  Amorphous ice has long been invoked as a means for trapping extreme volatiles
into solids, explaining the abundances of these species in comets and planetary
atmospheres. Experiments have shown that such trapping is possible and have
been used to estimate the abundances of each species in primitive ices after
they formed. However, these experiments have been carried out at deposition
rates which exceed those expected in a molecular cloud or solar nebula by many
orders of magnitude. Here we develop a numerical model which reproduces the
experimental results and apply it to those conditions expected in molecular
clouds and protoplanetary disks. We find that two regimes of ice trapping
exist: `burial trapping' where the ratio of trapped species to water in the ice
reflects that same ratio in the gas and `equilibrium trapping' where the ratio
in the ice depends only on the partial pressure of the trapped species in the
gas. The boundary between these two regimes is set by both the temperature and
rate of ice deposition. Such effects must be accounted for when determining the
source of trapped volatiles during planet formation.
