Word for when one uses the wrong word in a sentence

It's probably catachresis (although I'm not sure the stipulation that the resulting statement is acceptable English [though with an unintended meaning] holds):

n. 1. The misapplication of a word or phrase, as the use of blatant to mean "flagrant." [AHDEL]

Avoiding the implications of ludicrousness the term that applies is miswording.

miswording n. and adj. misword v. wrong wording or expression; an instance of this (OED).

When someone uses an incorrect word in place of a similar sounding word, it's called a malapropism.

To use your example, if I were to say, I empathize with you, when I mean to say that I sympathize with you, that would be a malapropism.