Fick’s law of diffusion
There are a number of factors that influence the rate of diffusion of gas through the alveolar/capillary interface, governed by Fick’s law of diffusion, which states that the volume of gas per unit time moving across the alveolar-capillary barrier is directly proportional to the surface area of the barrier, the diffusivity, and the difference in concentration between the two sides, but is inversely proportional to the barrier thickness. In equation form, it is described as the following:
Vgas = [A x D x (P1-P2)] / T
Where Vgas is the volume of gas diffusing per unit time A is the surface area, D is the diffusivity, (P1-P2) is the partial pressure difference across the barrier, and T is the barrier thickness.
When you exercise, there are more alveoli recruited for gas exchange, therefore the surface area available for gas exchange increases, and thus the rate of diffusion of gases such as oxygen will increase.