Electmchlmfca Acta, Vol. 38. No. 18, pp. 2663-2667. 1993 Printed in Great Britain 0013~4686/‘93 WYJ + 0.00 Q 1993. Pergunon Press Ltd zyxwvutsrq SOME COMMENTS ON THE THERMODYNAMIC DETERMINATION OF THE SIZE RATIO PARAMETER P. NIKITAS Laboratory of Physical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece (Receiued 18 May 1993; in revisedform 29 June 1993) Alwdract-The assumptions on which the thermodynamic method for the determination of tbe sixe ratio parameter, x, is based, are indicated and discussed. It is shown that these assumptions do not introduce any molecular or structural information and they are expected to have an insigni6cant effect on the value of n. It is also shown that the method can give any value of n, provided that the experimental data contain the relevant information. The value n = 1 obtained up to now for all substances examined is discussed and an interpretation of tbis result at a molecular level is given. Key words: adsorption on electrodes, thermodynamics, size ratio parameter. INTRODUCTION In adsorption studies the size ratio parameter, n, is defined as the number of solvent molecules displaced from the adsorbed layer upon the adsorption of one adsorbate molecule. The value of this parameter affects many other adsorption parameters, which are used for the clarification of the model and properties of the adsorption layer. In particular, it affects the adsorption isotherms when they are expressed in terms of molar surface fractions, the calculated excess thermodynamic functions of mixing, the stan- dard Gibbs energy of adsorption referred to the unsymmetrical choice of the standard states and finally the value of the particle-particle interaction parameter[l]. Thus its significance in adsorption studies is Let-y important[l-31. However, until very recently the inability to determine this parameter directly from experimental data had led to the use of a calculated size ratio parameter by assuming a certain model for the adsorbed layer. In this way though, the obtained results depend not only on the experimental data but also on the model we choose Q priori to calculate n. This limitation makes it diffi- cult to obtain an objective picture of the adsorption layer. Recently we have proposed a thermodynamic method, which allows the experimental evaluation of n[l, 4, 51. This method has heen applied to several systems and the value of n = 1 was found for all sub- stances examined[3-51. This result supports an earlier analysis by Damaskin[6] and views expressed several times by Trasatti[Z, fl. However, the same result has led Trasatti to wonder whether it has a physical meaning or it is a priori locked into the method[3]. I realise that similar doubts may reasonably arise for the following reason. Thermodynamics is con- cerned with the macroscopic behaviour of matter. For this reason, “if no information about structure is contained in the original experimental data, no such information can be obtained by the operation of thermodynamic transformations on these data”[8]. Therefore, since the size ratio parameter, as defined above, is a molecular parameter, it cannot be obtained thermodynamically, unless molecular infor- mation is included, in some way, in the treatment of the experimental data. These thoughts have led me to make the following clarifications in what concerns the thermodynamic method for the determination of n. In particular, below we discuss and show that (a) the assumptions made in this method do not introduce any molecular of structural information in the treatment of the experimental data, (b) these assumptions are expected to have an insignificant effect on the size ratio parameter, and (c) the size ratio parameter obtained by this method is a macroscopic thermodynamic quantity, defined as the ratio of the partial surface areas of the adsorbate and solvent. Therefore, there is no problem in its determination by a thermodynamic operation. Finally, the relation of this thermodynamic quantity to the correspond- ing molecular one defined as the number of solvent molecules replaced by one adsorbate molecule is also discussed. THERMODYNAMIC BASES OF THE METHOD The problem of whether molecular or structural information is included in the thermodynamic method we proposed in Cl, 41 is crucial for the cred- ibility of the obtained values of n. In order to clarify this point we briefly examine the basic equations on which the method is based and the assumptions needed for the determination of n, noting that the most rigorous presentation of the method is given in cu. Suppose that the adsorbed layer is composed of adsorbate (A) and solvent (S) molecules. Then the surface chemical potential of the ith species, i = A or 2663