In Sophocles' play Antigone, what is the purpose of the exchange between the Chorus and Chorus Leader?
The purpose of a Chorus Leader was to act as the spokesperson of the Chorus. The Chorus Leader expressed the most critical opinions of the Chorus. They also interacted with the other characters in the play, having critical dialogues (Greek Tragic Drama, faculty.musowls.org).
We see one exchange between the Chorus and Chorus Leader beginning with line 109. This exchange takes place after Antigone informs Ismene of her plans to bury her brother. For both the Chorus and the Chorus Leader, the purpose of their exchange is to give the audience an understanding of the history, so that we know why both of Antigone's brothers are dead. The Chorus waxes lyrical about the army and the battle, while the Chorus Leader zeros in on the most important part of the history--an explanation as to why the brothers battled each other and a statement that Zeus smiled down on neither of their actions and struck them both dead. Because of the Chorus Leader's references to Zeus, we know that morally the Chorus Leader considered both brothers to be guilty. Hence, by zeroing in on the brothers, the Chorus Leader acts as spokes person for the chorus by raising the Chorus's opinion that both brothers were morally wrong.
In all Greek drama, the chorus represents public opinion. In plays such as Antigone, exchanges between Chorus and characters such as Creon reveal what the citizens think. They often discuss the morality of the action performed in the play. If they approve (or disapprove) of the decisions that Creon has made regarding Antigone's death sentence, they voice their feelings (and thereby reflect the opinions of Creon's subjects). In Medea (Robinson Jeffers translation) the chorus is women and since Medea commits a series of acts that are offensive to the Chorus, Medea is acting in defiance of public opinion. In Oedipus Rex, the Chorus recalls the history of Thebes before and after the coming of Oedipus. However, they also give their opinions of all that has happened. Frequently, the exchange between the Chorus and the Chorus Leader is a means of conveying information or background.