Where is "Free Grace" in the New Testament?

The following analysis of charis (the Greek word for grace) is taken from Richard Trench's book Synonyms of the New Testament:

"THERE has often been occasion to observe the manner in which Greek words taken up into Christian use are glorified and transformed, seeming to have waited for this adoption of them, to come to their full rights, and to reveal all the depth and riches of meaning which they contained, or might be made to contain. Charis is one of these....Already, it is true,...there were preparations for this glorification of meaning to which charis was destined. These lay in the fact that already in the ethical terminology of the Greek schools charis implied ever a favour freely done, without claim or expectation of return—the word being thus predisposed to receive its new emphasis, its religious, I may say its dogmatic, significance; to set forth the entire and absolute freeness of the lovingkindness of God to men. Thus Aristotle, defining charis, lays the whole stress on this very point, that it is conferred freely, with no expectation of return, and finding its only motive in the bounty and free-heartedness of the giver (Rhet. ii. 7)...cf. Rom. 3:24, δωρεὰν τῇ αὐτοῦ χάριτι ['freely by His grace']; 5:15, 17; 12:3, 6; 15:15; Ephes. 2:8; 4:7...and compare Rom. 11:6, where St. Paul sets charis ['grace'] and erga ['works'] over against one another in directest antithesis, showing that they mutually exclude one another, it being of the essence of whatever is owed to charis that it is unearned and unmerited,—as Augustine urges so often, 'gratia, nisi gratis sit, non est gratia;' ['Grace, unless it is free, is not grace;']....charis has thus reference to the sins of men, and is that glorious attribute of God which these sins call out and display, his free gift in their forgiveness....We may say then that the charis of God, his free grace and gift, displayed in the forgiveness of sins, is extended to men, as they are guilty....God so loved the world..., that He gave his only begotten Son (herein the charis), that the world through Him might be saved...."[1]

Reference:

[1] Richard C. Trench, Synonyms of the New Testament (Grand Rapids: Wm. B. Eerdmans Publishing Company, 1958), pp. 166-171, ellipsis added. Note: I transcribed the Greek words into English and updated the Roman numerals of the Scripture references to the current format.