The Henry's constants of water, carbon dioxide, ethane, ethene, methane, oxygen, and nitrogen are computed in the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF(6)]) using test particle insertion and expanded ensemble Monte Carlo methods. The partial molar enthalpy and partial molar entropy of solvation are also computed for water, carbon dioxide, and oxygen. The results from the simulations are compared against experimental data from the literature. In addition, the accuracy and precision of the two methods in determining the Henry's constant are examined. Local organization of the ionic liquid around a solute molecule is analyzed, and the interactions responsible for the experimentally observed solubility trends are identified.