Example 1

A patient breathing air has an alveolar carbon dioxide partial pressure of 40 mmHg.  Is his alveolar oxygen normal?

First step:  Solve for P_I-O2

P_I-O2 = F_I-O2 x ( P_B - P_H2O )

P_I-O2 = 21% x (760 - 47) = 150 mmHg  

Note:  47 mmHg is the partial pressure of water vapor

Second step:  Use the alveolar air equation to solve for P_A-O2

Note: assume R = 0.8 unless otherwise stated

P_A-O2 = P_I-O2 - P_A-CO2/R

P_A-O2 = 150 - 40/0.8 = 150 - 50 = 100 mmHg

Answer:  Yes, his alveolar oxygen is normal.

Example 2

Suppose a patient is given a mixture of 50% Nitrous Oxide (a sedative gas) and 50% air to breath.  Will he become hypoxic?  (Assume alveolar CO₂ remains at 40 mmHg)

First step:  Solve for P_I-O2

P_I-O2 = F_I-O2 x ( P_B - P_H2O )

P_I-O2 = 10.5% x (760 - 47) = 75 mmHg  

Second step:  Use the alveolar air equation to solve for P_A-O2 

Note: assume P_A-CO2 = 40 mmHg and R = 0.8 unless otherwise stated

P_A-O2 = P_I-O2 - P_A-CO2/R

P_A-O2 = 75 - 40/0.8 = 75 - 50 = 25 mmHg

Answer:  He will become very hypoxic and might not survive.

Alternative:  Give a mixture of 50% Nitrous Oxide and 50% Oxygen.