PAO2 = FIO2(PATM - PH2O) - PACO2 / RQ
Understand the Problem
The question relates to the calculation of the partial pressure of alveolar oxygen (PAO2) using given physiological parameters, which includes atmospheric pressure, water vapor pressure, and partial pressure of carbon dioxide. The task involves applying the formula provided to understand how these variables interact.
Answer
The partial pressure of alveolar oxygen is approximately $99.73$ mmHg.
Answer for screen readers
The partial pressure of alveolar oxygen ($PAO_2$) is approximately $99.73$ mmHg.
Steps to Solve
- Identify Given Values
From the problem, the known values are:
- Fraction of inspired oxygen ($FIO_2$): 0.21
- Barometric pressure ($PATM$): 760 mmHg
- Water vapor pressure ($PH_2O$): 47 mmHg
- Partial pressure of carbon dioxide ($PACO_2$): 40 mmHg
- Respiratory quotient ($RQ$): 0.8
- Plug Values into the Formula
Using the provided formula for partial pressure of alveolar oxygen: $$ PAO_2 = FIO_2 \cdot (PATM - PH_2O) - \frac{PACO_2}{RQ} $$
Insert the values: $$ PAO_2 = 0.21 \cdot (760 - 47) - \frac{40}{0.8} $$
- Calculate the Terms Inside the Parentheses
First, calculate the term in the parentheses: $$ 760 - 47 = 713 \text{ mmHg} $$
- Calculate the First Part
Compute the first part of the equation: $$ 0.21 \cdot 713 = 149.73 \text{ mmHg} $$
- Calculate the Second Part
Now, compute the second part: $$ \frac{40}{0.8} = 50 \text{ mmHg} $$
- Combine the Results
Finally, substitute both results back into the equation: $$ PAO_2 = 149.73 - 50 = 99.73 \text{ mmHg} $$
The partial pressure of alveolar oxygen ($PAO_2$) is approximately $99.73$ mmHg.
More Information
This calculation demonstrates how to determine the alveolar oxygen pressure using physiological parameters. Understanding the influences of atmospheric and partial pressures on gas exchange is crucial in respiratory physiology.
Tips
- Confusing units (e.g., mmHg vs. torr): Always ensure you are using consistent units throughout your calculations.
- Not following the order of operations: Make sure to handle calculations in the correct sequence.
- Misplacing decimal points: Double-check each step to avoid calculation errors.
