Apparent molar volumes and compressibilities of selected electrolytes in dimethylsulfoxide

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Abstract

Densities at T = (293.15, 298.15, 303.15, 313.15, 323.15, and 333.15) K and sound velocities at T = 298.15 K of tetraphenylphosphonium bromide, sodium tetraphenylborate, sodium bromide, and sodium perchlorate in dimethylsulfoxide have been measured over the composition range from (0 to 0.3) mol · kg−1. From these data, apparent molar volumes and apparent molar isentropic compressibilities at infinite dilution as well as the expansibilities have been evaluated. The results have been discussed in terms of employing tetraphenylphosphonium tetraphenylborate as a reference electrolyte in splitting the limiting apparent molar volumes and apparent molar isentropic compressibilities into ionic contributions.

Introduction

It is desirable that any discussion and interpretation of thermodynamic properties of electrolytes is related to a single ion as ions are the species actually present in an electrolyte solution. Unfortunately, an extrathermodynamic assumption needs to be accepted in order to extract the respective ionic contributions from the standard values of the molar volumes and compressibilities.

Hefter and Marcus discussed in detail both the theoretical and empirical approaches used for obtaining partial volumes of electrolytes in non-aqueous solvents as well as the methods of splitting them into ionic contributions [1]. Detailed analysis led them to the conclusion that at the present time the least objectionable treatment is the method making use of the reference electrolyte, i.e. ‘the reference electrolyte method’. According to Hefter and Marcus, the ideal reference electrolyte should consist of univalent spherical cation and anion of exactly the same size, large enough so the ions’ charges do not affect the surrounding solvent causing electrostriction. They also emphasized some other more characteristic features of such an ideal electrolyte which in some cases exclude one another. Therefore, unfortunately such an electrolyte does not exist and we have to simplify the reference electrolyte method to the following reduced equation VΦ0(cation)=VΦ0(anion). The closest approximations of an ideal reference electrolyte are both tetraphenylphosphonium tetraphenylborate (Ph4PBPh4 or TPTB) and tetraphenylarsonium tetraphenylborate (Ph4AsBPh4 or TATB). According to Hefter and Marcus, the treatment based on the first salt known as the TPTB assumption makes use of the equation:VΦ0(Ph4P+)-VΦ0(BPh4-)=2·10-6m3·mol-1,which is valid for all solvents at T = 298.15 K and P = 1 atm. The respective equation underlying the TATB assumption has the following form:VΦ0(Ph4As+)-VΦ0(BPh4-)=8·10-6m3·mol-1.

As is seen, the differences between the cationic and anionic contributions vary for both electrolytes. However, in relation to the size of these ions the variation is relatively small. It is clear that it, in fact, may be considered as the effect resulting from the differences in interactions of the ions with solvent molecules and their orientation due to the ion sign.

Compressibility describes the effect of pressure on the volume of a solvent and solute. Thermodynamic quantities defining these effects for electrolyte solutions are adiabaticκS=-1VΦVΦPSand isothermalκT=-1VΦVΦPTcompressibility coefficients. The first of them can be obtained using the Laplace equationκS=1u2d,where u is the sound velocity and d denotes density of the solution. The apparent molar adiabatic compressibility is defined asKS,Φ=V·κS-n1V10κS0n2,where V and V10 denote the volume of solution and pure solvent, κS and κS0 are the respective values of adiabatic compressibilities, while n1 and n2 denote the number of moles of solvent and solute, respectively.

It is obvious that the limiting values of the apparent molar adiabatic compressibilities are additive. However, there is no agreement on method of splitting them into ionic contributions [2], [3], [4].

The present study was undertaken to check the validity of the TPTB approach for both molar volumes and adiabatic compressibilities for electrolytes in DMSO solutions.

Section snippets

Experimental

Tetraphenylphosphonium bromide (Fluka, puriss, >0.99), sodium tetraphenylborate (Fluka, puriss, >0.995), sodium bromide (Fluka, ultra, >0.995), and sodium perchlorate (Sigma, anhydrous, >0.99) were dried in a vacuum oven to constant weight at T = 308 K. Dimethylsulfoxide (Fluka, puriss, H2O <0.0001) stored over 0.4 nm molecular sieves was used without further purification. The density value of (1095.193 ± 0.0098) kg · m−3 at T = 298.15 K obtained for DMSO was in good agreement with the literature data

Molar volumes

The obtained values of density of the solutions of Ph4PBr, NaBPh4, NaBr, and NaClO4 in DMSO at temperatures between (293.15 and 333.15) K are collected in table 1. The apparent molar volumes of the electrolyte solutions were calculated using the following equation:VΦ=(d0-d)/(mSdd0)+M2/d0,where mS denotes the number of moles of the solute per kilogram of solution (molonity); d and d0 are the densities of solution and solvent, respectively; and M2 is the molar mass of the solute.

The limiting

Molar compressibilities

The speed of sound values obtained for the solutions of NaBr, NaClO4, NaBPh4, and Ph4PBr in dimethylsulfoxide over the composition range studied, together with the values of the isentropic compressibility and the apparent molar isentropic compressibility, are collected in table 6. As observed the sound velocities and the isentropic compressibilities decrease with increasing concentration for all electrolyte solutions studied in DMSO. The apparent molar compressibilities, however, increase with

Ionic molar volumes and expansibilities

Since solubility of tetraphenylphosphonium tetraphenylborate is too low in dimethylsulfoxide to be measured directly, the apparent molar volume of TPTB at infinite dilution was obtained by additivity from the following route:VΦ0(TPTB)=VΦ0(NaBPh4)+VΦ0(Ph4PBr)-VΦ0(NaBr).The respective values of the partial molar volumes of ions within the temperature range studied are listed in table 8 together with literature data at T = 298.15 K [23]. Figure 3 shows the plots of the difference (VΦ,T0-VΦ,293.15K0)

Ionic molar compressibilities

Table 10 shows the summarized results of the present work, that is the ionic partial molar compressibilities of the studied ions in DMSO calculated assuming the equality of compressibilities of TP+ and TB ions, i.e. KS,Φ0(Ph4+)=KS,Φ0(Ph4B-). Such assumption is, at least for today, the only method to split the limiting molar compressibilities. We decided to present the obtained data in table 10 in order to demonstrate imperfection of the underlying assumption and the arising differences.

Thus,

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