The priest offers the gifts of bread and wine on behalf of the faithful, recalls the words of Our Savior on the night on which He was delivered up for the life of the world and then, with fervent prayers (epiclesis), asks God to come down from heaven on the gifts of bread and wine to make the bread the Body of Christ, and the wine the Blood of Christ, changing them by the power of the Holy Spirit.
Once this sacred Mystery has taken place, prayers of petition and thanksgiving (eucharistia in Greek) are offered by the priest and the people. Following the Lord’s Prayer the faithful are invited to approach “with the fear of God, with faith and with love.”
This “fear of God” means tremendous reverence for God’s Mystical Presence and His intimate communion with us.** “With faith” means that we truly believe that this IS the Body and Blood of the risen Christ. “With love” means that we are at peace and have been reconciled with our brothers and sisters.**
The Eucharist, thus received, forgives us our sins and grants us a special intimacy with the Living Christ. If we are aware of sins which prevent us from God’s grace, or if we have anything against our brothers and sisters, we are obliged to abstain from receiving Holy Communion until we are reconciled through the Sacrament of Confession.
It was explained to me so. 1. Those outside of the Eucharist cannot receive the benefits of the Mass. The Eucharist and Communion of Saints is a communion as well among the faithful. If one is aware of sins against God or baptism, one needs reconciliation first.
Now, if someone is outside of the Eucharist, outside of the Communion of Saints, cannot receive absolution, of what purpose is it for you to offer Mass for them? You could though, offer Mass for your intention of hoping they enter the Church so they may also partake fully of the Eucharist.
If the Non Catholic is dead, they would be included in the prayers of faithful just as all souls in Purgatory are remembered and prayed for.