Objection 1. It would seem that we ought not to ask for anything definite when we pray to God. According to Damascene (De Fide Orth. iii, 24), "to pray is to ask becoming things of God"; wherefore it is useless to pray for what is inexpedient, according to James 4:3, "You ask, and receive not: because you ask amiss." Now according to Romans 8:26, "we know not what we should pray for as we ought." Therefore we ought not to ask for anything definite when we pray.
Objection 2. Further, those who ask another person for something definite strive to incline his will to do what they wish themselves. But we ought not to endeavor to make God will what we will; on the contrary, we ought to strive to will what He wills, according to a gloss on Psalm 32:1, "Rejoice in the Lord, O ye just." Therefore we ought not to ask God for anything definite when we pray.
Objection 3. Further, evil things are not to be sought from God; and as to good things, God Himself invites us to take them. Now it is useless to ask a person to give you what he invites you to take. Therefore we ought not to ask God for anything definite in our prayers.
On the contrary, our Lord (Matthew 6 and Luke 11) taught His disciples to ask definitely for those things which are contained in the petitions of the Lord's Prayer.
I answer that, According to Valerius Maximus [Fact. et Dict. Memor. vii, 2, "Socrates deemed that we should ask the immortal gods for nothing else but that they should grant us good things, because they at any rate know what is good for each one whereas when we pray we frequently ask for what it had been better for us not to obtain." This opinion is true to a certain extent, as to those things which may have an evil result, and which man may use ill or well, such as "riches, by which," as stated by the same authority (Fact. et Dict. Memor. vii, 2), "many have come to an evil end; honors, which have ruined many; power, of which we frequently witness the unhappy results; splendid marriages, which sometimes bring about the total wreck of a family." Nevertheless there are certain goods which man cannot ill use, because they cannot have an evil result. Such are those which are the object of beatitude and whereby we merit it: and these the saints seek absolutely when they pray, as in Psalm 79:4, "Show us Thy face, and we shall be saved," and again in Psalm 118:35, "Lead me into the path of Thy commandments."
Reply to Objection 1. Although man cannot by himself know what he ought to pray for, "the Spirit," as stated in the same passage, "helpeth our infirmity," since by inspiring us with holy desires, He makes us ask for what is right. Hence our Lord said (John 4:24) that true adorers "must adore... in spirit and in truth."
Reply to Objection 2. When in our prayers we ask for things concerning our salvation, we conform our will to God's, of Whom it is written (1 Timothy 2:4) that "He will have all men to be saved."
Reply to Objection 3. God so invites us to take good things, that we may approach to them not by the steps of the body, but by pious desires and devout prayers.
Source: Summa Theologica (New Advent)