Pharaoh asked Moshe to pray to end the plagues in a particular way. Why didn’t he?
Various plagues were wrought by HaShem, Moshe and Ahron.  Why was barad, in particular, brought about by Moshe?
“Try and test me†Moshe replied. “At precisely what time shall I pray ×עתיר for you, your servants and your people … ridding you and your homes of the frogs so that they will only remain in the canal [i.e. the Nile]?â€
— Shemos 8:5
Moshe and Ahron left the Pharaoh. Moshe cried out ויצעק to HaShem concerning the frogs that He’d brought upon the Pharaoh
— Shemos 8:8
Moshe replied “Behold I am leaving your presence. Tomorrow I will pray  ×עתיר to HaShem, the mixed wild beasts will go away from the Pharaoh,  his servants and his people … Moshe left the Pharaoh’s presence and prayed ויעתר  to HaShem.
— Shemos 8:25,26
[The Pharaoh asked them] “pray העתירו to Hashem. There’s been too much of this Elokim-induced thunder and hail. I will send you/ your nation away; you will not have to stay.†… Moshe left the Pharaoh’s presence and exited the city. As soon as he spread his palms up ויפרוש כפיו to HaShem the thunder and din ceased and the hail and rain no longer fell to the ground.
— Shemos 9:28,33
There are six things which HaShem hates, seven which His Soul abominates: 1. stuck-up eyes, 2. a lying tongue, 3. and hands that shed innocent blood; 4. A heart that works out malicious thoughts, 5. feet that are quick in running to evil; 6. A false witness who exhales lies, 7. and one who causes conflict among brothers.
— Mishlei 6:16-19
Rabbi Chanina the son of Dosa would say … One whose deeds surpass his wisdom, his wisdom endures. But one whose wisdom surpasses his deeds, his wisdom does not endure.
— Pirkei Avos 3:9
There are 10 different expressions [in Lashon Kodesh-the holy tongue;] for prayer …
— Sifri on Devarim 3:23
In an abstract way we are aware of the Chazal that teaches that there are 10 near-synonymous expressions in Lashon Kodesh to describe humans communicating with HaShem. On a theoretical level we are also cognizant of the fact that diverse words carry assorted shades of meaning and that, as such, there must be 10 different ways to pray, 10 distinct media for prayer.
Yet, we are accustomed to congregational prayer during which everyone must be on the same page, both figuratively and literally. We also pray using a liturgy fixed by the anshei k’nesses hagedolah-the men of the great assembly; with later accretions canonized by tradition. And so on a practical level for us there is only one way to pray. Gradations in the quality of our prayer vary according to levels of ones understanding of the liturgy and ones sincerity and depth of kavvanah-directing his heart and attention towards G-d. To us, the notion that varying circumstances require a different substance or even style of prayer seems utterly foreign.
In Parshas VaEra the Izhbitzer school teaches that the style and substance of prayer must react and respond to the particular needs being addressed and to the root causes of the distress that one is praying to resolve. Just as no two crises are exactly alike so too no two prayers can be clones of one another.
In each of the makkos-plagues; of frogs, mixed wild-beasts and hail we find the Pharaoh of Egypt beseeching Moshe to pray for the cessation of the makkah. The Pharaoh is consistent. Every time he requests Divine intercession of Moshe he employs a conjugation of the word עתירה atirah-pleading. Yet only in requesting the end of the makkah of the arov– mixed wild-beasts; does Moshe actually plead with HaShem. In order to get the frogs back into the Nile Moshe employs tzeakah-shouting or screaming;  and to stop the makkah of barad-hail composed of fire and ice; Moshe prays with perishas kapayim-spreading his palms outwards and upwards. The second Izhbitzer Rebbe, the Bais Yaakov, offers insight into the three crises and why the three different prayers were appropriate for each one.
Observing that both the makkos of tzefardea-frogs; and arov were incursions of wild animals into human habitats, the Bais Yaakov asserts that all creatures, both domesticated and wild, yearn for the proximity of human beings for they have a deep-seated, instinctive consciousness that their own actualization and fulfillment can only be brought about by human beings. But for the vast majority of baalei chaim-animals; hobnobbing with human beings is not the proper means through which man might perfect and fulfill them. Among the Creator’s creatures Man alone is endowed with free-will and thus, with the capacity to exercise free-will to serve G-d. These acts of avodah-serving HaShem; distinguish man from beast and are what drive away undomesticated animals from human habitats. The power inherent in various types of avodah is what make the different baalei chaim maintain their distance.
The croaking frogs and toads are distinguished by their ability to give voice to wordless cries, groans and screams. They have voices, but their voices cannot inform words. Correspondingly, the type of prayer-based avodah that keeps frogs separate and distinct from human society is human tzeakah which is similarly inarticulate and wordless. When tzeakah is wielded by a human being it is a non-verbal, yet voice-based, form of communication. This is why, when the time came to end the makkah of tzefardea, Moshe prayed with tzeakah.
A common thread running through human avodah is that it is orderly and organized. Before birkas Kohanim-the priestly blessing; we beseech Hashem to restore the seder ha’avodah-the order of Divine service; to Jerusalem. Many sugyos-topics and dialogues; in shas-the Talmud; are devoted to the correct sequence of mitzvos and blessings when there are many to do within a fixed time-frame. On leil Pesach-Passover eve; the many mitzvos and Torah learning with which we celebrate our very capacity for avodah is known as THE Seder-the ORDER. The Bais Yaakov avers that atirah refers to orderly characteristic of prayerful avodah and that predatory animals, perhaps due to their catch-as-catch-can opportunistic way of feeding themselves, are the very disorderly, riotous antithesis of seder. This is especially true when diverse species of animal predators are thrown together in an unnatural hodgepodge, as they were during the makkah of arov. For this reason when the time came to end the makkah of arov Moshe prayed with atirah.
The Mei Hashiloach masterfully explains how the seven makkos described in parshas VaEra correspond to the seven types of sinner whom HaShem hates and abominates, as described in Mishlei. In his system the makkah of barad corresponds to those sinners with “stuck-up eyes.†The Egyptians arrogance derived from their smugness in their material riches and their sense that their pantheon had been mashpia-caused a brimming over; of every possible divine munificence and overflow of resources. Even in the Nile-fed Egyptian civilization, the primary source of outpouring of sustenance from on-High is rain. Rain is the fundamental, baseline bounty that leads to the material riches, abundance and excess that breed arrogance and “stuck-up eyes.â€
But in a Jekyll-Hyde-like metamorphosis, makkas barad made a monster out of the rain. The incendiary projectiles encased in heavy, jagged ice were an acid rain that carpet-bombed Egypt. Instead of nourishing and sustaining the food-chain and enriching Egypt, the “rain†itself was now utterly destroying the food supply and impoverishing Egypt. Barad did not merely break unsheltered people, livestock, trees and plants; it shattered the pride of an egomaniacal civilization.  Perhaps most distinctively among all of the plagues,  makkas barad “belonged†to Moshe. Who better suited to deliver the blow that smashed Egyptian arrogance to smithereens than “the man Mosheâ€, he who was “very humble, more so than any man on the face of the earthâ€(Bemidbar 12:3)? The Mei Hashiloach explains that in the makkah of barad humility exposed arrogance to the wages of its own empty core and, in so doing, humbled it.
Based on his fathers understanding of the dynamics of barad the Bais Yaakov explains why Moshe prayed using persishas kapayim to end the plague. All arrogance derives from a sense of supremacy; feeling most-high in any given hierarchy. What affords even those men living in want and poverty a sense of arrogance is the human brain and mind. Lower beings, quadrupeds all, possess feet and “hands†as well. Only biped man possesses an erect posture allowing his head, receptacle of the mind that thinks, to maintain a loftiness relative to the balance of his physical plant, the implements of the ability to do. As the pen is mightier than the sword so too, does arrogant man reason, the mind is loftier than the hands. But when man raises his human hands above his head he is, symbolically, according supremacy to doing and acting over conceiving and cogitating.
When a free-will endowed human being prays with persishas kapayim he is checking his ego at the door. The posture of one who prays with persishas kapayim demonstrates that the reach of mans capacity to serve G-d exceeds his capacity to grasp the G-dly. It is the prayerful kol-voice; of Yaakov integrating and sublimating the yadayim-the hands; of Esav.
Moshe the humblest prays for the cessation of a makkah that assailed the conceit of the most arrogant. The appropriate medium for the message of humility and the lesson that mans conceptual faculties are imperfect, that his wisdom can only endure when his deeds surpass his wisdom, is the prayer of persishas kapayim. Persishas kapayim is body language that communicates this humble supplication of the G-d-slave: “I live to serve You Whom I can never grasp with my mind. I set my palms expansively above my head in the longing that the reach of my hands will exceed the grasp of my mind and that my deeds will surpass my wisdom.â€
IMPORTANT ADDENDUM
In Shulchan Aruch Orach Chaim 89:1 Rebee Akiva Eiger rules that we no longer pray using perishas kapayim. As it has been co-opted by non-Jews for idolatrous practices it is akin to a matzeivah that was “beloved in the era of the patriarchs but is now despised.â€
~adapted from Mei Hashiloach VaEra Dâ€H Inyan
Bais Yaakov ahl haTorah v’HaMoadim VaEra Dâ€H VaYeitzei
הקב”×” מת×וה לתפלתן של צדיקי×
Yevamos 64 A. This is not a question on the Izhbitzer but on the chumash. Even had Moshe employed generic atirah to get all of the makkos to cease your question still stands.
Very interesting. I am just not clear why Hashem would pay heed to the method of Moshe’s prayer. When it is time for the plague to go, it will go, regardless.