Hi-
I'm not sure I can get you the exact answer because there is not quite enough information, but I can at least get you most of the way there.
The thing you need to do is to first calculate alveolar PO2 (PAO2), then you need to subtract arterial PO2 (PaO2).
To calculate PAO2, you should use the alveolar gas equation:
PAO2 = PIO2 - PCO2/R; PIO2 is the PO2 of inspired air and R is the respiratory exchange ratio (they usually tell you what R is; I'll just use a typical value of 0.8; you can also try an R of 1 to calculate things faster).
For this question, I'm also going to assume the patient is at sea level, where the barometric pressure (PB) is 760 mmHg. The partial pressure of O2 at sea level is FIO2 x PB. However, when air is in the upper airways, it is warmed and moistened and water vapor pressure is 47 mm Hg. So, the dry gas pressure in the airways is PB - 47 mm Hg. Therefore,
PIO2 = FIO2 x (PB - 47 mm Hg). In this case, the FIO2 is 1.0, so
PIO2 = 1.0 x (760 mm Hg - 47 mm Hg) = 713 mm Hg. Now just plug everything into the alveolar gas equation:
PAO2 = 713 mm Hg - 49 mm Hg/0.8 = 652 mm Hg; If the PaO2 is 95 mm Hg, then,
PAO2 - PaO2 = 652 mm Hg - 95 mm Hg = 557 mm Hg. Considering there should be almost no difference in a healthy person, this person does seem to have lung disease.
So, the take home point is: use the alveolar gas eqn. to calculate PAO2, then substract PaO2.
Answer courtesy of MedTutor.com
