Can a Soul be Delivered from Hell through Our Prayers?

Like heaven, hell is an eternal state, so prayers cannot help the souls there. The Catechism of the Catholic Church states:

The teaching of the Church affirms the existence of hell and its eternity. Immediately after death the souls of those who die in a state of mortal sin descend into hell, where they suffer the punishments of hell, “eternal fire.” The chief punishment of hell is eternal separation from God, in whom alone man can possess the life and happiness for which he was created and for which he longs. (CCC 1035)

Since souls in heaven also have no need for our prayers, only those in purgatory are helped by prayers for the dead.