* This morning: This is an adverbial phrase, not a prepositional phrase.
* through the hallway: This is a prepositional phrase (preposition: "through," object: "the hallway").
* so that: This is a conjunction, not a prepositional phrase.
* to his classroom: This is a prepositional phrase (preposition: "to," object: "his classroom").
Therefore, there are two prepositional phrases in the sentence.