Equilibrium constant differential equations (ECDEs) are derived for several nanoconfined elemental bimolecular reactions, one termolecular reaction, and nanoconfined adsorption, in the framework of statistical mechanics. The ECDEs that complement the well-known equations of macroscopic systems are based on an original generalized expression for the equilibrium constant, which takes into account limited numbers of molecules by replacing the thermodynamic limit exponentiation with their falling factorials. Solving the ECDE numerically or analytically furnishes the reaction extent and its variance and skewness as functions of these numbers and the equilibrium constant. This new theoretical computational methodology fills a gap in our previous studies of the "nanoconfinement entropic effect on chemical equilibrium"(NCECE) by providing a consistent and convenient alternative to derivations based on direct employment of the system size-specific canonical partition functions. While the latter becomes more complex and time-consuming with increased numbers of molecules, the ECDE-based computations are equally efficient for small and larger numbers of reacting molecules. The methodology introduced here is confirmed by complete agreement with the partition function-based computations. As compared to binary reactions, application of the new methodology to termolecular reactions reveals a significantly greater NCECE-enhanced extent of product formation, especially for small numbers of nanoconfined molecules.