Angra Mainyu puts it perfectly. Also, chewing gum on an empty stomach is bad for you as it creates more stomach acid without the food for it to act on, which can give rise to ulcers. Id doubt it'd harm you as a one off, but meh.
After your fast, take a moment to ponder on how cleansed you feel for not having eaten for 24 hours. It will feel great. Apparently going on more ambitious fasts is a very fulfilling experience too.