Final answer:
The cell and mitochondrial membranes are permeable to gases like oxygen and carbon dioxide due to the ability of these small, non-charged molecules to freely diffuse across the lipid bilayer without the aid of transport proteins.
Step-by-step explanation:
The cell membrane and the mitochondrial membrane are permeable to gases such as oxygen (O₂) and carbon dioxide (CO₂). This is known because these gases can diffuse across a cell membrane through a process known as simple diffusion. Oxygen tends to diffuse into the cell because its concentration is usually lower inside the cell due to cellular metabolism. Conversely, carbon dioxide, which is produced as a metabolic byproduct, has a higher concentration inside the cell and thus diffuses out of the cell where its concentration is lower.
This diffusion happens due to the lipid bilayer's characteristics that make up the cell and mitochondrial membranes. Small, non-charged molecules like these gases can pass freely through the membrane without assistance. However, most other molecules, including those charged or large in size, require transport proteins to facilitate their movement across the membrane, through mechanisms like facilitated diffusion or active transport using energy in the form of ATP.