Final answer:
Small hydrophobic molecules can cross the cytoplasmic membrane without transport proteins due to their compatibility with the membrane’s hydrophobic core. Hydrophilic molecules and ions, however, require transport proteins due to their polarity or charge.
Step-by-step explanation:
The correct answer to which molecules can cross the cytoplasmic membrane rapidly and without the use of transport proteins is small hydrophobic molecules only. The cytoplasmic membrane or plasma membrane is made up of a phospholipid bilayer that creates a barrier to most polar or charged molecules. Small hydrophobic molecules, like gases and lipids, slip through because they can interact with the hydrophobic tails of phospholipids.
In contrast, large molecules, polar or hydrophilic molecules, and ions cannot easily pass through due to their size, polarity, or charge. Ions and hydrophilic substances require specific transport proteins, like channel proteins or carrier proteins, for facilitated diffusion. This is because the hydrophobic core of the membrane repels them or prevents their passage. CO2 and O2 are typical examples of molecules that can rapidly diffuse without assistance.