Whales
can't breathe through their mouths. Their nostrils are on top of their heads:
what's called the "blowhole" is really the whale's nostrils. The "spout"
the whale sends up is a plume of condensate from its breath as it exhales. The
pattern of the spout varies with whale species, and old-time whaling men could
tell a sperm whale from a right whale, and so forth by the pattern of its exhalation,
or "blow."
The blowhole is isolated anatomically from the pharynx. There's a direct connection between the blowhole and the trachea, and a whale, unlike a dog or a human, can't choke on his food by aspirating it.
The weirdest thing about this arrangement is that in at least some species, the trachea can be detached from the ventral side of the blowhole. The upper end of the trachea fits into a muscular sphincter, and the whale can apparently pop it loose and put it back if he wants to! The first time I saw this I almost didn't believe it; I was assisting at a post-mortem on a pygmy sperm whale, and the pathologist showed it to me. I was flabbergasted. Not until I'd pulled it out and put it back several times did I accept it as fact. It just goes to show you that we don't have to find life on other planets to see weird stuff, we have plenty of it here on Earth.
Needless to say, "breathing through the mouth" is a bit of a misstatement anyway. Non-cetaceans really breathe through the trachea, and take in the air that passes into the pharynx from the nose or the mouth.