What has become of Cassio's hope to appeal to Othello through Desdemona by the end of Act III?

Cassio hopes to have Desdemona put in good words for him (to Othello) concerning his position.  Cassio is hopeful that by Desdemona pleading his case, it will help him.  However, he is unaware that Iago has already made him a part of Iago's evil plot to make Othello jealous, although there is actually nothing for Othello to be jealous of.  Desdemona, too, is unaware that by her pleading Cassio's case, she is setting the stage for her own murder by Othello.