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, among others. The ignition of stoichiometric hydrogen-air mixtures was studied using 0D numerical simulations with time-dependent specific volume variations. The competition between chemical energy release and expansion-induced cooling was 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 were analyzed near the critical conditions.