The Gunpowder can be found in the Great Wall of China (1593 AD) time period of Time Tangled Island.
It is used to blast open the cave in the time period of the Vikings (831 AD). To put it to use, go in front of the cave with the entrance blocked by a bunch of rocks. Click on the rocks to use your Gunpowder, and the entrance will be cleared. Inside this cave unlocked by the Gunpowder is the Golden Vase.