What is the relative humidity of the inspired gas of a patient who is intubated if the humidity deficit is 33 mg/L?

To determine the relative humidity of the inspired gas for an intubated patient when provided with the humidity deficit, it's important to understand what relative humidity represents and how it is impacted by humidity deficit.

In this context, normal inspired air at body temperature (37°C) and at 100% relative humidity holds approximately 44 mg/L of water vapor. The humidity deficit indicates how much moisture is missing from the inspired gas compared to saturated air. If the humidity deficit is 33 mg/L, it means the inspired gas is 33 mg/L less than the maximum capacity of 44 mg/L.

To calculate the actual humidity (in mg/L) of the inspired gas, you subtract the humidity deficit from the maximum:

44 mg/L (saturated at 100% humidity) - 33 mg/L (humidity deficit) = 11 mg/L.

Next, to determine the relative humidity, you take the actual humidity and divide it by the maximum, then multiply by 100 to get a percentage:

(11 mg/L / 44 mg/L) × 100 = 25%.

Therefore, the relative humidity of the inspired gas in this scenario is 25% because it represents a significant reduction from the normal saturation level due to the humidity deficit