Final answer:
The best determining factors for whether a molecule crosses a cell membrane are its polarity and concentration gradient. This is because the cell membrane's selective permeability and structure primarily allow nonpolar molecules to pass through easily, while polar molecules often require transport proteins. Temperature also has an effect on the membrane's fluidity and therefore the rate of passive transport.
Step-by-step explanation:
The question of which best determines whether a molecule crosses a cell membrane is addressed through understanding how cell membranes function. Cell membranes are described by the fluid mosaic model and are selectively permeable due to their structure, allowing them to control the movement of substances in and out of the cell. The membrane's lipid bilayer is hydrophobic and permits nonpolar molecules to easily diffuse through. However, polar molecules and ions require assistance from transport proteins due to the hydrophobic nature of the membrane's interior. Passive transport, such as diffusion, operates without energy and moves molecules from an area of higher to lower concentration, while facilitated transport employs specific proteins to aid polar molecules like glucose across the membrane.
Therefore, the factors most relevant to whether a molecule can cross a cell membrane are its polarity and the concentration gradient present, rendering option D the best answer. Additionally, the temperature can influence the fluidity of the membrane and hence affect passive transport across it.