Compare this description of the alchemist, "A young mans face, ordinary, with full cheeks and the shadow of a beard. A scar showed faintly on his right cheek. He had a hooked nose, and a mat of dense black hair that curled tightly around his ears," (IV: 15) with this one: "Jaqen passed a hand down his face from forehead to chin, and where it went he changed. His cheeks grew fuller, his eyes closer; his nose hooked, a scar appeared on his right cheek where no scar had been before. And when he shook his head, his long straight hair, half red and half white, dissolved away to reveal a cap of tight black curls." (II: 505)
It seems clear that the "alchemist" is Jaqen H’ghar (see 6.2.3 Who is Jaqen H’ghar) in his latest guise. After killing Pate, it seems obvious that he then takes on Pate’s form as we see at the end of the novel (IV: 684) to carry out whatever his purpose is in the Citadel.