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Reply to Comment: “Equilibrium Constants and Rate Constants for Adsorbates: 2D Ideal Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator Models” Charles T Campbell, Lynza H. Sprowl, and Líney Árnadóttir J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07756 • Publication Date (Web): 15 Aug 2016 Downloaded from http://pubs.acs.org on August 21, 2016
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Reply to Aditya Savara’s Comment on: “Equilibrium Constants and Rate Constants for Adsorbates: 2D Ideal Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator Models” Charles T. Campbell1,* Lynza H. Sprowl2, and Líney Árnadóttir2,** 1. Department of Chemistry, University of Washington Seattle, WA 98195-1700 USA 2. School of Chemical, Biological and Environmental Engineering Oregon State University Corvallis, OR 97331-2702 USA
We are glad that Savara has made these comments1, as they address some issues that are confusing even to experts in the field. Our paper has over eighty equations, and it is difficult for anyone to keep track of all the details. It appears to us that his comments are based on his missing or misunderstanding some of these details, and we appreciate this opportunity to restate and clarify these important details for the community. Perhaps these details should have been reiterated in our paper, so that they would come through more clearly. However, nothing in Savara’s Comment moves us to change what we wrote in our paper about standard state entropies for adsorbates. We respond only to clarify what he has stated in his Comment and to correct some of his incorrect statements about our paper. Savara writes: “Campbell et al.1 argued that a specified relative coverage should be used for the 2-D lattice confined adsorbate, based on the idea that such a choice will cause some terms to cancel out when comparing entropies of the 2-D gas standard state and the 2-D lattice confined standard state. The relative coverage specified by Campbell et. al.1 is θ° = 0.012.” That is not true. We said that one should choose a standard-state coverage for a 2D lattice gas that is the same (in units of adsorbates per unit area) as the standard-state coverage one would use for an 2D ideal gas, which depends upon the temperature. Even for the same temperature, if expressed in units of adsorbates per site (fractional coverage), our recommended standard state coverage will also depend on the site density. The value of θ° = 0.012 that we used was only an example value, for the specific case of 1015 sites cm-2 and 298 K. To quote from our paper2:
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“This comparison suggests another logical choice for the standard state concentration of adsorbed 2D lattice gases: That is, to define it as the same number of adsorbates per unit area as the standard state concentration of ideal 2D gases (i.e., the value (N/A)0 given by Eqs. (7)), so that θ0 = (N/A)0/(M/A), or θ0 = 0.012 at 298K if M/A = 1015 cm-2). Doing this sets the contributions of surface concentration to the standard-state molar entropies of ideal 2D lattice gases and ideal 2D gases to be essentially equal. This is perhaps preferable to using θ0 = ½ as done most frequently. This standard state has the added advantages that it is in the linear regime of Fig. 2, and at such low coverage that ideal behavior is more likely to occur.”
Thus, it is also not true when Savara writes: “There are two shortcomings associated with Campbell’s method for specifying the 2-D lattice confined standard state: 1) the coverage of θ° = 0.012 was chosen by Campbell et al. "arbitrarily" based on using a value of 1015 sites cm-2 -so the 0.012 coverage does not enable appropriate general comparison for the same adsorbate on different surfaces nor different adsorbates on the same surface, since the saturation densities will not generally be 1015 sites cm-2.” Savara goes on to write: “2) such a choice confuses the issue because Campbell is trying to cancel part of the translational entropy of the 2-D gas term with a spatial configurational entropy of the immobile adsorbate.” We were not trying to cancel anything here. We are simply saying that, since both the ideal 2D gas and the ideal 2D lattice gas have a concentrationdependent contribution to their entropies that is large but essentially exactly the same at all coverages (except above 0.1 fractional coverage), it is therefore convenient to choose the same concentration as the standard-state concentration for both 2D gas and 2D lattice gas models. This allows one to more easily compare standard-state entropies between different classes of adsorbates, since such differences are then only due to other reasons besides concentration differences. This became very important when we developed the hindered-translator model for adsorbates, since this choice of standard concentrations allows one to follow the standard-state entropy of an adsorbate treated as a hindered translator as it smoothly goes between these two limits (2D lattice gas at high diffusion barrier relative to kT, and 2D ideal gas when the diffusion barrier is low compared to kT), without any abrupt change due to some arbitrary change in standard concentration between these two limits. Future scientists who use the more accurate hindered-translator model (which works at both limits but also at intermediate temperatures) will
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want to compare standard-state entropies calculated using it to those from the 2D lattice gas and 2D ideal gas models. It is by far easiest to understand such comparisons when the concentrationdependent part is the same in all three models. We note that our introduction of a hindered translator model that transitions smoothly from the 2D lattice gas to the 2D ideal gas models2, 3 surely must challenge Savara’s claim that “The standard states should thus be chosen independently for a 2-D lattice confined adsorbate and a 2-D gas adsorbate.” Although the first several paragraphs of Savara’s comments make it sound like there is a big difference between our preferred standard-state concentration for 2D ideal gases and his choice for that, they only differ by a constant factor of 1.40. We prefer a standard state for such an adsorbate whereby its translational entropy is 2/3 that for the standard state of the corresponding 3D ideal gas at the same temperature. Savara claims that he makes the same choice, but he does not really make that same choice. Since an ideal 3D monatomic gas (in its ground electronic and nuclear states) has only translational degrees of freedom, its translational entropy is the entire entropy given by the full Sackur-Tetrode equation. It is clear from his comment that Savara does not agree with this, but instead thinks that one must subtract his “nRln(e)” term from the full Sackur-Tetrode equation to get the translational part. We disagree, but note that this is not very important, since it changes our preferred standard-state concentration by only a constant factor of 1.40. We wrote in our original paper, “Note that the Sackur-Tetrode equation used here is derived using only the translational partition function38 and therefore gives translational entropy only.” It appears that Savara disagrees with this, and
maintains instead that it contains some other type of entropy. We do not understand what type of entropy that might be. Acknowledgment is made to the donors of the American Chemical Society Petroleum Research Fund for support of this research. References: 1.
Savara, A., Comment on “Equilibrium Constants and Rate Constants for Adsorbates: 2D Ideal
Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator Models”. J. Physical Chemistry C submitted. 2.
Campbell, C. T.; Sprowl, L. H.; Arnadottir, L., Equilibrium Constants and Rate Constants for
Adsorbates: Two-Dimensional (2D) Ideal Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator 3 ACS Paragon Plus Environment
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Models. Journal of Physical Chemistry C 2016, 120, 10283-10297. ://WOS:000376417500021. 3.
Sprowl, L. H.; Campbell, C. T.; Arnadottir, L., Hindered Translator and Hindered Rotor Models
for Adsorbates: Partition Functions and Entropies. Journal of Physical Chemistry C 2016, 120, 97199731. ://WOS:000375969000021.
* Corresponding author. Email:
[email protected], tel. = 206-616-6085 ** Corresponding author. Email:
[email protected] 4 ACS Paragon Plus Environment
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