Alma uses the idea of physical death to create a way of describing the second effect of the fall. Physical death (our first death) is a separation of body and spirit. The second “death” also refers to a separation, but of the unrepentant from God’s presence. This death occurs at the time of the judgment when the unrepentant person stands before God and God righteously precludes such a one from his presence.
“Things pertaining unto righteousness” would be the repentant soul’s welcome into heaven, the location of righteousness. The unrepentant will go to another realm (v. 17).