"...who are expiating their sins in Purgatory..."
The text tells you that they are expiating their own sins.
You are adding the word 'own' to imply that they are by themselves atoning for their sins. This word 'own' is not in the sources you have quoted now is it.
I cannot make this any clearer, I understand that you feel the need to continue with this poor understanding of semantics, because you have built your whole argument around it.
And does this take place in Purgatory?
Why are you punished for your sins, when Christ was already punished for your sins (er, for the sake of this conversation)?
Yes it happens in purgatory. Why? Because no matter how much some want to eliminate the fact that God is Just as well as merciful; the simple fact is that we worship a Just God.
Jesus' method of atonement was for two purposes to meet God justice and was an act of His mercy. All sin merits eternal damnation, no matter how small. Christ's atonement met God's justice by His sacrifice, and God's mercy comes from the fact that it was God who became man to die in our place. Due to the Son's actions, we are redemned from what we deserve and can now through faith be saved by Christ's death and resurrection. The reason why the Son must be the sacrifice, was that we could not possibly redeem ourselves. It required a much greater sacrifice than what we fallen human beings could possibly give. It required an infinitely great sacrifice to meet God's justice. Thus the crucifixion of God Himself. But how do we tie ourselves to that Sacrifice? Christ gave us a sacrament that accomplishes this which is baptism, as St. Paul says. So through baptism we are justified through Christ's death and resurrection, and are made righteous as Adam and Eve were righteous before the fall.
The problem occurs after baptism. If we live for any period of time after our baptism, we are going to commit sin. When we commit sin, we can be forgiven, and made righteous once more, but it requires three things for this to occur: repentance, confession, and restitution. The first two I would assume is straight forward, but it is the last one that you probably are hung up on.
Sin has consequences, we should be able to agree upon this. When we commit an act contrary to the divine law there are people who are injured, and there consequences to those actions, and there must be restitution. God know humanity far better than we know ourselves, and we understand that mercy usually requires justice as well.
For example when my kids were little, they would do things that were against the rules of the household. When I found out I immediately forgave them, but I would also punish them. Why? Was I being unmerciful because I punished them? No I do not think so. Rather if I did not teach them that there were consequences to their actions, how would they learn what the right way was? Can you imagine if there were no need for restitution when we committed trasspasses against God? What kind of Christian would that make? Well I would imagine the type of Christian you would get was a spoiled one who has no desire to make themselves in Christ's image, just like a child that isn't punished appropriately for their actions becomes spoiled and unruly.
Purgatory exists because of God's mercy and His justice. It is a simple fact that nothing or no one impure can survive the Presence of God. It just isn't possible. Thus purgatory is a mercy in that it purifies the individual so that they can enter into the Divine Presence and see the Beatific Vision. It is an act of justice in that the individual makes restitution of the sinful acts that they committed on earth and were not able to make full restitution for.
So then, you don't believe the blood of Christ cleanses from all sin?
Oh I believe it.
Actually, it says that sin will not be forgiven in the world to come.
actually in that passage it is speaking of a specific sin, which is blasphemy against the Holy Spirit.