Surface concentration standard states

There is an advantage in using the constant surface pressure standard state since it yields molar properties (enthalpies and entropies of adsorption) analogous to those associated with phase changes evaluated from the Clapeyron equation [80]. The use of the standard state with constant surface concentration provides differential quantities for the enthalpy and entropy changes which are not directly comparable with those calculated using the methods of statistical thermodynamics. The values of AS calculated by these two standard states differ only by the gas constant, B, and are readily interconverted. 

Only those components which are gases contribute to powers of RT. More fundamentally, the equiUbrium constant should be defined only after standard states are specified, the factors in the equiUbrium constant should be ratios of concentrations or pressures to those of the standard states, the equiUbrium constant should be dimensionless, and all references to pressures or concentrations should really be references to fugacities or activities. Eor reactions involving moderately concentrated ionic species (>1 mM) or moderately large molecules at high pressures (- 1—10 MPa), the activity and fugacity corrections become important in those instances, kineticists do use the proper relations. In some other situations, eg, reactions on a surface, measures of chemical activity must be introduced. Such cases may often be treated by straightforward modifications of the basic approach covered herein. 

The methodology of surface electrochemistry is at present sufficiently broad to perform molecular-level research as required by the standards of modern surface science (1). While ultra-high vacuum electron, atom, and ion spectroscopies connect electrochemistry and the state-of-the-art gas-phase surface science most directly (1-11), their application is appropriate for systems which can be transferred from solution to the vacuum environment without desorption or rearrangement. That this usually occurs has been verified by several groups (see ref. 11 for the recent discussion of this issue). However, for the characterization of weakly interacting interfacial species, the vacuum methods may not be able to provide information directly relevant to the surface composition of electrodes in contact with the electrolyte phase. In such a case, in situ methods are preferred. Such techniques are also unique for the nonelectro-chemical characterization of interfacial kinetics and for the measurements of surface concentrations of reagents involved in... 

However, in practice it is frequently difficult to obtain results at such low surface concentrations either by direct measurement or by extrapolation. Consequently it is convenient to have an alternative definition in terms of surface covered, e.g., Barrer (3) and Foster (4) take 8 = as the standard state. A knowledge of the amount of material required to complete a monolayer is needed to apply this definition. Where such information is not available, one has to fall back on a definition in terms of so much adsorbate per cubic centimeter or per gram of adsorbent, and this makes interpretation more difficult. The accuracy of the determination will be greater when the heat of adsorption is known for adsorption directly to the standard state rather than as an average over the isotherm as a whole. 

Standard state free energies (AG°,js) and entropies (ASacjs) may also be determined from GSC retention data if ideal conditions are assumed. For the adsorbate behaving as an ideal gas in the mobile phase, the standard state is defined as a partial pressure of 1 atm. The adsorbed standard state is defined as a two-dimensional perfect gas at 1 atm where the mean distance between adsorbed molecules is the same as in the three dimensional gas phase standard state. Thus, the sorbate equilibrium surface concentration Cg becomes 4.07 x 10 9/T (moles/cm2) and the gas phase sorbate concentration becomes 4.07 x 10- /TK ,. 

XPS measurements demonstrated that loaded Ni is predominantly located between the layeres of the catalyst and little remains on the external surface.15) For sensitivity reasons, a sample with 1 wt% Ni-loading was used. Comparison of the Ni2p3/2 peak intensity in the catalyst with that in a reference sample (which was also 1% Ni-loaded KNb03 with almost the same BET surface area as that of K4Nb6017) has shown that the surface concentration of Ni in the former is about 100 times less than that of the reference sampled EXAFS spectra for 1 wt% Ni-loaded samples both before and after the reduction procedure, as well as for Ni and NiO as standards, indicated that after reduction by H2 at 500°C for 2 b the loaded Ni was completely reduced to the metallic state.15) Even after reoxidation by 02 at 200°C for 1 h, most of the Ni remained metallic. (By XPS, the Ni, which remained on the external surface, was found to be in the oxidized form.) The formation of metallic nickel on a 0.1 wt% Ni-loaded catalyst was also confirmed by ESR measurements.7 The appearance of an intense resonance line after the reduction and reoxidation indicates the formation of ferromagnetic metallic nickel in the sample. 

The apolar contribution to AS0, ASap, is better characterized than AHap. The value of Tt has been shown to be a universal temperature for all processes involving the transfer of an apolar surface into water and has a value of 112°C (Murphy et al., 1990). At this temperature the AS0 of transfer, ASf, represents the mixing entropy of the process. The universal value of Tt was determined using mole fraction concentration units, so that the liquid transfer ASf takes on a value of zero. The value of Tt remains the same using the local standard state of Ben-Naim (i.e., molar concentration units) (Ben-Naim, 1978), but the value of Ais increased by R ln(55.5), where R is the gas constant and 55.5 is the molarity of water. 

The value of AadsGjgp determined in this manner is linearlydependent on the concentration of PNP. Extrapolating to zero PNP concentration gives AadsGjBP = —31.4 0.8 kJ mol, which is consistent with the value determined by surface pressure and surface tension measurements at low TBP concentrations [50,51] (when corrected for the different interface standard states, see Appendix). 

In natural waters, other surface reactions will be occurring simultaneously. These include protonation and deprotonation of the >FeOH site at the inner o-plane and complexation of other cations and anions to either the inner (o) or outer (IS) surface planes. Expressions similar to Equation (5) above can be written for each of these reactions. In most studies, the activity coefficients of surface species are assumed to be equal to unity thus, the activities of the surface sites and surface species are equal to their concentrations. Different standard states for the activities of surface sites and species have been defined either explicitly or implicitly in different studies (Sverjensky, 2003). Sveijensky (2003) notes that the use of a hypothetical 1.0 M standard state or similar convention for the activities of surface sites and surface species leads to surface-complexation constants that are directly dependent on the site density and surface area of the sorbent. He defines a standard state for surfaces sites and species that is based on site occupancy and produces equilibrium constants independent of these properties of the solids. For more details about the properties of the electrical double layer, methods to calculate surface specia-tion and alternative models for activity coefficients for surface sites, the reader should refer to the reference cited above and other works cited therein. 

In these equations ff is the formal potential of the adsorbed, redox active species, Po/Pr is related to the difference in the standard Gibbs free energies of adsorption for O and R, p (i = O or R) is the surface concentration of the adsorbed species, and P is the total surface concentration of the species regardless of oxidation state [39]. For... 

Fig. 2 Comparison of SO4, Cl , Br , and 1 adsorption at the Au (111) electrode surface from 0.1 M HCIO4 + 10 M K2SO4 and 0.1 M KCIO4 + 10 M KCl, KBr, and KI solutions, (a) Cyclic voltammograms at u = 10 mV s (b) Gibbs surface excess versus potential, (c) Gibbs energy of adsorption versus potential. The standard state corresponds to the surface coverage / = 1 ion per cm and bulk concentration c = 1 mol dm [36].

The standard state for the surface phase is a hypothetical monolayer of the surfactant at its closest packing (minimum surface area /molecule) but at a surface pressure of zero. For nonionic surfactants at dilute concentrations (<1 x 10 2 M) in the solution phase, we can substitute mole fractions for activities and the relation becomes... 

The initial work at Bartlesville has concentrated on measurements of enthalpy changes from dilution and adsorption for surfactant systems. From the observed dilution enthalpy changes, critical micelle concentrations have been determined, and standard state enthalpies of micel lization have been calculated. In the studies on adsorption, several properties are of interest the enthalpy of adsorption, the amount of surfactant adsorbed, the surface area of the solid and determining whether the adsorption is reversible. The kinetics of adsorption and desorption are also of interest. 

Gas-phase concentrations in the vicinity of the external surface of the catalyst are calculated using the ideal gas law. Under standard-state conditions, 1 mol of any ideal gas occupies 22.4 L. Furthermore, the ideal gas law suggests that molar density varies inversely with temperature. Hence,... 

II.2a) Reactive primary ion bombardment Yield enhancement is brought about by direct implantation of a reactive species in the sample by using an O2+ (or 0") or a Cs+ primary beam. Liebl [5] has described the build-up in the surface concentration of implanted species during sputter erosion. After sputtering to a depth of approximately Rp + 2ARp, where Rp is the projected range and p the standard deviation, the sputter rate of previously implanted primary ions will exactly balance the implantation rate. In this steady state situation, an equilibrium surface composition is achieved and the secondary ion yields stabilize. Figure 5 shows that upon commencement of bombard-... 

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