We demonstrate that the ubiquitously-used Langmuir-Hinshelwood formalism is an incomplete kinetic description and is inappropriate even for catalytic reactions as simple as A + A → A2. The Langmuir-Hinshelwood description is predicated on the Hinshelwood assumption – that all adsorbates are randomly-distributed on the surface. The utility of this approximation is in reducing coverages of multi-site ensembles (e.g. A*–A*) to a product of coverages of constituent single-site ensembles (e.g. A*). For example, the rate of surface reaction between two A* species is rigorously r = krθA*– A* where θA*–A* is the fraction of pairs of sites which contain two A* species. The Langmuir-Hinshelwood formalism simplifies the rate to r = krθA*2 by application of the Hinshelwood approximation – mathematically, that the mean-field metric, μij = θij(θiθj)-1, is unity for all site pairs ij, giving θA*–A* = θA*2. The Hinshelwood approximation, however, crucially neglects the propensity of multi-site steps (e.g. two-site A*–A* → *–* + A2) to engender (i) aggregation (μij &gt;&gt; 1) of slowly-consumed ensembles and (ii) partitioning (μij &lt;&lt; 1) of rapidly-consumed ensembles. For example, Scheme 1 illustrates derivation of the ensemble-specific rate of surface reaction with respect to A*–A* pairs, dθA*–A*/dt, which is characterized by a coverage-dependent stoichiometric coefficient (1 + 6θA*–A*/θA*) that captures spatial coupling unique to the A*–A* ensemble. Per the [A*–A*]-specific stoichiometric coefficient, as many as seven A*–A* pairs are annihilated per surface reaction – engendering partitioning of A*–A* pairs (i.e. μA*–A* &lt;&lt; 1). Configurationally non-ideal phenomena such as A*–A* partitioning are neglected by the Langmuir-Hinshelwood formalism and result in a ‘poorly-mixed’ surface. Poor ‘surface-mixing’ effects profound changes in rates, selectivities, and identities of rate-determining steps incognizable in the Langmuir-Hinshelwood formalism – as we demonstrate in the context of (i) the A + A → A2 reaction and (ii) industrially-relevant catalytic ammonia synthesis.

How to write the rate of A* + A*

ACS Fall 2021

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