Originally Posted by
teacher
My bike is only a double.
Blamp 28 called it when he said "You can see a popped chain link in the second picture. My guess is that the chain failed and got caught in the derailleur as it entered the lower wheel
....so my current quandry is whether the chain was properly installed in the first place. "
I doubt that the chain came apart and got caught in the derailer. There's a lot of room between the plates of the derailer arm and the chain. To catch on the arm, the chain would have to be a long way out of place and would likely separate before causing this kind of damage. A chain with a damaged link is very weak. The pin would slip out of place and the chain would separate...especially if you were to put enough torque on the derailer to tear it apart.
If, on the other hand, the chain had caught on itself...like you'd see in a little ring/little cog combination with a chain that is too long...it would still have enough strength to tear the derailer apart. The derailer is folded back on itself in this combination. When the chain catches on itself, the jockey arm could swing backwards and around the rear cluster. Since you don't have a replaceable hanger, the hanger is strong enough to hold on and the next weakest link in the drivetrain breaks. In this case it's the derailer arm. It's more common to have this happen (still rare, however) with a triple but I could see it happening with a double and a short cage derailer.
I would argue that your chain shouldn't have been left that long when the bike was set up but if you were riding in the little/little combination, you are partly culpable. If you weren't in that combination, dropping the chain from the big ring to the little one can cause the derailer to bounce around a lot...especially if the chain is too long. The end result would be the same.