Explain why the steroid hormone estradiol (MW 272) readily crosses membranes by simple diffusion but the much smaller H requires transport proteins

Estradiol has a higher partition coefficient than H+ ions

Explanation

Estradiol is a non-polar and hydrophobic molecule that has a higher partition coefficient than H+ ions, it means that the cell membrane is more permeable to this molecule because it can dissolve in and diffuse within the hydrophobic phase of the membrane. The movement of polar charged molecules (even small H+ ions) requires the input of energy to be able to dissolve within the lipid bilayer. In consequence, the movement of H+ ions requires proteins capable of transporting these protons through the membrane.