Final answer:
Desdemona asks the Duke for his blessing to her union with Othello in Act I, Scene III of Othello.
Step-by-step explanation:
Desdemona asks the Duke for his blessing to her union with Othello. This can be seen in Act I, Scene III of Othello, where Desdemona says, "That I may profess due gratitude / For requited love which endures not mine / To him, and Heaven defend your good souls that / You think I will your serious and great business scant / When he himself will his full fortune make / And during his vocal cuckold with exultation / Breeds brats of doubts and reconciled faces".