We have studied the kinetics of spontaneous capillary rise and of the concurrent vapor adsorption in nanoporous, monolithic samples of Vycor glass with a mean pore diameter of 7.5 nm. As liquids, we have chosen n-alcohols (n=4-10) whose vapor pressures at room temperature range from p_{0}=965 Pa down to p_{0}=0.743 Pa. Dielectric measurements allow us to achieve spatial selectivity to predefined parts of the porous Vycor glass. In this way, we are able to measure the overall uptake of molecules as well as vapor adsorption from the surroundings in unfilled parts of the pore network, i.e., above the liquid menisci of the rising imbibition front. We show that the latter process is unaltered compared to free adsorption in samples suspended above a liquid reservoir. Only at low vapor pressures, i.e., for long alcohols, vapor adsorption can be neglected and the capillary rise follows the theoretical predictions of the Lucas-Washburn sqrt[t] law. The more volatile the alcohol, the more important the additional adsorption of molecules becomes. We show that the overall filling process in the pore network is well described by a superposition of the Lucas-Washburn law and the measured vapor adsorption. In addition, the experiments give insight into the vapor diffusion dynamics in the porous matrix.