העתירו אל ה', "Implore God, etc." Why did Pharaoh not simply go to his home as he had done during the first plague? After all, his magicians had demonstrated in both instances that they were able to duplicate Moses' and Aaron's magic? Actually, we should interpret Pharaoh's beliefs as reflected by his reactions. He would not have called in Moses and Aaron to pray for him unless he had been afraid of the deathly effect of the plague in question.
The plague of blood did not represent a threat to life as people could still their thirst by either digging for water in the vicinity of the river or buying same from the Israelites. As a result, Pharaoh did not become overly agitated at that plague.
The plague of frogs contained two elements. 1) It was accompanied by an overpowering noise orchestrated by all those frogs; 2) the frogs invaded people's entrails as we know from 7,29 "and the frogs shall come upon you, etc." This plague was very frightening, no one being certain of his survival. These considerations are what prompted Pharaoh to implore Moses to remove this plague accompanied by a promise that he would release the Israelites to offer sacrifices to their God. When he said: ממני, he referred to his entrails, which was the most frightening aspect of the plague.
Pharaoh did not ask Moses for removal of the third plague, the insects, even though he had watched his magicians' impotence and admission that this plague was indeed a "finger of God;" his heart remained obstinate as the plague, painful though it was, did not constitute a danger to life.
The fourth plague, that of wild animals invading Egypt's urban areas was truly fear-inspiring and resulted in Pharaoh instructing Moses and Aaron to go and take the Israelites to sacrifice to their God within the country. For the first time, Pharaoh was prepared to negotiate where this could take place. At any rate, he pleaded with Moses to pray on his behalf.
The plague of pestilence did not move Pharaoh particularly as its main effect was on the animals, though none of the livestock owned by the Israelites died. Pharaoh remained obstinate, did not release the Israelites and did not ask Moses to pray to stop the plague.
The sixth plague, painful boils on the skin, also did not move Pharaoh to prayer as it was not a life-threatening situation although for the first time even his magicians did not remain immune.
The plague of hail was a major spectacle not only ruining the crops but killing people who had not heeded God's warning. For the first time Pharaoh reacted by admitting that he and his people had sinned against God. He pleaded with Moses to pray and not only promised to release the Israelites but did so without attaching conditions.
During the eighth plague, the locusts, the Torah quotes Pharaoh's alarm when, for the first time, his servants move him to negotiate the Israelites' release before the onset of the plague. Negotiations having broken down, the plague does occur and Pharaoh pleads for God "to remove this death."
We do not find that Pharaoh asked Moses to pray on his behalf during the plague of darkness; perhaps this was due to his attempt during the first three days of that plague to counter it by lighting all kinds of lanterns, etc. During the following three days when no one could even rise from his seat, Pharaoh was incommunicado and could not send a messenger to call Moses to intercede on his behalf. After the seven days of darkness were complete, Pharaoh immediately sent for Moses to tell him that he and his people could leave and that they only had to leave their livestock behind as insurance that they would return. Moses immediately refused the condition. Seeing that the plague of darkness was already over, there was no point in asking Moses to pray for its removal.