Objection 1. It would seem that Christ's death did not conduce in any way to our salvation. For death is a sort of privation, since it is the privation of life. But privation has not any power of activity, because it is nothing positive. Therefore it could not work anything for our salvation.
Objection 2. Further, Christ's Passion wrought our salvation by way of merit. But Christ's death could not operate in this way, because in death the body is separated from the soul, which is the principle of meriting. Consequently, Christ's death did not accomplish anything towards our salvation.
Objection 3. Further, what is corporeal is not the cause of what is spiritual. But Christ's death was corporeal. Therefore it could not be the cause of our salvation, which is something spiritual.
On the contrary, Augustine says (De Trin. iv): "The one death of our Saviour," namely, that of the body, "saved us from our two deaths," that is, of the soul and the body.
I answer that, We may speak of Christ's death in two ways, "in becoming" and "in fact." Death is said to be "in becoming" when anyone from natural or enforced suffering is tending towards death: and in this way it is the same thing to speak of Christ's death as of His Passion: so that in this sense Christ's death is the cause of our salvation, according to what has been already said of the Passion (48). But death is considered in fact, inasmuch as the separation of soul and body has already taken place: and it is in this sense that we are now speaking of Christ's death. In this way Christ's death cannot be the cause of our salvation by way of merit, but only by way of causality, that is to say, inasmuch as the Godhead was not separated from Christ's flesh by death; and therefore, whatever befell Christ's flesh, even when the soul was departed, was conducive to salvation in virtue of the Godhead united. But the effect of any cause is properly estimated according to its resemblance to the cause. Consequently, since death is a kind of privation of one's own life, the effect of Christ's death is considered in relation to the removal of the obstacles to our salvation: and these are the death of the soul and of the body. Hence Christ's death is said to have destroyed in us both the death of the soul, caused by sin, according to Romans 4:25: "He was delivered up [namely unto death] for our sins": and the death of the body, consisting in the separation of the soul, according to 1 Corinthians 15:54: "Death is swallowed up in victory."
Reply to Objection 1. Christ's death wrought our salvation from the power of the Godhead united, and not consisted merely as His death.
Reply to Objection 2. Though Christ's death, considered "in fact" did not effect our salvation by way of merit, yet it did so by way of causality, as stated above.
Reply to Objection 3. Christ's death was indeed corporeal; but the body was the instrument of the Godhead united to Him, working by Its power, although dead.
Source: Summa Theologica (New Advent)