Explosivity of rhyolite domes depends on bubble nucleation and growth. To understand these processes, we measure millimeter-scale variations in H2O by synchrotron Fourier transform infrared (FTIR) spectromicroscopy on interlayered obsidian-pumice samples. The H2O contents of all samples are above the 1-atm solubility value (~0.10 wt.%) and decrease systematically towards vesicular zones, indicating that gas bubbles were growing and that degassing of melt to atmospheric pressure was incomplete. H2O profiles are compared with models for water diffusion in order to constrain the temporal scale of vesiculation. Diffusion timescales range from 0.4 to 15 days, and represent the time between bubble nucleation and quenching. We use these results to estimate the duration of volatile exsolution and evaluate the timing of the formation of explosion pits frequently found on the surfaces of obsidian domes, though never witnessed.