We report the terahertz time-domain spectroscopy (THz-TDS) study of hydrophobic and hydrophilic silica aerogels, and the adsorption of several molecular vapors in the hydrophilic silica aerogel. The hydrophobic and hydrophilic samples have similar but discernible indices of refraction in the frequency range of 0.2-3.0 THz. Below 1.0 THz, the two samples have the same absorption, but starting from 1.0 THz, the absorption of the hydrophilic sample increases more rapidly with frequency. For the hydrophilic aerogel, a strong effect on adsorption is observed by THz-TDS for the vapors of water, heavy water, ammonia, methyl chloride, and methyl fluoride. The surface -OH groups can be replaced by -OD groups by dosing with heavy water, causing the change in the index of refraction and absorption. This replacement can be reversed by dosing the hydrophilic aerogel with water vapor. The volumetric method is used to determine the adsorption amount, which shows that the adsorbed molecules are in the submonolayer form. The equivalent index of refraction and equivalent power absorption coefficient are determined for adsorbed water, ammonia, methyl chloride, and methyl fluoride; for water and ammonia, they are quite different from the corresponding bulk properties. Dosing with hydrogen and carbon monoxide shows no observable adsorption effect.