Classical atomistic simulations are used to compute the enthalpy of vaporization of a series of ionic liquids composed of 1-alkyl-3-methylimidazolium cations paired with the bis(trifluoromethylsulfonyl)imide anion. The calculations show that the enthalpy of vaporization is lowest for neutral ion pairs. The enthalpy of vaporization increases by about 40 kJ/mol with the addition of each ion pair to the vaporizing cluster. Non-neutral clusters have much higher vaporization enthalpies than their neutral counterparts and thus are not expected to make up a significant fraction of volatile species. The enthalpy of vaporization increases slightly as the cation alkyl chain length increases and as temperature decreases. The calculated vaporization enthalpies are consistent with two sets of recent experimental measurements as well as with previous atomistic simulations.