  Equilibrium Constant Differential Equations (ECDE) are derived for several
nanoconfined elemental bimolecular reactions in the frameworks of statistical
mechanics and the ideal gas model. The ECDEs complement the well-known
equilibrium-constant ordinary equations that are used for macroscopic systems.
Solving the ECDE numerically or analytically furnishes the average reaction
extent, as well as its variance and skewness. This original
theoretical-computational methodology fills the gap in studies of nanochemical
equilibrium providing a consistent and convenient alternative to derivations
based on direct employment of the canonical partition-functions. Whereas the
latter become more complex and time-consuming with increased number of
molecules, the ECDE-based computations are equally efficient for small as well
as large numbers of nanoconfined reacting molecules. The ECDE methodology
introduced here is confirmed by a complete agreement with partition-function
computations. In addition, the new approach is applied to nanoconfined
adsorption.
