Equilibrium Constants and Rate Constants for Adsorbates: Two-Dimensional (2D) Ideal Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator Models

The thermodynamic state functions and partition functions for adsorbates on solid surfaces are often treated with two-dimensional (2D) ideal gas and 2D ideal lattice gas models. These are idealized limits of the real situation for adsorbates on solid surfaces, which are more accurately described as hindered translators. We describe a simple extension of the ideal 2D gas model to a more realistic ideal hindered translator model based on our recent approximation for the partition function of ideal hindered translators [Sprowl et al., J. Phys. Chem. C., 2016, DOI: 10.1021/acs.jpcc.5b11616]. Expressions for equilibrium constants and rate constants within transition-state theory (TST) are derived in a self-consistent formalism based on both partition functions and standard-state entropies. The mixing of these three adsorbate models (ideal 2D gas, ideal 2D lattice gas, and ideal hindered translator) within the same equilibrium or rate constant calculation is sometimes necessary but requires careful and consistent choices of standard-state concentrations. The formalism used here facilitates such mixing, using activities instead of concentrations to do so, and also to enable inclusion of nonidealities. We propose a standard state for 2D (and one-dimensional) ideal gases defined such that their translational entropy is 2/3 (or 1/3) that for the corresponding ideal three-dimensional (3D) gas, which offers intuitive advantages for estimating equilibrium and rate constants. This sets the standard-state concentration of the ideal 2D gas to be approximately the 2/3 power of the standard-state concentration of the corresponding 3D ideal gas (i.e., the concentration at 1 bar pressure). We show that in the derivation of the TST rate of elementary steps for ideal 2D lattice gases, the concentration of the transition state often increases as the adsorbate's activity, theta/(1 - theta), rather than simply as theta, the fractional population of sites, and discuss the implications of this result.