PROBLEM SESSION ANSWERS: Problem 7

Step 1: Compute the inhaled oxygen concentration

P_I-O2 = 0.21( P_B - P_H2O ) = 0.21 ( 200 - 47 ) = 0.21 x 153 = 32 mmHg

Step 2: Compute the alveolar P_O2 using the alveolar air equation

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

Assuming P_A-CO2 remains normal (as given) and assuming R = 0.8 gives

P_A-O2 = 32 - 40/0.8 = 85 - 50 = -18 mmHg

So O₂ would diffuse out of the blood in the pulmonary circulation.

Clearly, the person would not survive.

But, breathing pure oxygen at that altitude gives

Step 1: Compute the inhaled oxygen concentration

P_I-O2 = 1.00( P_B - P_H2O ) = 1.00 ( 200 - 47 ) = 153 mmHg

Step 2: Compute the alveolar P_O2 using the alveolar air equation for breathing pure oxygen:

P_A-O2 = P_I-O2 - P_A-CO2

Assuming P_A-CO2 remains normal(as given) gives

P_A-O2 = 153 - 40 = 113 mmHg

This P_A-O2 is even higher than when breathing air at sea level.

Clearly, the person could survive without difficulty breathing pure oxygen at this altitude.

Question: How long does the person have to put on the oxygen mask? Answer: about 20 seconds.