This is the passage used by Calvinists to support their theory of election for damnation (some call it double predestination, but it matters not):
ROMANS 9: GOD ALREADY KNOWS WHO WILL REPENT AND WHO WILL NOT
15 For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion. [Note: Romans 11: 32 says that God will have mercy on all, which means that none are excluded from His grace]
16 So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy. [Note: This means that salvation is not by human effort, but purely by the grace and mercy of God]
17 For the scripture saith unto Pharaoh, Even for this same purpose have I raised thee up, that I might shew my power in thee, and that my name might be declared throughout all the earth. [Note: the divine judgment of Pharaoh and the Egyptians became known throughout the ancient world]
18 Therefore hath he mercy on whom he will have mercy, and whom he will he hardeneth. [Note: God hardens hearts only after sinners repeatedly harden their hearts]
19 Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will?
20 Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?
21 Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour? [Note: God's foreknowledge
sees in advance those who will repent (honour) and those who will not (dishonour)]
22 What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction:
23 And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory,
24 Even us, whom he hath called, not of the Jews only, but also of the Gentiles?
Paul uses this evil Pharaoh who opposed God and Moses as an example of a sinner who hardened his heart over and over again until God hardened his heart and he could not repent.
The narrative shows us that this evil man could have chosen to repent at any time while those plagues came upon Egypt (or even before), since God has no pleasure in the death of the wicked (Ezek 18:23; 33:11). But every time Pharaoh had the opportunity, he refused to repent, and hardened his heart even more. God endured his lack of repentance with longsuffering (v 22) but eventually he became a "vessel unto dishonour" and "a vessel of wrath fitted to destruction" (eternal Hell).
But Calvinists turn this on its head and claim that just as God had already predestined Pharaoh for Hell, He predestines some sinners for Hell. Indeed the Westminster Confession of Faith says that God does this by an eternal decree, which means that there is no hope for some people,