Classical Reformed theologians hold that:
“[I]t was the will of God that Christ by the blood of the cross, whereby He confirmed the new covenant, should effectually redeem out of every people, tribe, nation, and language, all those, and those only, who were from eternity chosen to salvation and given to Him by the Father; that He should confer upon them faith, which, together with all the other saving gifts of the Holy Spirit, He purchased for them by His death; should purge them from all sin, both original and actual, whether committed before or after believing; and having faithfully preserved them even to the end, should at last bring them, free from every spot and blemish, to the enjoyment of glory in His own presence forever.”( Second Head Of Doctrine, Article 9) 
This Reformed view of the extent of the atoning work of Christ Jesus reverberates with Christ Jesus’ proclamation that “[a]ll that the Father gives [him] will come to [him], and whoever comes to [him He] will never cast out”(John 6:37) and that He will “lose nothing of all that [the Father] has given Him, but raise it up on the last day.” (John 6:39-40)
Holding a Reformed position, J. I. Packer correctly summarized Reformed doctrine of particular atonement, when he defined definite redemption as the finished work of Christ that “ actually put away the sins of all God’s elect and ensured that they would be brought to faith through regeneration and kept in faith for glory, and that this is what it was intended to achieve.”(Packer 1995: n.p)
Strengths of Particular Atonement
Particular atonement makes sense of Christ Jesus’ exclusively John 17’s prayer, namely He prayed not for the world, but for those whom God the Father gave Him, for they belong to the Father.
Charles Hodge noted that “[t]he high-priest interceded for all those for whom he offered sacrifice. The one service did not extend beyond the other.”(Hodge 1997: 553). He argued as high-priest bore the names of the twelve tribes upon his breast when representing them as he offered sacrifices for their sins on the day of atonement, Christ Jesus bore the names of those whom God the Father gave Him.
Moreover, particular atonement is the only view that would lead, I believe, to Romans 9:14 reaction, namely “Is there injustice on God’s part?” and that of Romans 9:16b: “Why does he[God] still find fault? For who can resist his will?” position. God showing mercy on whom He shows mercy and our inability to come to Christ Jesus unless the Father particularly show us mercy by drawing us to his Son and the Son will raise all whom the Father gave up on the last day (John 6:44 cf Roman 9:16) does prima facie sound injustice on God’s part.
Particular atonement explains why the cross of Christ is still a stumbling block to Jews and folly to Gentiles, as Paul explained to the Corinthians, but to those whom the Father particularly called and draw to His Son, “both Jews and Greeks, Christ [crucified is] the power of God and the wisdom of God”(1 Cor. 1:24) On the Soul, 1, Tertullian awesomely observed: “For, who can know truth without the help of God? Who can know God without Christ? Who has ever discovered Christ without the Holy Spirit? And who has ever received the Holy Spirit without the gift of faith?” It is those whom faith is given as a gift who see the power of God and the wisdom of God displayed at the Cross.
Reflecting on this view, William G. T. Shedd brilliantly resolve that “[t]he tenet of limited redemption rests upon the tenet of election, and the tenet of election rests upon the tenet of the sinner’s bondage and inability.”(Shedd 2003: 744)
Concurring with Shedd, Wayne Grudem concluded that all whom the Father had, according to the purpose of his will and praise of his glorious grace, already destined before the creation of the world, to become the children of God “are the same people for whom Christ also came to die, and to those same people the Holy Spirit will certainly apply the benefits of Christ’s redemptive work, even awakening their faith (John 1:12; Phil. 1:29; cf. Eph. 2:2) and calling them to trust in him.”(Grudem 1994: 595)
Weakness of Particular atonement
One of the weaknesses of the doctrine of Particular atonement is that it stands or fall by the truthfulness of the doctrine of Radical depravity viz., fallen creatures are spiritually dead, hostile to God and have no ability to come to Christ Jesus because the things of Spirit are foolish to them, the doctrine Unconditional election viz., those whom the Father gave to His Son, Effectual grace viz., the awaking of a spiritual dead person by the saving work of the Holy Spirit to see the power and beauty of cross, and Eternal assurance viz., those whom the Father gave to His Son are “sealed with the promised Holy Spirit, who is the guarantee of [their] inheritance until [they] acquire possession of it, to the praise of his glory.”(Eph. 1:13-14)
Particular atonement necessarily requires a particular assembly of people from all nations, all tribes, all tongues, who were hostile to God, drawn by the Father to His Son with a power that awakes unquenchable delight and joy to the things of Spirit and are forever kept, never to perish because “no one can snatch them out of [Christ Jesus] hand”(John 10:28).
Question To Reformed Theologians: Am I correct in viewing particular atonement as solely dependent on the truthfulness of radical depravity, effectual call, unconditional election and assurance of salvation to the elect?
 Historic Creeds and Confessions. 1997 (electronic ed.). Oak Harbor: Logos Research Systems, Inc.
Packer, J. I. (1995). Concise theology : A guide to historic Christian beliefs. Wheaton, Ill.: Tyndale House.
Shedd, W. G. T., & Gomes, A. W. (2003). Dogmatic theology (3rd ed.). Phillipsburg, N.J.: P & R Pub.