OK, I will try myself if nobody else dare.
Humans produce a certain amount of CO2 and uses a certain amount of O2 pr minute, and we need to fill our lungs with the volume of air that contains at least the amount of O2 consumed, and removes the exact amount of CO2 produced. The volumes are therefore more critical for CO2, and I will do the calculation for CO2.

The difference between the amount of CO2 dissolved at venous blood pCO2 (46 mm Hg) and the amount dissolved at arterial pCO2 (40 mm Hg) is approximately 40 ml CO2 pr liter blood. Therefore, we need an amount of air (pr liter of blood) that can take away the excess 40 ml CO2 pr liter blood, but not take away too much, because then the pCO2 in arterial blood would fall below 40 mm Hg (which our biochemistry doesn’t like). In other words, we would like the amount of air that dilutes 40 ml 100% CO2 down to 5.3% CO2 (which corresponds to 40 mm Hg). 40 ml CO2 in 800 ml air gives 5% CO2 (which is close enough for this demonstration). Therefore, for each liter of blood through the lungs (giving off 40 ml CO2) we need 800 ml of air to dilute the CO2 down to ~5% (or 40 mm Hg).