Is there a problem of Chometz with Smoking on Pesach?
See here even the Mishnah Berurah disallows tabaco PDF of Chometz and Smokiing
The Lubavitcher Rebbe reports that the Previous Rebbe said that the Rebbe Rashab (the fifth Lubavitcher Rebbe) would smoke on Pesach after the Afikoman.
The Rebbe Rashab also requested from his son (the previous Lubavitcher Rebbe) to bring him cigarettes for Pesach.
However, the bulletin put out by the Crown Heights Beis Din warns that people have found Chometz in cigarettes lately, so one should avoid them.
Just about any food, personal care, or medical product is required to reveal far more about its formulation than cigarettes do. So it's incredibly hard to tell what they're putting in there.