Assuming that the alveolar gas is at a temperature of 37°C, the partial pressure of oxygen in the alveoli can be calculated using the following formula:
PAO2 = (Pb - PH2O) x FiO2
Where:
Pb = total barometric pressure = 645 mmHg
PH2O = partial pressure of water vapor = 47 mmHg (at 37°C)
FiO2 = fraction of inspired oxygen = 0.137
Substituting the values into the formula, we get:
PAO2 = (645 - 47) x 0.137
PAO2 = 84.7 mmHg
Therefore, the partial pressure of oxygen in the alveoli is approximately 84.7 mmHg.