Question: It states multiple times throughout the chapters discussing the plaques that the Lord hardened pharaoh's heart. I realize Pharaoh considered himself a god and was stubborn to begin with and also understanding that continued rebellion against God will cause the heart to be hardened, but how does the Lord continuing to harden his heart affect Pharaoh's free will?
Answer: We are delving into an area that we do not and cannot completely understand. The Scripture is very clear that God is sovereign and all powerful. It also indicates that man has some sort of freewill and responsibility. We as humans tend to think of God exercising His sovereignty as somehow being unjust in that it is violating man's freewill. Theologians come down on both sides with arguments either defending God's sovereignty or man's freewill. Paul deals with...
the issue in Romans 9:1-11:32 and particularly uses the hardening of Pharaoh's heart as an example in Romans 9:14-18.
"What shall we say then? There is no injustice with God, is there? May it never be! For He says to Moses, "I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion." So then it does not depend on the man who wills or the man who runs, but on God who has mercy. For the Scripture says to Pharaoh, "For this very purpose I raised you up, to demonstrate My power in you, and that My name might be proclaimed throughout the whole earth." So then He has mercy on whom He desires, and He hardens whom He desires."
The New American Commentary has a good analysis of this passage and what was going on with the hardening of Pharaoh's heart.
"The point is that God's favors are not determined by anyone or anything outside of himself. God's purpose in election rests not upon human will (thelo in v. 16 can express desire or purpose) or effort (a participle from trecho, "run") but upon divine mercy. Although God elects with sovereign freedom, it does not follow that Israel had nothing to do with their rejection. Later in the chapter we will learn that Israel failed to attain a right standing with God because they pursued it on the basis of works (vv. 30-32). The sovereignty of God does not set aside human responsibility.
Paul used the case of Pharaoh (an individual rather than a nation as in vv. 7-13) to demonstrate that God withholds mercy and hardens whomever he chooses (cf. Exodus 7:3; 14:17). Pharaoh, that implacable enemy of God's people, was raised to the position of king of Egypt so that God might display in him the evidence of his power (Exodus 9:16). Although Pharaoh's rise to a position of authority undoubtedly had a secular interpretation, God was at work in his career, bringing him to prominence. God did it in order to display his power by bringing Pharaoh to his knees and so that his character as the one who delivered the children of Israel from Egyptian bondage might be known throughout the world. Verse 18 summarizes the argument. It provides the principle of divine action on which the preceding events were based. God shows mercy as he chooses, and he hardens people's hearts as he chooses. He is sovereign in all that he does. Although the text says repeatedly, however, that God hardened Pharaoh's heart, it also stresses that Pharaoh hardened himself (cf. Exodus 7:13-14, 22; 8:15, 19, 32; 9:7, 34-35). Morris notes that "neither here nor anywhere else is God said to harden anyone who had not first hardened himself."
So Pharaoh can be seen to be exercising his freewill in response to things God had sovereignly put before him, things God knew Pharaoh would respond to just as he did.