Question

The volume percentage of oxygen in inspired air is \(20%\) and that of expired air is \(16%\). A person is breathing at a rate of 12 breaths per minute. Each breath is 500 ml in volume. The cardiac output is 5 liters per minute. Assuming ideal, healthy lung and cardiac conditions, what is the change in percentage of oxygen in blood over 1 minute? (Round off the answer to one decimal place.)

Hint:

- Use \(\dot V_{O_2}=(F_{I O_2}-F_{E O_2})V_E\) and distribute by cardiac output to get the blood-side percentage change. - Keep units consistent (liters per minute).

Answer 1

Correct Answer: 4.8

Step 1: Minute ventilation \(V_E = 0.5~\text{L}\times 12 = 6~\text{L/min}\). Oxygen uptake per minute (Fick for lungs): \[ \dot V_{O_2} = (F_{I O_2}-F_{E O_2})\,V_E = (0.20-0.16)\times 6 = 0.24~\text{L/min}. \] Step 2: Distribute this \(O_2\) into the blood flow (cardiac output \(Q = 5~\text{L/min}\)). Increase in \(O_2\) volume fraction in blood \[ \Delta % O_2 = \frac{0.24}{5}\times 100% = 4.8%. \] Thus, the oxygen content of blood increases by \(4.8%\) across the lungs per minute.