The gases travel faster when they are bound to hemoglobin.
By competing for hemoglobin, the carbon dioxide can force the oxygen into the tissues. At the lungs, the oxygen forces the carbon dioxide off of this molecule so that it can be released into the air.
This helps the blood pull oxygen into the blood from the air and carbon dioxide into the blood from the tissues.
By removing the oxygen and carbon dioxide from solution in the plasma, a gradient for these gases can be maintained to favor diffusion.