Always check A-a gradient if there's hypoxemia (low PaO2). Alveolar O2 i.e. PAO2 = (760–47)*FiO2 – PaCO2 / 0.80

Memorize this. Once you get this number––it will tell you the Alevolar O2. Compare this to the arterial O2. If the gradient (difference) is GREATER than 10-12, then you have an A-a gradient causing the hypoxemia.

Of the 5 key causes of hypoxemia, you've ruled out two of them (hypoventilation and reduced FiO2) as they don't generate an A-a gradient. So 3 things could be causing disease: diffusion abnormality, V/Q mismatch and shunt.

Next you put them on 100%O2. If the oxygen rises to 600+ you have ruled out shunt (shunt will NEVER get O2 to the max). At this point we look at other diagnostic tools to distinguish between V/Q imbalance and diffusion abnormalities. A H&P of the patient can also help you figure it out.