A better understanding of chemical kinetics under volumetric expansion is important for a number of situations relevant to industrial safety including detonation diffraction and direct initiation, reflected shock-ignition at obstacles, ignition behind a decaying shock, etc. In the present study, the ignition of stoichiometric hydrogen-air mixtures has been studied using 0-D numerical simulations with time- dependent specific volume. The competition between chemical energy release and expansion-induced cooling has been characterized for different cooling rates and mathematical forms describing the shock decay rate. The critical conditions for reaction quenching were systematically determined, and the thermo-chemistry dynamics has been analyzed near the critical conditions.