Figuring out whether to use “that” or “which” can be tricky. Strunk and White states “that” is a defining, or restrictive, pronoun, while “which” is nondefining, therefore, nonrestrictive.
Restrictive clauses limit the focus to identify a certain noun.
Nonrestrictive clauses add extra information about one, and only one, noun.
The definitive illustration appears on page 59 of Strunk and White.
“The lawnmower that is broken is in the garage. (Tells which one.)
The lawnmower, which is broken, is in the garage. (Adds a fact about the only mower in question.)”
And here is my example of a sentence with a nonrestrictive clause.
The Chicago Bears’ offensive line, which showed itself to be weak and ineffective, contributed to Sunday’s loss.
(There is only one Chicago Bears’ offensive line discussed in the sentence, to the great disdain of many fans.)
I think I like the lawnmower example better. At least I do not have any emotional investment in it.