It doesn't actually explode, it just releases the CO2 in the Coke rapidly. There was a great discussion of this on the Absolute Science Podcast. Surface tension, the attraction between water molecules in the soda, keep the dissolved CO2 dissolved, and as the temperature of the soda increases, the soluability of the CO2 decreases, which is why the bubbles form and soda goes flat. Mentos breaks the surface tension in the water and releases the CO2 very fast because it has lots of surface imperfections for the CO2 to nucleate bubbles on them. The Mentos also contains oils (coconut oil and gum arabic), which also lends to the reaction because the oil repels the water, and the water is attracted to other water molecules.
Mythbusters also did a show on it, but I missed that.
However, this reaction is nowhere near powerful or sudden enough to do any damage to a plane, unless you spill it on the controls.

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Mentos+Coke= Explosives
Wait, so something in the mentos combines with the coke right? Could you explain what chemicals exactly in the mentos that caused this? I'm just curious.
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