How much oxygen does he need?

      
   

 

      
      So the patient has a PaO2 of 41mmHg on FiO2 of 40% or, more accurately 0.4

You need to figure out his alveolar to arterial (A - aO2) oxygen gradient:

This is calculated by PAO2 = PiO2 - PaCO2 / R where PiO2 = the partial pressure of inspired Oxygen (barometric pressure - water vapor pressure multiplied by the FiO2: 760mmHg - 47mmHg x 0.4 = 285.2) R is the respiratory quotient, which is the amount of carbon dioxide produced for every molecule of oxygen consumed - usually about 0.8)

Inserting this patient's information into the equation:
PAO2 = 285.2 - 25/0.8 = 265.2
The Alveolar to arterial oxygen gradient is thus a whopping 225.2mmHg (PAO2 - PaO2)

To calculate the inspired oxygen tension that will lead to a PaO2 of 60mmHg, we just add 60 to 225.2 = 285.2 and work backways through the equation, where FiO2 is the required quantity:

PAO2 = (713 x FiO2) - PaCO2 /R - rearranged as  FiO2 = (PAO2 + PaCO2 / R ) / 713
Inserting the data: FiO2 = 285.2 + 20/713 = 43%

The patient requires an FiO2 of 0.43 to achieve a PaO2 of 60mmHg