I believe there is a reason for distinct words in Scripture, even when possibly synonymous, just as we use nearly synonymous words to give subtly to ideas.
NOTE: I hold to primarily Mosaic authorship by divine inspiration.
The term "heart" (לֵב, lēḇ) herein refers to Pharaoh's mind, spirit, and will, i.e., the "inner person" per what the lexicons (BDB, HALOT, etc.) indicate. This inner self can be broken down to subcategories (as HALOT does).
There are 20 relevant uses of the 3 terms (1 not noted in the question is qšh in 13:15). I believe a pattern and consistency in usage is evident.
Examination of usage
ḥzq in piel is used when YHWH is subject and heart is object (4:21; 9:12; 10:20, 27; 11:10; 14:4, 8, 17). The piel indicates three possibilities:1
- YHWH caused Pharaoh's heart to enter into a state of hardness. But God did not cause multiple reentries into the state during the main process, so that eliminates this idea.
- YHWH causes the heart to harden itself. God is in some way actively hardening the will of Pharaoh.
- YHWH permitted the heart to harden itself. God is passively allowing the will of Pharaoh to become hard.
Further analysis shows that God is actively involved in the hardening. The idea of ḥzq as "being strong" (qal) or "causing to be strong" (piel) is the primary meaning given in the lexicons.
ḥzq in qal is used in the imperfect when the heart is the subject (7:13, 22; 8:19, 9:35), confirming #1 occurs. It is never used with Pharaoh as the subject. But the heart is in reference to Pharaoh's "inner man," so this is a subtle distinction, yet relevant since kbd and qšh each are used with Pharaoh as subject and his heart often as the explicit object. So distinction can be made between Pharaoh and his heart.
- kbd as adjective is used once as a predicate adjective in a verbless clause describing the heart (7:14). The common lexical meaning is "heavy."
- kbd in qal is used once in the imperfect when heart is the subject (9:7). The qal is the state of being heavy.
- kbd in hiphil is used, conveying "cause to be heavy/make heavy":
- once in the infinitive when heart is the object and Pharaoh is the subject linked to it (8:15),
- twice in the imperfect when Pharaoh is the subject and heart is the object (8:32, 9:34),
- once in the perfect when YHWH is subject and heart is the object (10:1).
Pharaoh acting upon the heart during the "making heavy" events show that Pharaoh can affect his "inner man", implying that heart refers specifically to his will (decision point), rather than his mind/emotions, for it would be his mental/emotional aspects that would affect his will. The perfective use with YHWH reflects back that YHWH caused the heaviness.
- qšh in hiphil is used:
- once in the imperfect with YHWH as subject and heart as object (7:3)
- once in the perfect with Pharaoh as subject and heart implied from context (13:15).
Examination of the Texts
A strong relationship exists between the terms, but recall we are seeking clues in the text to determine patterns of subtle distinctions.
#1, etc., refer to the above; translations are NKJV; references are to the English version.
And the LORD said to Moses, “When you go back to Egypt, see that you do all those wonders before Pharaoh which I have put in your hand. But I will harden his heart, so that he will not let the people go.
(#1 ḥzq[p]) YHWH states He will be strengthening (future progressive) Pharaoh's heart. He links the "wonders" as necessary to this, and that the purpose of this is "so that [Pharaoh] will not let the people go."
- Strengthening is linked to the wonders Moses would do.
- Strengthening is so Pharaoh would not let Israel go.
2 You shall speak all that I command you. And Aaron your brother shall tell Pharaoh to send the children of Israel out of his land. 3 And I will harden Pharaoh’s heart, and multiply My signs and My wonders in the land of Egypt. 4 But Pharaoh will not heed you, so that I may lay My hand on Egypt and bring My armies and My people, the children of Israel, out of the land of Egypt by great judgments. 5 And the Egyptians shall know that I am the LORD, when I stretch out My hand on Egypt and bring out the children of Israel from among them.”
(#6 qšh[h]) YHWH states as a prologue to the coming events that He will be hardening (future progressive) Pharaoh's heart. The command of Moses and Aaron "to send the children of Israel out of his land" (v.2) is what will bring this. Why the different word? The lexical emphasis is on "difficulty" or "stubbornness," so God will make Pharaoh stubbornly against the command in order to "multiply My signs and wonders" (which 4:21 indicated were needed for ḥzq). Since Pharaoh would "not heed" (v.4), the "judgments" could come, and these judgments were so that the Egyptians shall know that the true God is YHWH (v.5).
- Stubbornness would be caused by the command to free Israel.
- Stubbornness was prerequisite to bringing all the signs and wonders that would cause the strengthening of the heart to not let Israel go; it is the start of the process.
- Not heeding the words is tied here to qšh, so later references to Pharaoh not heeding implies a reference back to this verse and this verb.
- The word is used in the prologue leading to Moses and Aaron going to their first encounter with Pharaoh.
9 “When Pharaoh speaks to you, saying, ‘Show a miracle for yourselves,’ then you shall say to Aaron, ‘Take your rod and cast it before Pharaoh, and let it become a serpent.’ ” 10 So Moses and Aaron went in to Pharaoh, and they did so, just as the LORD commanded. And Aaron cast down his rod before Pharaoh and before his servants, and it became a serpent. 11 But Pharaoh also called the wise men and the sorcerers; so the magicians of Egypt, they also did in like manner with their enchantments. ... 13 And Pharaoh’s heart grew hard, and he did not heed them, as the LORD had said.
(#2 ḥzq[q]) The heart grows stronger, caused by the sign of the rod/serpent (matched by the sorcerers, v.11). The miracle God called for as anticipated response to Pharaoh, who would call for a miracle by Moses and Aaron to prove themselves (v.9). Moses and Aaron did "just as the LORD commanded" (v.10); they delivered the message of letting Israel go (7:2), which Pharaoh did not heed (v.13).
This is the beginning of YHWH actively making Pharaoh's heart strengthened against Israel by signs and wonders.
- Strengthening is caused by the miracle requested by Pharaoh, and given by YHWH through Moses and Aaron (per 4:21).
- Strengthening is the outworking of Pharaoh's stubbornness in not heeding the command to let Israel go (per 7:3).
NOTE: Context changes from 7:13, as YHWH speaks to Moses in between the previous and next encounter, v.13 anticipating the latter.
So the LORD said to Moses: “Pharaoh’s heart is hard; he refuses to let the people go.
(#3 kbd[a]) The heart, in growing strong (v.13), is described as "heavy" by the only adjectival use of kbd. Why the different word? Since ḥzq was not repeated here in YHWH's declaration to Moses about Pharaoh's heart, it suggests possible evidence that a distinction is intended. Yet this term relates to proving Pharaoh is hardening by YHWH's follow-up statement that "he refuses to let the people go," which relates to the ḥzq of 7:3. This term shows up at the transition point from the first miracle, which was not a judgment, and the later miracles, which are all judgments on Egypt. At this point, the reader has no further clue as to why a distinct term is chosen—it could be a synonym for variety or an intentional shift of meaning.
- Heaviness describes Pharaoh's heart at this point after the initial miracle, prior to the judgment miracles.
- Heaviness is related to not letting Israel go, just as ḥzq is in 4:21 and qšh is in 7:3—that does not exclude subtle distinctions of meaning between the three terms.
19 Then the LORD spoke to Moses, “Say to Aaron, ‘Take your rod and stretch out your hand over the waters of Egypt ... 21 ... So there was blood throughout all the land of Egypt. 22 Then the magicians of Egypt did so with their enchantments; and Pharaoh’s heart grew hard, and he did not heed them, as the LORD had said. 23 And Pharaoh turned and went into his house. Neither was his heart moved [שׁית (šîṯ)] by this. ... 25 And seven days passed after the LORD had struck the river.
(#2 ḥzq[q]) The heart grows harder because of the sign (water to blood), matched by the sorcerers. God called for the miracle (v.19), so God is actively causing the hardening through the signs. Again, Pharaoh does not heed the command (v.22), hearkening back to his qšh.
However, "Neither was his heart moved by this [miracle]" (v.23). The שׁית (šîṯ) has the idea of "place" or "set," specifically here "to turn one’s attention to" something (HALOT, 3.b). Is not "Pharaoh's heart grew hard" enough to indicate that? "Neither was..." indicates the condition being referred to here is not the ḥzq or the failing to heed, both of which the heart was set towards. So his heart was not set in a way opposite; i.e. there was no hint of weakness or repentance. Could this lack of repentance relate then to the third word, kbd, introduced at the beginning of this encounter in 7:14? More evidence is needed, but Pharaoh does not even ask for relief from the judgment, and 7 days pass (v.25).
- Strengthening is caused by the sign from YHWH.
- Pharaoh is still not heeding the command, per the prophesied stubborn heart (qšh) YHWH gave him through the command to let Israel go.
- The heart not being set in a particular direction indicates that there is some other aspect related to Pharaoh's hardening in play, perhaps related to the new word kbd introduced at the beginning of this section.
- Pharaoh is showing no indication at all of breaking, not even asking for relief from the judgment.
8 Then Pharaoh called for Moses and Aaron, and said, “Entreat the LORD that He may take away the frogs from me and from my people; and I will let the people go, that they may sacrifice to the LORD.” ... 10 So he said, “Tomorrow.” And he said, “Let it be according to your word, that you may know that there is no one like the LORD our God. ... 13 So the LORD did according to the word of Moses. ... 15 But when Pharaoh saw that there was relief, he hardened his heart and did not heed them, as the LORD had said.
(#5 kbd[h]) Pharaoh's strength (ḥzq) appears to wane, for he seeks a relief and promises "I will let the people go" (v.8). But the 2nd use (1st verbal use) of kbd is the next clue as to Why the different word? There is a play on words here, for the cause of this heaviness is the relief from the judgment, not the judgment itself. This relief was tied to Pharaoh knowing "that there is no one like the LORD our God" (v.10). But the heaviness of heart shows no admitting the supremacy of YHWH in the relief brought, and he stubbornly reverses and does not heed the command.
- Pharaoh's strength weakens as he seeks relief through a promise.
- The heaviness (kbd) is caused by the relief from the judgment and what that would admit.
- Promising to let them once relieved, Pharaoh reneges because of kbd and does not heed, per what YHWH said the stubborn heart (qšh) would do.
18 Now the magicians so worked with their enchantments to bring forth lice, but they could not. So there were lice on man and beast. 19 Then the magicians said to Pharaoh, “This is the finger of God.” But Pharaoh’s heart grew hard, and he did not heed them, just as the LORD had said.
(#2 ḥzq[q]) The heart is strong again with no weakness (no promises). The sorcerers are not able to match the sign (v.18) and even they admit God is at work (v.19).
- Strengthening is caused by the miracle.
- Pharaoh does not heed, per what the stubborn heart (qšh) would do.
25 Then Pharaoh called for Moses and Aaron, and said, “Go, sacrifice to your God in the land.” ... 28 So Pharaoh said, “I will let you go, that you may sacrifice to the LORD your God in the wilderness; only you shall not go very far away. Intercede for me.” ... 31 And the LORD did according to the word of Moses; He removed the swarms of flies ... 32 But Pharaoh hardened his heart at this time also; neither would he let the people go.
(#5 kbd[h]) Again, his strength of heart is weakening as he promises "Go... Intercede for me ... I will let you go" (v.25, 28). But the heart is made heavy again in conjunction with the relief from the judgment (v.31), and he reneges again about Israel going (v.32).
- Another weakening as Pharaoh gives a promise upon relief.
- The heaviness of heart (kbd) is caused by the relief from the judgment, and prevents him fulfilling his promise.
Then Pharaoh sent, and indeed, not even one of the livestock of the Israelites was dead. But the heart of Pharaoh became hard, and he did not let the people go.
(#4 kbd[q]) The heart is declared to be heavy (the only qal usage), and upon hearing the news that YHWH spared the Israelite livestock while having killed the Egyptian livestock, his heart remained unchanged from the previous encounter, and the relief God gave Israel from this judgment kept the heaviness in place.
- The heaviness is continued from previously, by learning of Israel's relief from the judgment.
11 And the magicians could not stand before Moses because of the boils, for the boils were on the magicians and on all the Egyptians. 12 But the LORD hardened the heart of Pharaoh; and he did not heed them, just as the LORD had spoken to Moses.
(#1 ḥzq[p]) For the first time within the set of events YHWH is stated as the active cause of Pharaoh's strengthening heart. Previously the term indicated the heart changing, but not directly referencing all the time the cause being YHWH (4:21). The miracle causes it, and this time the sorcerers were not even able to come to Pharaoh (v.11), who "did not heed them" (v.12).
- Strengthening is caused by the miracle.
- Pharaoh does not heed, per what the stubborn heart (qšh) would do.
- There is no hint of breaking, as again Pharaoh does not seek relief or make a promise.
9:34 & 35 w/context
27 And Pharaoh sent and called for Moses and Aaron, and said to them, “I have sinned this time. The LORD is righteous, and my people and I are wicked. 28 Entreat the LORD, that there may be no more mighty thundering and hail, for it is enough. I will let you go, and you shall stay no longer.” ... 34 And when Pharaoh saw that the rain, the hail, and the thunder had ceased, he sinned yet more; and he hardened his heart, he and his servants. 35 So the heart of Pharaoh was hard; neither would he let the children of Israel go, as the LORD had spoken by Moses.
(v.34 #5 kbd[h]) Pharaoh weakens, admitting his sinfulness and YHWH's righteousness (v.27), asking for relief (v.28), and again promising he would "let [Israel] go" (v.28). But his response to relief was in increasing his heavy heart (v.34), which is conjoined with "he sinned yet more." This tells the reader two things, (a) the previous hardening reactions were sin, and (b) this sin was an increase of those former sins.
(v.35 #2 ḥzq[q]) The heart, as it grows heavy (kbd) at every display of God's grace to relieve judgment (v.34) upon Pharaoh's promises (v.28), gains strength against letting Israel go (v.35). These two verses show the relationship between the two verbs: "So the heart of Pharaoh was hard" (v.35); the kbd and ḥzq are tied together. Pharaoh kbd's against God's grace, which ḥzq's his resolve to not let Israel go.
- Heaviness comes from relief of the judgment.
- Strengthening comes in conjunction with the heaviness of heart.
Now the LORD said to Moses, “Go in to Pharaoh; for I have hardened his heart and the hearts of his servants, that I may show these signs of Mine before him, 2 and that you may tell ... the mighty things I have done in Egypt, and My signs which I have done among them, that you may know that I am the LORD.”
(#5 kbd[h]) The only use of YHWH making Pharaoh's heart (and his servants' hearts) heavy is in the perfect tense. The heaviness is completed (the word kbd is not used again). The purpose was (a) so YHWH could do these signs to Pharaoh, which matches previous analysis that kbd was prerequisite to some of the ḥzq and (b) so Israel might remember what YHWH did (v.2).
This final use completes answering the Why the different word?. The heaviness is the heart's state of being after the initial, non-judgment miracle (7:14). The hifil imperfect are consistently in contexts when Pharaoh's ḥzq is weakening—admitting of sin, promising to let Israel go, asking for relief—but then he reacts to relief by kbding his heart, opposing setting on letting Israel go (like the šîṯ in 7:23). The one qal in 9:7 continues the kbd. So the pattern for the kbd/ḥzq relation is that increasing of kbd shows up when ḥzq is weakening:
- 7:14 kbd: heart already heavy after 1st, non-judgment (a relief) miracle
- 7:22 ḥzq: miracle strengthens heart
- 8:15 kbd (ḥzq weakened, 8:8): relief causes heaviness
- 8:19 ḥzq: no weakness shown, miracle hardens heart
- 8:32 kbd (ḥzq weakened, 8:25, 28): relief causes heaviness
- 9:7 kbd (ḥzq not weakened, nor kbd increased, just maintained status quo): continuation of heaviness caused by learning of relief for Israel
- 9:12 ḥzq: no weakness shown, miracle hardens heart
- 9:34 kbd (ḥzq weakened, 9:27-28): relief causes heaviness of his heart...
- 9:35 ḥzq: ...so the strength of his heart is increased
- 10:1 kbd: Perfect tense reflects back to previous verses, showing YHWH caused and has finished causing kbd.
Thus kbd is a heaviness from God's grace of relief that effected a turning away from a weakness of heart (maintaining strength) and away from a temporary repentance of letting Israel go according to Pharaoh's promises. From here on, with kbd complete, Pharaoh will not make promises, but in fact commands (two qualified) that Israel can go.
- Heaviness is completed.
- Heaviness was part of YHWH's work as well.
7 Then Pharaoh’s servants said to him, “How long shall this man be a snare to us? Let the men go, that they may serve the LORD their God. Do you not yet know that Egypt is destroyed?” 8 So Moses and Aaron were brought again to Pharaoh, and he said to them, “Go, serve the LORD your God. Who are the ones that are going?” 9 And Moses said, “We will go with our young and our old; with our sons and our daughters, with our flocks and our herds we will go, for we must hold a feast to the LORD.” 10 Then he said to them, “The LORD had better be with you when I let you and your little ones go! Beware, for evil is ahead of you. 11 Not so! Go now, you who are men, and serve the LORD, for that is what you desired.” And they were driven out from Pharaoh’s presence. ... 16 Then Pharaoh called for Moses and Aaron in haste, and said, “I have sinned against the LORD your God and against you. 17 Now therefore, please forgive my sin only this once, and entreat the LORD your God, that He may take away from me this death only.” ... 19 ... There remained not one locust in all the territory of Egypt. 20 But the LORD hardened Pharaoh’s heart, and he did not let the children of Israel go.
(#1 ḥzq[p]) Two distinctions with kbd finished: (A) Pharaoh shows weakness at the threat of judgment, but unlike his servants, who are broken and entreat him to let them go (v.7), which he considers (v.8). But (B) Moses's insistence that everyone goes (v.9) is not heeded, for Pharaoh is only willing to let the men go (v.11). Still, this concession to let part of Israel go is new for Pharaoh with kbd gone. The concession unacceptable, so judgment comes, Pharaoh admits his sin (v.16), asks forgiveness (v.17), and after relief, he is still not truly humble (see 10:3) and strengthens his heart against letting all Israel go.
- The kbd ended and for the first time Pharaoh, by mere threat of judgment, concedes and commands the men of Israel to go (which is unacceptable).
- Strengthening comes with Israel's men not going as Pharaoh had allowed, while a judgment still comes and its relief.
24 Then Pharaoh called to Moses and said, “Go, serve the LORD; only let your flocks and your herds be kept back. Let your little ones also go with you.” 25 But Moses said, “You must also give us sacrifices and burnt offerings, that we may sacrifice to the LORD our God. ... 27 But the LORD hardened Pharaoh’s heart, and he would not let them go. 28 Then Pharaoh said to him, “Get away from me! Take heed to yourself and see my face no more! For in the day you see my face you shall die!”
(#1 ḥzq[p]) Pharaoh weakens from the darkness (v.21), reversing his previous stance, commanding all Israel to go, but without their livestock (v.24). Moses refuses the condition as it prevents sacrificing to YHWH (v.25), causing Pharaoh's heart to strengthen and not let them go (v.27). He does not ask for relief and instead threatens Moses with death (v.28).
- The kbd ended and for the second time Pharaoh commands Israel to go, all of the people, but not their livestock (which is unacceptable).
- Strengthening results from Moses's refusal of the condition.
- Strengthening yields Pharaoh's death threat to Moses.
9 But the LORD said to Moses, “Pharaoh will not heed you, so that My wonders may be multiplied in the land of Egypt.” 10 So Moses and Aaron did all these wonders before Pharaoh; and the LORD hardened Pharaoh’s heart, and he did not let the children of Israel go out of his land.
(#1 ḥzq[p]) This verse reflects back on previous strengthenings by wonders, as YHWH had said (4:21), which wonders came because Pharaoh would not heed their words (v.9), as He had said would happen by making Pharoah's heart stubborn (qšh, 7:3).
The summary is just after Pharaoh refuses the warning of the death of the firstborn (v.4, 8), a reply to Pharaoh's death threat of Moses (10:28), right before Moses leaves Pharaoh for good (v.8). No more hardening against Israel occurs until after YHWH breaks Pharaoh's heart.
Pharaoh's strength breaking at the firstborn's death contrasts to YHWH's earlier declaration "Now you [Moses] shall see what I will do to Pharaoh. For with a strong [hzq] hand he will let them go, and with a strong [hzq] hand he will drive them out of his land" (6:1). The strength Pharaoh had been building against Israel flips, and Pharaoh pushes Israel out (12:31-36), still an instrument of YHWH (13:3, 16).
- Strengthening has occurred as YHWH promised.
- The summary is before the break of heart to let Israel go on YHWH's terms.
- The kbd has ended and the summary anticipates what is the third time Pharaoh will command Israel to go, this time without conditions and for good.
15 And it came to pass, when Pharaoh was stubborn about letting us go, that the LORD killed all the firstborn in the land of Egypt ...
(#6 qšh[h]) The 2nd/last use of qšh. The heart is clearly implied, for "Pharaoh was stubborn about letting us go" relates to the preceding hardening of hearts. First, qšh was noted in prologue as an overarching foundation of stubbornness that YHWH would cause in order that wonders would come to further strengthen Pharaoh's heart (7:3); here qšh is in epilogue as an overarching summary of the stubbornness from Pharaoh, which transpired up to the final killing of the firstborn that breaks Pharaoh's stubbornness and strength of heart. The two uses bookend the sequence of hardening unto freedom.
- Stubbornness is the inclusive idea of Pharaoh's not heeding the command of YHWH to let Israel go.
- Stubbornness was caused by Pharaoh (13:15) and by YHWH (7:3)
- Stubbornness allowed for wonders that strengthened his heart (4:21)
- The summary is given just after the break of heart when Pharaoh's stubbornness to let them go ends (12:31-32), acting as the epilogue bookend to the prologue use in 7:3.
14:4, 8 w/context
3 For Pharaoh will say of the children of Israel, ‘They are bewildered by the land; the wilderness has closed them in.’ 4 Then I will harden Pharaoh’s heart, so that he will pursue them; and I will gain honor over Pharaoh and over all his army, that the Egyptians may know that I am the LORD.” And they did so. 5 Now it was told the king of Egypt that the people had fled, and the heart of Pharaoh and his servants was turned against the people; and they said, “Why have we done this, that we have let Israel go from serving us?” ... 8 And the LORD hardened the heart of Pharaoh king of Egypt, and he pursued the children of Israel; and the children of Israel went out with boldness.
(v.4 #1 ḥzq[p]) Pharaoh's strength has been broken, he lets Israel go (13:17). But YHWH is not done strengthening Pharaoh's heart about letting the people go. Pharaoh will contemplate that Israel in the wilderness will be easy to overtake (v.3), so pursuit to regain the Israelites will be on his mind when YHWH strengthens (future progressive) his heart again (v.4). This occurs immediately after Pharaoh hears news that Israel has departed; the hearts that had been broken are again "turned against the people" (v.5).
(v.8 #1 ḥzq[p]) The cause of the hardening is Pharaoh and his servants self-contemplative greed against the wonder God did in freeing Israel, for Egypt has lost her slaves (v.5), and so Pharaoh pursues as YHWH said (v.4). This strengthening was so that (a) YHWH "gain honor over Pharaoh and over all his army" and (b) that the Egyptians know the true God was YHWH (v.4).
- Strengthening will begin again after Pharaoh's will broke and Israel left, not letting Israel continue going.
- Strengthening comes from Pharaoh and his servants own greed in having lost their slaves to YHWH's work of freedom.
16 ... And the children of Israel shall go on dry ground through the midst of the sea. 17 And I indeed will harden the hearts of the Egyptians, and they shall follow them. So I will gain honor over Pharaoh and over all his army, his chariots, and his horsemen. 18 Then the Egyptians shall know that I am the LORD....
(#1 ḥzq[p]) The final reference to YHWH strengthening hearts (of all the Egyptians) is in order that they pursue Israel even into the midst of the Red Sea (v.16-17), so that the honor sought by YHWH is gained by their destruction (v.18). This comes to pass, though without reference to hardening (v.22-23).
Summary of Patterns and Conclusion
Each word has a purpose in the context of the set of events, evidenced in the texts they are found. Patterns emerged:
- qšh, the bookends of stubbornness unto freedom: inclusio to the set of events before any miracles (7:3) and after (13:15) the final miracle that breaks of Pharaoh's heart to let Israel go (12:31-32). YHWH will make Pharaoh stubborn in heeding the command for freedom for the purpose of bringing many signs, wonders, and judgments on Egypt (7:3), which signs were necessary for the ḥzq process. Stubbornness was needed because the judgments were so severe that a normal reaction would have broke sooner.
- kbd, the heaviness that returns weakness to strength: first expressed in his not heeding the initial, non-judgmental miracle (7:14). It increases at every point in which Pharaoh promises to let Israel go on condition of relief, causing a renege on the promise (8:8 & 15; 8:28 & 32; 9:28 & 34). It maintains a previous increase (8:32) once, when the following judgment Pharaoh sees Israel's relief opposed to Egypt (9:7). Making his heart heavy (kbd) is what keeps Pharaoh's strength of heart (ḥzq) in the times of wavering, seen in the vacillating between them and the connection in 9:34-35. After YHWH declares He completed kbd (10:1), the final three encounters have Pharaoh command Israel to go, showing it is completed.
- ḥzq, the strength to not let go: used broadly of YHWH strengthening Pharaoh's heart against letting Israel go by the wonders He does. It keeps Pharaoh from breaking and letting Israel go as YHWH wishes. After breaking, it reforms when Israel leaves, by the greatest wonder of all: Israel already being free.
YHWH actively caused Pharaoh's heart to harden by means of the command He gave, the grace shown, and the wonders done.
1 Ronald J. Williams, Williams' Hebrew Syntax, 3rd. ed. (Toronto: University of Toronto Press, 2007), 59-60. The other ideas given are not relevant in these contexts.