My rat makes a rasping noise when breathing.
Is he dying?

Possibly. See above for treatment. Also keep him warm and out of drafts. Nutri-Cal vitamin supplement is great for times like this as the rat might not be eating as well. Note: Some rats will wheeze and rattle from irreparable lung damage. If this is the case treatment may not be indicated. If the rat actually is sick enough to be close to death, then treatment with the suggested drugs is not even close to being good enough. Gentocin injectable (.05cc per pound injected Subcutaneously once daily) is pretty fast acting, and combined with Cefa-Drops (.20cc per pound orally every 12 hours) is a life saver in most cases of severe respiratory infection. You should see improvement within a few days. (Gentocin and Cefa-Drops are mostly available from a vet. )