This is the 15357th most frequent Polish word.
smogiem
"Smogiem" is the instrumental case of "smog," meaning "with smog" in English.
In this sentence, 'smogiem' is used as an instrument noun form ('with smog'), showing the means by which the sky is polluted.
Niebo nad miastem jest zanieczyszczone smogiem.
The sky above the city is polluted with smog.
Here, 'smogiem' functions as a direct object in an instrumental case, specifying what is being breathed and indicating the effect it has.
Oddychając smogiem, narażamy nasze zdrowie.
By breathing smog, we endanger our health.
In this usage, 'smogiem' acts as an objective reference in an instrumental case, emphasizing the entity against which efforts are directed.