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.)
This solution details the steps to calculate the change in the percentage of oxygen in the blood based on respiration and cardiac output.
Inspired Oxygen = Breathing Rate × Tidal Volume × Percentage of Oxygen Inspired
Inspired Oxygen = $12 \text{ breaths/min} \times 500 \text{ ml/breath} \times 0.20 = 1200 \text{ ml/min}$
Expired Oxygen = Breathing Rate × Tidal Volume × Percentage of Oxygen Expired
Expired Oxygen = $12 \text{ breaths/min} \times 500 \text{ ml/breath} \times 0.16 = 960 \text{ ml/min}$
Oxygen Consumed = Total Inspired Oxygen - Total Expired Oxygen
Oxygen Consumed = $1200 \text{ ml/min} - 960 \text{ ml/min} = 240 \text{ ml/min}$
This represents the amount of oxygen removed from the blood circulation by the body's tissues each minute.
The question asks for the change in the percentage of oxygen in the blood over 1 minute. This is interpreted as the proportion of the total blood circulated (cardiac output) that carries the oxygen consumed by the tissues.
Cardiac Output = $5 \text{ liters/min} = 5000 \text{ ml/min}$
The oxygen consumed ($240 \text{ ml/min}$) is transported by the blood pumped by the heart.
Percentage Change = $ \frac{\text{Oxygen Consumed}}{\text{Cardiac Output}} \times 100\% $
Percentage Change = $ \frac{240 \text{ ml/min}}{5000 \text{ ml/min}} \times 100\% $
Percentage Change = $ 0.048 \times 100\% = 4.8\% $
The change in the percentage of oxygen in the blood over 1 minute is $4.8\%$.