Nice problem indeed, thank you. I guess we assume that nitrogen and oxygen mix immediately in the whole volume.
The whole volume is , the proportion of oxygen at time (in minutes) is , so and probably .
During an infinitesimal time interval , the initial volume of oxygen becomes (since is the volume that was taken away, among which a proportion was composed of oxygen). So:
Stated differently, , so that . The proportion hence decreases exponentially fast.