Standard States for Adsorption on Solid Surfaces: 2D Gases, Surface

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Standard States for Adsorption on Solid Surfaces: 2D Gases, Surface Liquids, and Langmuir Adsorbates Aditya Savara* Chemical Sciences Division, Oak Ridge National Lab, 1 Bethel Valley Road, Oak Ridge, Tennessee 37830, United States S Supporting Information *

ABSTRACT: Standard states are utilized to compare thermodynamic data obtained from different experiments and calculations, and this ability to compare thermodynamic data plays an important role in science and society. For molecules adsorbed on surfaces, there are currently no universally accepted standard states. Here, standard states are proposed for the different types of molecular adsorbate phases, with the intent to enable physical insight to be gained by tabulating experimental/calculated values, such that comparison between different systems and existing societal tabulations of chemical standard state tabulated values can be done directly. A “density based” standard state is proposed for 2D gases, and a “relative coverage based” standard state is proposed for immobile adsorbates and nonislanding 2D liquids. These units are chosen based upon the units which the activity depends on. The standard states recommended here are chosen due to the entropies associated with them, such that physical insight can be gained by direct comparison to existing tabulated data. For 2D gases adsorbed on solid surfaces, the recommended standard state is σ° = 1.39 × 10−7 mol m−2. For immobile adsorbates and nonislanding liquid states on solid surfaces, the recommended standard state is θA° = 0.5 (which implies a standard state for the surface sites of of θS° = 1 − θA° = 0.5). With the standard states recommended here, tabulated values at a common temperature are expected to display the following approximate hierarchy for decreasing entropy: 3D gas > 2D gas > liquid > surface liquid > solid > lattice confined. Recommended standard states are also provided in the Supporting Information for cases with dissociative adsorption.

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INTRODUCTION In chemical thermodynamics, reference states are often convenient or necessary, with energies or entropies defined as relative to those of a reference state. The reference state can sometimes be arbitrarily chosen but must have a specified pressure and temperature, as well as specification of other attributes that are necessary to define the state thermodynamically unambiguously (for example, the number of molecules or volume could be required for certain situations). Standard states are specific sets of reference states that are adopted as a convention for use by society or subsets of the scientific community. Standard states enable tabulation and facile comparison of thermodynamic data obtained from differing experiments or theory for varied substances and reactions. Note that universal use of the same standard state(s) is not mathematically or physically necessary but is societally desirable. Keeping the reason for standard states in mind (tabulation and comparison of data from different experiments/ calculations), this paper is an attempt to define societally useful choices of standard states for molecules confined to solid surfaces and other lattice confined states (such as adsorption on molecular organic frameworks). Currently, there are no universally accepted standard states for molecules adsorbed on surfaces;1 this lack of standard states for adsorbates inhibits the tabulation of data for direct © 2013 American Chemical Society

comparison between different adsorbate/substrate systems. For pure substances, thermodynamic values are generally tabulated with a standard state of Po = 1 bar following the IUPAC recommendation,2 and these tabulated values have been fruitful resources for academic research and industrial applications. Having universal standard states for adsorbates would allow similarly fruitful tabulation of thermodynamic values, enabling direct comparison of results between different experiments/calculations. Further, with the standard states recommended in this paper, the standard thermodynamic values of adsorbates can also be compared to existing tabulated data for solids, liquids, and 3D gases to gain insight about the phase based on tabulated molar entropy values. The principle of recommending standard states that enable physical insight from direct comparison with existing tabulated values is a guiding principle for this work. (Sidenote: The IUPAC recommendation for the standard state does not include a specified temperature. Thus, the IUPAC definition is technically an infinite set of states, as noted in ref 2. The current IUPAC recommendations for pure substances are to use 1 bar for the reference pressure and to specify the Received: May 3, 2013 Revised: July 7, 2013 Published: July 12, 2013 15710

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Table 1. Standard Molar Entropies Using the Standard States Recommended Herea species Ag (3D gas) Ag (2D gas) Ag (solid) Ag (ads-L) Ag (ads-L) H2 (3D gas) H2 (3D gas) H2 (3D gas) H2 (2D gas) H2 (2D gas) H2 (liquid) H2 (liquid) H2 (ads-L) H2 (ads-L) H2 (ads-L) H2 (ads-L) H2 (ads-L) CH4 (3D gas) CH4 (3D gas) CH4 (3D gas) CH4 (2D gas) CH4 (liquid) CH4 (surface liquid) a

reference

T (K)

Sm° (T, J mol−1 K−1)

tabulated calculated tabulated24 indirect25 indirect26 tabulated24 tabulated27 tabulated27 calculated calculated extrapolated from tabulated data tabulated27 experimental15 experimental15 experimental15 calculated, all rotations present calculated, no rotations present tabulated24 extrapolated from tabulated data extrapolated from tabulated data calculated calculated indirect19,20

298.15 298.15 298.15 298.15 298.15 298.15 120 20.2 298.15 120 120 20.2 ∼115 ∼115 ∼120 298.15 298.15 298.15 112 77 77 112 77

173.0 120.0 42.6 42.6 5.2 130.7 100.8 60.0 94.3 75.7 42.3 15.9 42 39 27 24.8 11.7 186.3 153 141 114 80 49.5

substrate/site 24

pure phase pure phase pure phase Ru(001) W(110) pure phase pure phase pure phase pure phase pure phase pure phase pure phase zeolite metal cation (Na-ZSM-5) zeolite metal cation (K-ZSM-5) zeolite Metal Cation (Mg, Na−Y) zeolite Metal Cation (for arbitrary cation) zeolite Metal Cation (for arbitrary cation) pure phase pure phase pure phase pure phase pure phase MgO(100) surfaces of MgO nanocrystals

Not all values are at 298.15 K. See Supporting Information for details.

temperature used in the text, or in parentheses. Thermodynamic values for pure substances are typically tabulated for a pressure of 1 bar at temperatures between 273.15 and 298.15 K. For many applications, the thermodynamic values in this temperature range have sufficiently small variation that the data can be used interchangeably, even when the data has been tabulated with different reference state temperatures.) For molecular adsorbates, there are three main classes of molecular adsorbates: 2D gas adsorbates (freely mobile), immobile adsorbates (bound to sites), and surface liquids. These adsorbates constitute different chemical phases, and to maintain compatibility with existing tabulated values, different standard state valueswith different unitsare required. In the Supporting Information, recommended standard states are also provided for cases where immobile adsorbates are produced from dissociative adsorption.

entropy is included in the Sackur-Tetrode equation as shown below, for an arbitrary number of dimensions: D ⎛⎛ ⎞ D⎞ 2πmkT ⎞ LD ⎟ ⎛⎜ + 1 + ⎟R Sm ≅ R ln⎜⎜⎜ ⎟ ⎟ ⎝ h 2⎠ ⎠ nNA ⎠ ⎝⎝

(1)

where k is the Boltzmann constant, R is the ideal gas constant, m is the molecular mass, n is the total number of moles, NA is Avogadro’s number, D is the number of dimensions the gas is confined to, and L is the length of the box the particles are confined to. Note that evaluating LD gives volume when D = 3 and evaluating LD gives area when D = 2 (in principle, noninteger dimensions are possible5). If the value of L is held constant and D is changed from 3 to 2 (comparing a cube to a square), then the entropy contribution from Sackur-Tetrode is reduced by a factor of approximately one-third; this reduction is logical since one out of three translations is removed when going from a cube to a square. Using the first term in the Sackur-Tetrode equation, it is possible to find the 2D density that corresponds entropically to a loss of one translation from a given 3D density at a given temperature. We will use this approach to find the single 2D gas density which is entropically analogous to the 3D gas standard state. (Although the SackurTetrode equation is commonly referred to as the translational entropy contribution of a perfect gas, the Sackur-Tetrode equation actually comprises both the translational entropy contribution for a perfect gas and the configurational term for indistinguishable gas particles. The conventional choice to combine these terms is made for mathematical ease and is followed in this manuscript.) The 3D gas standard state consists of a gas at 1 bar, and chemical molar entropy values are generally tabulated at 298.15 K. To maintain compatibility with the largest number of existing chemical thermodynamic tables, we will find the entropically analogous 2D gas density, relative to a 3D gas at 1

I. STANDARD STATE FOR 2D GASES (FREELY MOBILE ADSORBATES) Experimental evidence has shown that gases adsorbed on solid surfaces may behave like a 2D gas when the activation energy for migration is sufficiently low compared to kT (where k is the Boltzmann constant and T is the temperature in K) such that the molecules are “freely mobile”(see ref3 and p. 181 of ref4). To choose the standard state for such a 2D gas phase, we will make a conceptual comparison to the 3D gas phase standard state. When comparing a 2D gas to a 3D gas of the same molecule, there is no substantial difference in the molar enthalpies, but there is a substantial difference in the molar entropies: The molecules of a two-dimensional gas have the entropy associated with two degrees of translation while the gas molecules of a three-dimensional gas have the entropy associated with three degrees of translation. From statistical thermodynamics, the translational contribution of the molar 15711

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in which the surface consists of discrete binding sites upon which impinging gas (or liquid) molecules bind. As shown in the Supporting Information, when gas/liquid molecules adsorb to discrete sites, the Langmuir isotherm (eq 2) can be derived from both kinetics and thermodynamics. The derivations provided in the Supporting Information apply to cases with either immobile or hopping adsorbates, and yield

bar and 298.15 K. The molar volume for a 3D perfect gas at 1 bar and 298.15 K is 0.0248 m3. Using the relationship ((Am,analog‑T)/(NA)) = ((Vm)/(NA))2/3 yields the entropically analogous molar area for a 2D gas: Am,analog‑298.15K = 7.18 × 106 m2. This molar area corresponds to an absolute density of σ° = 1.39 × 10−7 mol m−2. As with 3D gases, the 2D gas standard state will be a hypothetical state based upon extrapolation of the low density perfect behavior (for 2D gas adsorbates, perfect adsorbate behavior corresponds to the low adsorbate densities where the adsorbate density is linear with 3D gas pressure). Using σ° = 1.39 × 10−7 mol m−2 and the Sackur-Tetrode equation, we provide example perfect 2D gas standard state entropies calculated for some chemical species, shown in Table 1 (see Supporting Information for calculation details). As can be seen, for gases at 298.15 K, the proposed standard state for a 2D gas results in molar entropies that correspond to a loss of one translation from the 3D gas standard state (approximately 1/3 of the entropy for a monatomic gas like silver). Note that the 2D gas standard state entropy values provided in Table 1 are for pure 2D gas phases lacking any interactions with a surface: for a 2D gas species adsorbed on a surface, the entropy would generally be below the type of pure phase values shown for 2D gases in Table 1. As shown in the Supporting Information, this standard state choice enables facile calculation of the theoretical entropy for the 2D gas standard state using values tabulated for the 3D gas standard state (which is a hypothetical state based on parameters from real gases). The 2D gas standard state choice presented here is similar to one used by De Boer6 and differs greatly from the standard state used by Kemball.7,8 Within IUPAC recommendations, a standard state can be defined either as a pressure or as a concentration. Historically, recommendations for the standard state of a 2D gas have generally been to use a 2D pressure for the reference state. However, the entropy and the adsorption isotherm for a 2D gas are both a function of the absolute 2D density, σ. Additionally, in many experiments for adsorption on solid surfaces, the value for σ can be calculated/estimated while the 2D pressure is generally not obtainable. Thus, we recommend setting the standard state for a 2D gas adsorbed on a solid surface to the absolute coverage of σ° = 1.39 × 10 −7 mol m −2 . Experimentalists do not need to be aware of the statistical thermodynamics origin of this standard state in order to use it, though experimentalists may benefit from comparing their data to theoretical values for the 2D gas standard state obtained using the Sackur-Tetrode equation (see Supporting Information for method details). At 298.15 K, this standard state corresponds to a 2D pressure of π = 3.16 × 10−4 N m−1 for a perfect gas, and at other temperatures the density provided can be converted to a 2D pressure using πA = nRT. (Under the recommendation provided here, the standard state for the 2D gas on solid surfaces remains a constant absolute density regardless of temperature, while the 2D pressure associated with this standard state varies with temperature.) It should be noted that for molecules at gas−liquid interfaces9 and liquid− liquid interfaces,10 the surface pressure is often easier to measure, and it may be appropriate to define the standard state by pressure rather than density for 2D gases at those interfaces.

KL =

θ (1 − θ )P

(2)

where KL is the Langmuir equilibrium constant, and θ is the relative coverage. Equation 2 is called the Langmuir isotherm. The terms “Langmuir model” and “Langmuir isotherm” cannot be used interchangeably: the term Langmuir model describes a chemical model (see first sentence of this section), while the term Langmuir isotherm is the equilibrium equation shown as eq 2. Equation 2 has been found to adequately describe adsorption for many situations where the Langmuir model does not apply. Note that the theoretical isotherms of mobile adsorbates are similar in shape to the Langmuir isotherm.6,11 It has been shown that fitting with the Langmuir isotherm can describe mobile adsorbates and that such fits cannot be used to exclude mobility without further analysis.5,9 Therefore, determination of whether an adsorbate is immobile/hopping must be made based on chemical knowledge and/or thermodynamic analysis.5 In this paper and the Supporting Information, all statements made about the Langmuir isotherm are specifically in the context of the Langmuir model where the adsorbates are immobile or hopping between sites. As can be seen, for immobile adsorbates, the activity is defined by the relative adsorbate coverage (θA). Therefore, the standard state for immobile adsorbates must be a relative coverage, θA°, and not a 2D density or 2D pressure. Several relative coverages have been suggested for θA°.5,12,13 Here, we follow the principle of choosing a standard state that allows for the easiest withdrawal of physical insight from direct comparison to existing tabulated values, as described below. In practice, one typical experimental procedure for finding the enthalpy and entropy of adsorption for immobile adsorbates is to obtain KL at multiple temperatures, and to then make a Van’t Hoff Plot.14−16 During this process the unitless standard equilibrium constant, K°17a special case of a thermodynamic equilibrium constantis obtained by dividing the unreferenced equilibrium constant, K, by the standard states, and then ln K° is plotted versus 1/T, as discussed previously5 (sometimes the units are simply “dropped” from the unreferenced equilibrium constant; doing so implies using the units provided as the standard state and also that the chemical potentials of the species are linear with concentration). In the thermodynamic derivation of the Langmuir isotherm for immobile adsorbates (see Supporting Information), it is shown that KL is not a Boltzmann equilibrium constant (because KL ≠ Nproducts/Nreactants) and that the entropy associated with KL is a partial molar entropynot an integral molar entropy. (For perfect 2D gas and 3D gas states the integral molar entropy and the differential molar entropy are equal in value. However, as shown in the Supporting Information, the partial molar entropy and integral molar entropy are not equal to each other for lattice-confined species. Some authors prefer the term “differential molar entropy”. We use the term “partial molar entropy” to be consistent with the broader physical chemistry nomenclature.) It is not a problem that the entropy and enthalpy associated with KL are partial

II. STANDARD STATE FOR IMMOBILE ADSORBATES (LATTICE CONFINED/LANGMUIR MODEL) The simplest and most common model for adsorption to surface sites from a 3D gas (or liquid) is the Langmuir model, 15712

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be neglected as a first approximation if insufficient data is available to accurately calculate the relative coverage, θA. The molar molecular entropy contributions of the adsorbates (vibrational, rotational, translational, electronic contributions) are likely constant at very low coverages with weak coverage dependence at higher coverages where adsorbate interactions become more important (the data of Magnacca et al.22 do indicate only a weak dependence of the entropy with coverage, but show the opposite trend which is ascribed to surface heterogeneity). The data from Arnold et al.20,21 measure adsorption entropies at arbitrary submonolayer coverages, and the analysis by Sellers et al.18 assumes no coverage dependence of the molecular entropy of the adsorbate entropy by assuming a constant pre-exponential for desorption. On the basis of the aforementioned studies, it seems that the coverage dependences for the entropy of mixing and for the molar molecular entropy are both not very large in practical measurements of real surface liquidsimplying that entropy values obtained at unknown coverages could be tabulated with only a relatively small introduction of error relative to the recommended standard state (we might guess a 10−30% error would be introduced by tabulating values at unknown coverages for surface liquids). For islanding surface liquidsnonislanding surface liquids may island at sufficiently low temperaturesthe molecules are in a pure phase of one geometric or lattice monolayer.5 Thus, for islanding surface liquids, the standard state would be full coverage with either a geometric or lattice monolayer, as the case may be. Thermodynamic analysis would need to account for the fact that the islanding surface liquid is present as patches on the substrate, and researchers should consider the possibility that the “open” patches could include either a nonislanding surface liquid, a 2D gas, or no molecules. Additionally, when studying an islanding surface liquid at a coverage greater than one monolayer, researchers should consider the various possibilities that may exist for the state of the second monolayer (i.e., 2D gas, islanding surface liquid, nonislanding surface liquid, etc.).

molar quantities: tabulations of thermodynamic values for immobile adsorbates should simply note that the tabulated values are partial molar entropies/enthalpies. Additionally, for tabulated values, the functional form of the equation which was used to obtain KL from the isotherm should be provided (e.g., Langmuir isotherm, Freundlich isotherm). When the data is obtained at sufficiently low coverages that Henry’s law applies, then Henry’s Law could be noted in lieu of an isotherm equation. For the Langmuir isothermas applied to molecular adsorption resulting in an immobile or hopping statewe recommend θA° = 0.5 for the standard state, corresponding to a hypothetical perfect adsorbate state based on the low coverage limit with no interadsorbate interactions. In this case, the standard state for the surface sites is θS° = 1 − θA° = 0.5 and the configurational term for the entropy of the surface is zero. Thus, a standard molar entropy for a lattice confined state based on the partial molar entropy of the surface at θA° = 0.5 reflects solely the partial molecular entropy of the adsorbate, as shown in Table 1 (see Supporting Information for details). Often, explicit use of a standard state for the surface/adsorbates is omitted during thermodynamic analyses of a Langmuir isotherm, which implies that the configurational term for the entropy of the surface is zero, as recommended here. The recommendation of θA° = 0.5 is intended for adsorption when there is only one site type, and when the adsorption is molecular rather than dissociative. This standard state would still apply for adsorbates which display interadsorbate interactions, as the standard state is a hypothetical “perfect adsorbate” state based on the low coverage behavior (much like for 3D gases). Recommended standard states for two cases of dissociative adsorption are described in the Supporting Information. Adsorption to surfaces with multiple site types is beyond the scope of the present work, though in the simplest case (with uncorrelated adsorption for different sites) θA° = 0.5 can be used for each site type.

III. STANDARD STATE FOR SURFACE LIQUIDS Recent experiments from temperature programmed desorption18,19 and adsorption isotherms19−22 have shown evidence that physisorbed adsorbates can display entropies that are near the values of the bulk liquid entropies for the same molecule (i.e., the entropies of adsorption are similar to the entropies of condensation). Presumably, such molecules do not behave as a 2D gas but rather as a liquid. The effects of rotational enhanced diffusion on surfaces is only beginning to be studied.23 The below discussion applies to the case of nonislanding surface liquids. For these adsorbates, submonolayer coverages do not constitute a pure phase and have a contribution from an entropy of mixing. The work by Magnacca et al.22 shows that the data of unsaturated hydrocarbons on silica is consistent with eq 2, which suggests that the entropy of mixing of a nonislanding surface liquid can be described by the Langmuir isotherm. Consequently, for nonislanding surface liquids, we recommend the same standard state as for immobile adsorbates: a hypothetical “perfect adsorbate” state of θA° = 0.5 and θS° = 1 − θA° = 0.5 extrapolated from low coverage (Henry’s law) behavior, such that the contribution from configurational term for the entropy of mixing is zero at the standard state. In practice, the entropy of mixing will usually be small compared to the molecular entropy of the adsorbed liquid phasefor example, < 10−20% of the total entropyand can

IV. COMPARISON OF VALUES USING THE RECOMMENDED STANDARD STATES As shown in Table 1, the recommended standard states provided here enable physical insight to be drawn from tabulated values of standard entropies. With the standard states recommended here, tabulated values at a common temperature are expected to display the following approximate hierarchy for decreasing entropy: 3D gas > 2D gas > liquid > surface liquid > solid > lattice confined. This order enables physical insight to be gained from tabulated values of standard state entropies. As can be seen in Table 1, the temperature dependence of the standard entropy is not negligible and should be accounted for when comparing measurements at different temperatures (see Supporting Information for details of calculations). In Table 1, the two standard adsorbate entropies shown for Ag atoms on other metals were obtained indirectly for the purposes of illustration. Note that the indirectly calculated standard entropy value for Ag/Ru(001) turns out to be the same value as the standard entropy of Ag(solid): this is likely a coincidence, the value for the Ag adatom entropy displayed in Table 1 for the Ag/Ru(001) system is too high to be realistic for an immobile metal adatom, and this value presumably arose due to either experimental error or a (physical) violation of the assumptions used in the Supporting Information. The value 15713

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implies a standard state for the surface sites of θS° = 1 − θA° = 0.5). For islanding surface liquids, the recommended standard state is one monolayer. As shown in Table 1, these standard states enable physical insight to be drawn by direct comparison of standard state entropies to those of the existing tabulated values for the 3D gas standard state of 1 bar. Recommended standard states are also provided in the Supporting Information for cases with dissociative adsorption. With the standard states recommended here, tabulated values at a common temperature are expected to display the following approximate hierarchy for decreasing entropy: 3D gas > 2D gas > liquid > surface liquid > solid > lattice confined. This order will enable physical insight to be gained from tabulated values of adsorbate standard state entropies.

shown for Ag/W(110) is reasonable for an immobile metal adatom. However, given that the values for Ag/Ru(001) and Ag/W(110) were both calculated indirectly within the assumption of lattice-confined adatoms, it’s possible that “direct” measurements using calorimetry or isotherms may show entropies more consistent with the adatoms behaving as surface liquids. In Table 1, the experimental values for the standard entropy of H2 molecules adsorbed as immobile adsorbates on zeolite cations are higher than expected. The authors of the studies attributed the relatively high adsorbate entropies observed to more degrees of freedom relative to those of a typical adsorbate. Specifically, the translations may not be completely frozen out, and may have been converted to vibrational modes (a frustrated translation can be considered a loose vibration or a “site confined” translation, and might contribute on the order of 10−40 J mol−1 K−1 to the adsorbate entroy).5 Alternatively, the fact that multiple sites were present may have resulted in deviation from the perfect adsorbate assumptions used, resulting in the high apparent entropy observed. While the obtained entropies of H2 molecules adsorbed on zeolite cations are very similar to that of the entropy for liquid hydrogen extrapolated to the same temperature, the infrared data suggest that the H2 molecules are indeed lattice confined on metal cation sites. As can be seen, the distinction between a surface liquid and a loosely bound lattice-confined state may not be easy based on entropy values alone, since the theoretical limit for the entropy of a loosely bound lattice-confined molecule can approach that of a liquid. It is important to point out that the analysis to obtain the experimental entropies for hydrogen adsorbed on zeolites was done assuming a lattice-confined state. If the analysis were performed assuming a 2D gas state (i.e., using a 2D gas standard state), then a different numerical value would be obtained, though the result would still be far lower than the standard entropy expected for a 2D gas. Table 1 shows that the measured entropy for the CH4 surface liquid is below that of CH4(liquid). In general, we would expect a surface liquid for polyatomic molecules to have an entropy lower than the bulk liquid, due to the loss/frustration of some rotations. Physically speaking, a surface liquid at low coverages behaves as a rapidly hopping adsorbate that is weakly adsorbed and constantly changing conformations. In this context, perhaps it is unsurprising that the entropy of a surface liquid might be similar to the theoretical limit of a weakly bound lattice confined adsorbate.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information includes explanations of how to calculate the standard state entropy of 2D gases, 2D liquids, and immobile adsorbates from experimental data. Additionally, recommendations are included for standard states in systems with dissociative adsorption. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 865-576-6311. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. A.S. thanks James Kindt for useful discussions regarding the configurational entropy of immobile adsorbates.

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REFERENCES

(1) Donaldson, D. J.; Ammann, M.; Bartels-Rausch, T.; Poschl, U. Standard States and Thermochemical Kinetics in Heterogeneous Atmospheric Chemistry. J. Phys. Chem. A 2012, 116, 6312−6316. (2) Cox, J. D. Notation for States and Processes, Significance of the Word Standard in Chemical Thermodynamics, and Remarks on Commonly Tabulated Forms of Thermodynamic Functions. Pure Appl. Chem. 1982, 54, 1239−1250. (3) Bruch, L. W.; Diehl, R. D.; Venables, J. A. Progress in the Measurement and Modeling of Physisorbed Layers. Rev. Mod. Phys. 2007, 79, 1381−1454. (4) Jaycock, J.; Parfitt, G. D. Chemistry of Interfaces; E. Horwood: Tyler, TX, 1981. (5) Savara, A.; Schmidt, C. M.; Geiger, F. M.; Weitz, E. Adsorption Entropies and Enthalpies and Their Implications for Adsorbate Dynamics. J. Phys. Chem. C 2009, 113, 2806−2815. (6) Boer, J. H. The Dynamical Character of Adsorption, 2nd ed.; Clarendon P.: Oxford, 1968; pp xvi, 240. (7) Kemball, C. Entropy of Adsorption. Adv. Catal. 1948, 2, 233− 250. (8) Kemball, C.; Rideal, E. K. The Adsorption of Vapours on Mercury. I. Non-Polar Substances. Proc. R. Soc. London, Ser. A 1946, 187, 53−73. (9) Donaldson, D. J.; Anderson, D. Adsorption of Atmospheric Gases at the Air-Water Interface. 2. C-1-C-4 Alcohols, Acids, and Acetone. J. Phys. Chem. A 1999, 103, 871−876. (10) Hansen, R. S.; Baikerikar, K. G. Surface Equations of State in Adsorption from Solution. Pure Appl. Chem. 1976, 48, 435−439.

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SUMMARY When calculating thermodynamic values for adsorbates, such as entropy, it is necessary to first decide whether the adsorbate is freely mobile (2D gas), immobile/hopping, or a surface liquid. If there is no way of knowing whether the adsorbate is freely mobile vs immobile/hopping vs surface liquid, then the adsorption entropy may be calculated assuming each of the cases and compared to theoretical or tabulated values to gain insight into the nature of the adsorbate phase.5 Following a principle of choosing standard states that allow physical insight to be gained from comparison with existing standard state tabulated values, recommendations have been made in this manuscript for various cases of molecules adsorbed on solid surfaces. For 2D gases adsorbed on solid surfaces, the recommended standard state is σ° = 1.39 × 10−7 mol m−2. For immobile adsorbates and nonislanding surface liquids, the recommended standard state is θA° = 0.5 (which 15714

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The Journal of Physical Chemistry C

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NOTE ADDED IN PROOF A paper by Goldsmith entitled "Estimating the Thermochemistry of Adsorbates Based Upon Gas-Phase Properties" was recently published.28 The Goldsmith paper includes a method for estimating the enthalpy, entropy, and heat capacity for adsorbates on metals based upon the energy of adsorption, and may be of interest to readers.

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dx.doi.org/10.1021/jp404398z | J. Phys. Chem. C 2013, 117, 15710−15715