The effect of the ideal gas law assumption on auto-ignition and NOx-formation in a rapid compression machine is studied. For both processes the simulations are compared to a reference simulation using a Redlich-Kwong equation-of-state based on the critical properties of all constituents. Auto-ignition is studied for several n-heptane/air mixtures and the results show that the ideal gas assumption can impose large deviations. However, only marginal differences (< 7%) appear if the pressure history is used. A simplified theory is presented that explains these observations. For the case of NOx-formation similar observations can be made. Large deviations from the full simulation occur for the case of a prescribed pressure and volume history (approximate to 100%). This, however, is mainly due to the fact that in engine like applications NOx concentrations never reach their equilibrium value. Equilibrium values only differ by a maximum of 20%.