Compositional heterogeneities within Europa's ice shell likely impact the dynamics and habitability of the ice and subsurface ocean, but the total inventory and distribution of impurities within the shell are unknown. In sea ice on Earth, the thermochemical environment at the ice-ocean interface governs impurity entrainment into the ice. Here, we simulate Europa's ice-ocean interface and bound the impurity load (1.053-14.72 g/kg [parts per thousand weight percent, or ppt] bulk ice shell salinity) and bulk salinity profile of the ice shell. We derive constitutive equations that predict ice composition as a function of the ice shell thermal gradient and ocean composition. We show that evolving solidification rates of the ocean and hydrologic features within the shell produce compositional variations (ice bulk salinities of 5-50% of the ocean salinity) that can affect the material properties of the ice. As the shell thickens, less salt is entrained at the ice-ocean interface, which implies Europa's ice shell is compositionally homogeneous below~1 km. Conversely, the solidification of water filled fractures or lenses introduces substantial compositional variations within the ice shell, creating gradients in mechanical and thermal properties within the ice shell that could help initiate and sustain geological activity. Our results suggest that ocean materials entrained within Europa's ice shell affect the formation of geologic terrain and that these structures could be confirmed by planned spacecraft observations. Plain Language Summary Europa, the second innermost moon of Jupiter, likely houses an interior ocean that could provide a habitat for life. This ocean resides beneath a 10-to >30-km-thick ice shell which could act as a barrier or conveyor for ocean-surface material transport that could render the ocean chemistry either hospitable or unfavorable for life. Additionally, material impurities in the ice shell will alter its physical properties and thus affect the global dynamics of the moon's icy exterior. That said, few of the interior properties of the ice shell or ocean have been directly measured. On Earth, the composition of ocean-derived ice is governed by the chemistry of the parent liquid and the rate at which it forms. Here, we extend models of sea ice to accommodate the Europa ice-ocean environment and produce physically realistic predictions of Europa's ice shell composition and the evolution of water bodies (fractures and lenses) within the shell. Our results show that the thermal gradient of the ice and the liquid composition affect the formation and evolution of geologic features in ways that could be detectable by future spacecraft (e.g., by ice penetrating radar measurements made by Europa Clipper).