What transports oxygen and carbon dioxide across the capillary membrane?

Concentration gradient moves oxygen and carbon dioxide across the alveolar membrane.

Blood that enters the alveolus has a higher concentration of carbon dioxide compared to the air in our lungs; so the carbon dioxide literally falls out of the blood and into the air. Blood that enters the alveolus has a lower concentration of oxygen than the air in our lungs, so the oxygen falls into solution with our blood and is carried back to the heart for distribution to our bodies. This process is passive, meaning that no energy is required for the gasses to move. They are merely seeking to equalize their own concentrations across a semi-permeable membrane. This passive diffusion drives many processes in our bodies.