Yes, oxygen molecules can travel directly through the phospholipid bilayer of the cell membrane. This movement occurs through a process known as diffusion, which is the natural movement of particles from an area of higher concentration to an area of lower concentration.
The cell membrane is composed of a phospholipid bilayer, which has hydrophobic (water-repelling) interior regions. Oxygen, being a small, nonpolar molecule, can easily pass through this layer without the need for any energy input or specific transport proteins. This is because of the principle that small nonpolar molecules can diffuse freely across cell membranes, while larger or charged molecules often require assistance to cross.
When it comes to the concept of equilibrium, once oxygen has diffused into the cell and the concentrations of oxygen inside and outside the cell are equal, the overall movement of oxygen does not stop. Molecules are always in constant motion due to thermal energy. Therefore, oxygen molecules will continue to move across the membrane but at equal rates in both directions, resulting in no net change in concentration. This phenomenon means that while oxygen can still cross the cell membrane after equilibrium is reached, the rate of entry will be equal to the rate of exit.
In summary, oxygen molecules can directly pass through the phospholipid bilayer through diffusion. Even after reaching equilibrium, they can still cross the membrane, but the rate at which they do so becomes balanced in both directions.