The scenario you described, where all air molecules randomly end up on one side of a room, would indeed be a violation of the second law of thermodynamics as commonly understood. The second law states that in an isolated system, the entropy (a measure of disorder or randomness) tends to increase over time or, at best, remains constant. This means that the spontaneous concentration of all air molecules in one side of the room would represent a decrease in entropy, which contradicts the second law.
However, it's important to note that the scenario you mentioned is highly improbable and violates the statistical nature of thermodynamics. The second law of thermodynamics is based on statistical probabilities and describes the behavior of large ensembles of particles rather than individual particles. While it's theoretically possible for individual molecules to momentarily gather on one side due to random fluctuations, the statistical likelihood of all molecules consistently gathering on one side and remaining there is incredibly low.
The second law does allow for temporary and localized decreases in entropy (or apparent violations of the law) as long as the overall entropy of the system and its surroundings increases or remains constant. For example, energy could be expended to deliberately concentrate the air molecules on one side of the room, but in doing so, the energy expended and the increase in entropy elsewhere would compensate for the localized decrease.
In summary, while it's theoretically possible for all air molecules to randomly gather on one side of a room, this scenario would be an extremely rare and temporary fluctuation. In the broader context of thermodynamics and statistical mechanics, the second law remains valid and governs the overall behavior of systems.