Non-statistical recrossing in ketene cycloadditions with alkenes, heavy-atom tunneling and the mechanism of the decarboxylation of Mandelylthiamin is investigated in this dissertation. A combination of experimental kinetic isotope effects and theoretical models and kinetic isotope effects is utilized for this endeavor. This dissertation also describes how the use of quasiclassical dynamic trajectories, microcanonical RRKM calculations, and canonical variational transition state theory in combination with small-curvature tunneling approximations is utilized to help advance our research methodology to better understand mechanism. In the cycloaddition of dichloroketene with cis-2-butene, significant amounts of recrossing is observed using quasiclassical dynamic trajectories. An unusual inverse 13C intramolecular KIE lead us to investigate the role that heavy atoms play in non-statistical recrossing. More importantly, this discovery has uncovered a new phenomena of entropic intermediates that not only applies to ketene cycloadditions, but can also be applicable to other "concerted" reactions such as Diels-Alder reactions. The ring-opening of cyclopropylcarbinyl radical has revealed that heavy-atom tunneling plays a major role. The intramolecular 13C kinetic isotope effects for the ring-opening of cyclopropylcarbinyl radical were unprecedentedly large and in combination with theoretical predictions and multidimensional tunneling corrections, the role of tunneling in this reaction can be better understood. The mechanism decarboxylation of mandelylthiamin has been extensively studied in the literature. However, until the use of theoretically predicted KIEs and theoretical binding motifs the rate-limiting step of this reaction has been hotly debated. In this dissertation, a discussion of how the theoretical KIEs indicate the initial C-C bond as the rate-limiting step and chelating binding motifs of pyridinium and mandelylthiamin to explain the observed catalysis is given.