Which two factors of a molecule determine whether or not it can cross the membrane? a. color and weight b. shape and texture c. mass and speed d. polarity and size

D. Polarity and size. 
The size, polarity, and charge of a substance will determine whether or not the substance can cross the cell membrane by diffusion. The cholesterol was an example of a lipid, and is highly soluble in the nonpolar environment of the lipid bilayer. You saw, in the animation above, the cholesterol freely passing into the hydrophobic environment of the membrane. Cholesterol distributes freely in the membrane and then some fraction will dissolve in the aqueous environment of the cytoplasm. Water, on the other hand, while polar, is small enough to cross the membrane at a slow rate. Note that specialized transport proteins in certain cell membranes can provide a channel for the water, greatly increasing its rate of crossing the membrane. The lipid bilayer is much less permeable to the ion, because of its charge and larger size. As a general rule, charged molecules are much less permeable to the lipid bilayer.