The World
The only two New Testament uses of ἱλασμός, propitiation are in First John.
He is the propitiation for our sins, and not for ours only but also for the sins of the whole world. (2:2)
In this is love, not that we have loved God but that he loved us and sent his Son to be the propitiation for our sins. (4:10)
In both ἱλασμός is without the article, meaning Jesus Christ is propitiation for sins, ours and the world's. There is one propitiation for all sins.
World, κόσμος is used 186 times in the New Testament. 1 It is predominantly Johannine as 54% occur in this letter (23) and John's Gospel (78). According to the BDAG Lexicon the meaning in verse 2:2 is humanity in general, the world. 2 John also uses the term with the meaning the system of human existence in its many aspects, the world and in particular, "the world, and everything that belongs to it, appears as that which is hostile to God." 3
1 John 5:19
We know that we are from God, and the whole world lies in the power of the evil one.
John addressed those who are no longer enemies of God yet live in a world which for remains hostile to God and hate Christ and His followers (cf. John 15:18-19).
Propitiation
Georg Strecker gives this explanation of verse 2:2 (emphasis added):
The author uses primitive Christian concepts here. ἱλασμός can be translated either as "expiation" or "propitiary sacrifice." The word occurs also at 4:10, but nowhere else in the NT. The idea of the ἱλαστήριον (Romans 3:25, probably a baptismal tradition) is related, as is the ἱλάσκεσθαι of the "faithful high priest" who "atones" for the sins of the people (Hebrews 2:17)... The author is using the same idea of atonement already introduced in 1:7c with the term αἷμα Ἰησοῦ. The advocacy that the exalted Christ exercises for the community before the Father is based on the atonement for sins accomplished in Jesus Christ's redeeming sacrifice. Christ's standing before God as δίκαιος and acting as advocate for the community is founded on his atoning death. Because he, who is sinless, has made atonement on the cross, he can stand before God's throne in the present as the trustworthy Paraklete and perform effective intercession for those who are his own. But his atonement is not esoterically restricted to the community; it has a universal application. Jesus' atoning act is "for the whole world (περὶ ὅλου τοῦ κόσμου). Thus it can be said in 4:14 that the Father sent the Son as "savior of the world" (σωτῆρα τοῦ κόσμου cf. 4:), and even in the Fourth Gospel the world is the object of atoning and saving action of Christ (John 1:29: the lamb of God who takes away the sin of the world; cf John 3:16) 4
Jesus Christ made propitiation for all sins because propitiation for all sins was needed. This act was done before anyone believed.
Romans 5:8
but God shows his love for us in that while we were still sinners, Christ died for us.
Romans 5:10
For if while we were enemies we were reconciled to God by the death of his Son, much more, now that we are reconciled, shall we be saved by his life.
Conclusion
When Christ died, the world was at war with God.
A distinction between our sins and the sins of the whole world exists in the present only because some responded to what Christ did. However, one would be mistaken to conclude those who have not responded now define a new group.
The world is no different than before those who responded. In other words, when Christ died, all sins were included in the sins of the world.
Like the Fourth Gospel, 1 John testifies to a tension between God's compassion toward the world in the Son and the negative qualification of the world. On the one hand, the false teachers are from the world, and the world listens to them (4:5); on the other hand, the believers are "from God' and thus separated from the world (5:4-5; cf. 3 John 11). The world's hatred pursues the community (1 John 3:1, 13; cf. 4:17), and the antichrist is in the world (4:3-4). This negative judgment culminates in the statement that "the whole world lies under the power of the evil one" (5:19). The world is thus within the realm of evil power, and the evil one is in the world. Nevertheless, these statements do not negate the truth that God's atoning action is intended precisely for the world, that is human beings. The message of God's forgiving action in the Christ-event promises human beings the opportunity to regard themselves either as belonging to the world or as having their human existence derived "from God," to have faith in this offer and thus overcome the world (5:4: "Whatever is born of God conquers the world. And this is the victory that conquers the world, our faith." 5
He is the propitiation for our sins, and not for ours only but also for the sins of the whole world. Is simply reminding the community, that Christ's death had universal effect and remains as effective now for those who are still in the world as it was for those who no longer are in the world.
1. mGNT Greek text
2. Fredrick William Danker, A Greek-English Lexicon of the New Testament and Other Early Christian Literature, The University Chicago Press, 2000, p. 562
3. Ibid.
4. Georg Strecker, The Johannine Letters, A Commentary on 1, 2, and 3 John, translation by Linda M. Maloney, edited by Harold Attridge, Fortress Press, 1966, pp. 39-40.
5. Ibid., p. 40