Defining the transfer coefficient in electrochemistry: An assessment (IUPAC Technical Report)

The transfer coefficient α is a quantity that is commonly employed in the kinetic investigation of electrode processes. In the 3rd edition of the IUPAC Green Book, the cathodic transfer coefficient αc is defined as –(RT/nF)(dlnkc/dE), where kc is the electroreduction rate constant, E is the applied potential, and R, T, and F have their usual significance. This definition is equivalent to the other, -(RT/nF)(dln|jc|/dE), where jc is the cathodic current density corrected for any changes in the reactant concentration at the electrode surface with respect to its bulk value. The anodic transfer coefficient αa is defined similarly, by simply replacing jc with the anodic current density ja and the minus sign with the plus sign. It is shown that this definition applies only to an electrode reaction that consists of a single elementary step involving the simultaneous uptake of n electrons from the electrode in the case of αc, or their release to the electrode in the case of αa. However, an elementary step involving the simultaneous release or uptake of more than one electron is regarded as highly improbable in view of the absolute rate theory of electron transfer of Marcus; the hardly satisfiable requirements for the occurrence of such an event are examined. Moreover, the majority of electrode reactions do not consist of a single elementary step; rather, they are multistep, multi-electron processes. The uncritical application of the above definitions of αc and αa has led researchers to provide unwarranted mechanistic interpretations of electrode reactions. In fact, the only directly measurable experimental quantity is dln|j|/dE, which can be made dimensionless upon multiplication by RT/F, yielding (RT/F)(dln|j|/dE). One common source of misinterpretation consists in setting this experimental quantity equal to αn, according to the above definition of the transfer coefficient, and in trying to estimate n from αn, upon ascribing an arbitrary value to α, often close to 0.5. The resulting n value is then identified with the number of electrons involved in a hypothetical rate-determining step or with that involved in the overall electrode reaction. A few examples of these unwarranted mechanistic interpretations are reported. In view of the above considerations, it is proposed to define the cathodic and anodic transfer coefficients by the quantities αc = –(RT/F)(dln|jc|/dE) and αa = (RT/F)(dlnja/dE), which are independent of any mechanistic consideration.

Analysis of Binary Adsorption Excess Isotherms at the Liquid/Solid Interface

Adsorption excesses of binary liquid mixtures are the primary experimental quantity in liquid-phase adsorption onto porous or disperse solids. Binary liquid adsorption isotherms can be easily measured and allow statements to be made about the characteristics of solid and liquid mixtures, immersion behaviour at the liquid/solid interface, multi-component adsorption, etc. In this paper, a brief summary is given of different ways of interpreting and analysing binary isotherms over the whole concentration range. Experimental data and calculation examples show that thermodynamics provides a powerful tool for obtaining relevant information from such isotherms.

Loss Due to Leakage in Unshrouded Radial Impellers

Unshrouded impellers of centrifugal compressors and centripetal turbines manifest an increase of the flow losses in comparison with the shrouded ones. Assuming that the controlling factor in such increase of loss is the leakage through the gap between wheel and casing, the author develops a simple theory leading to a formula for the volumetric efficiency. Only one experimental quantity is required for applying the formula; and tentative values, based on some experimental evidence, are presented.