Objection 1. It seems that the entire punishment due to sin is forgiven through this sacrament. For through this sacrament man receives the effect of Christ's Passion within himself as stated above (1,2), just as he does through Baptism. But through Baptism man receives forgiveness of all punishment, through the virtue of Christ's Passion, which satisfied sufficiently for all sins, as was explained above (69, 2). Therefore it seems the whole debt of punishment is forgiven through this sacrament.
Objection 2. Further, Pope Alexander I says (Ep. ad omnes orth.): "No sacrifice can be greater than the body and the blood of Christ." But man satisfied for his sins by the sacrifices of the old Law: for it is written (Leviticus 4, 5): "If a man shall sin, let him offer" (so and so) "for his sin, and it shall be forgiven him." Therefore this sacrament avails much more for the forgiveness of all punishment.
Objection 3. Further, it is certain that some part of the debt of punishment is forgiven by this sacrament; for which reason it is sometimes enjoined upon a man, by way of satisfaction, to have masses said for himself. But if one part of the punishment is forgiven, for the same reason is the other forgiven: owing to Christ's infinite power contained in this sacrament. Consequently, it seems that the whole punishment can be taken away by this sacrament.
On the contrary, In that case no other punishment would have to be enjoined; just as none is imposed upon the newly baptized.
I answer that, This sacrament is both a sacrifice and a sacrament. it has the nature of a sacrifice inasmuch as it is offered up; and it has the nature of a sacrament inasmuch as it is received. And therefore it has the effect of a sacrament in the recipient, and the effect of a sacrifice in the offerer, or in them for whom it is offered.
If, then, it be considered as a sacrament, it produces its effect in two ways: first of all directly through the power of the sacrament; secondly as by a kind of concomitance, as was said above regarding what is contained in the sacrament (76, 1,2). Through the power of the sacrament it produces directly that effect for which it was instituted. Now it was instituted not for satisfaction, but for nourishing spiritually through union between Christ and His members, as nourishment is united with the person nourished. But because this union is the effect of charity, from the fervor of which man obtains forgiveness, not only of guilt but also of punishment, hence it is that as a consequence, and by concomitance with the chief effect, man obtains forgiveness of the punishment, not indeed of the entire punishment, but according to the measure of his devotion and fervor.
But in so far as it is a sacrifice, it has a satisfactory power. Yet in satisfaction, the affection of the offerer is weighed rather than the quantity of the offering. Hence our Lord says (Mark 12:43; cf. Luke 21:4) of the widow who offered "two mites" that she "cast in more than all." Therefore, although this offering suffices of its own quantity to satisfy for all punishment, yet it becomes satisfactory for them for whom it is offered, or even for the offerers, according to the measure of their devotion, and not for the whole punishment.
Reply to Objection 1. The sacrament of Baptism is directly ordained for the remission of punishment and guilt: not so the Eucharist, because Baptism is given to man as dying with Christ, whereas the Eucharist is given as by way of nourishing and perfecting him through Christ. Consequently there is no parallel.
Reply to Objection 2. Those other sacrifices and oblations did not effect the forgiveness of the whole punishment, neither as to the quantity of the thing offered, as this sacrament does, nor as to personal devotion; from which it comes to pass that even here the whole punishment is not taken away.
Reply to Objection 3. If part of the punishment and not the whole be taken away by this sacrament, it is due to a defect not on the part of Christ's power, but on the part of man's devotion.
Source: Summa Theologica (New Advent)