You'd think so. But it's not like euthanising an animal where they inject a tranquiliser then a barbiturate. For a capital crime they use three chemicals. I don't know exactly what they are (varies) or what they do but on at least one occasion the recipient screamed that he was on fire and every vein in his body was burning. It took a long time for him to die.

Capital punishment is meant to be cruel. If it wasn't, they'd simply put the offender to sleep, painlessly, by breathing pure nitrogen.