielectric relaxation time of pure solvent at 25°C   : Bulk viscosity of pure solvent at 25°C
applied F.B.Z equation for tetra-alkylammonuim salts in MeOH, EtOH, n-PrOH and n-BuOH at 25°C.They expound the scattering of the points and difference between the (ri intercept) and (ri slope) values to certain specific parameters such as solvation which are neglected in the continuum model and these show a very important role in determining mobility of ions.El-Hammamy et al.[8], calculated the hydrated radii and hydrodynamic radii for acetylcholine ion and

TABLE III :
APPLICATION OF ZWANZIG EQUATION FOR TRIMETHYLSULFONIUM ION IN DIFFERENT SOLVENTS AT 25°C

TABLE IV :
APPLICATION OF ZWANZIG EQUATION FOR BROMIDE IN  R 11 10

TABLE V :
APPLICATION OF ZWANZIG EQUATION FOR IODIDE IN DIFFERENT  R 11 10

TABLE VI :
HYDRODYNAMIC RADII FROM INTERCEPT AND ALSO HYDRATION RADII FROM SLOPE OF F.B.Z EQUATION FOR DIFFERENT IONS: