Whether suffrages profit those who are in purgatory?

Objections

Objection 1 : It would seem that suffrages do not profit even those who are in purgatory. For purgatory is a part of hell. Now "there is no redemption in hell" [*Office of the Dead, Resp. vii], and it is written (Ps. 6:6), "Who shall confess to Thee in hell?" Therefore suffrages do not profit those who are in purgatory.
Objection 2 : Further, the punishment of purgatory is finite. Therefore if some of the punishment is abated by suffrages, it would be possible to have such a great number of suffrages, that the punishment would be entirely remitted, and consequently the sin entirely unpunished: and this would seem incompatible with Divine justice.
Objection 3 : Further, souls are in purgatory in order that they may be purified there, and being pure may come to the kingdom. Now nothing can be purified, unless something be done to it. Therefore suffrages offered by the living do not diminish the punishment of purgatory.
Objection 4 : Further, if suffrages availed those who are in purgatory, those especially would seem to avail them which are offered at their behest. Yet these do not always avail: for instance, if a person before dying were to provide for so many suffrages to be offered for him that if they were offered they would suffice for the remission of his entire punishment. Now supposing these suffrages to be delayed until he is released from punishment, they will profit him nothing. For it cannot be said that they profit him before they are discharged; and after they are fulfilled, he no longer needs them, since he is already released. Therefore suffrages do not avail those who are in purgatory.