By God's righteousness here [Isa. 51:8] is meant his faithfulness in fulfilling his covenant promises to his church, or his faithfulness towards his church and people in bestowing the benefits of the covenant of grace upon them. . . .
So the word righteousness is very often used in Scripture for his covenant faithfulness; so 'tis in Neh. 9:8, "Thou hast performed thy words for thou art righteous." And so we are to understand righteousness and covenant mercy to be the same thing, as in Ps. 24:5, "He shall receive the blessing from the Lord and righteousness from the God of [his salvation]"; Ps. 36:10, "O continue thy lovingkindness to them that know thee; and thy righteousness to the upright"; and Ps. 51:14, "Deliver me from bloodguiltiness, O God, though God of my salvation; and my tongue shall sing aloud of thy righteousness"; and Dan. 9:16, "O Lord, according to thy righteousness, I beseech thee, let thine anger and thy fury be turned away"; and so in innumerable places.—Jonathan Edwards, A History of the Work of Redemption (ed. John F. Wilson; vol. 21, Works; New Haven: Yale University Press, 1989), 114-115.