According to Berkhof, (see his systematic for the complete article):

Scripture says that we are justified dia pistis, ek pistis, or pistei (dative) --(Romans 3:25, 28, 30; 5:1, Galatians 2:16; Philippians 3:9, etc). The preposition dia stresses the fact that faith is the instrument by which we appropriate Christ and His righteousness. The preposition ek indicates that faith logically precedes our personal justification. The dative is used in the instrumental sense. However, Scripture never says we are justified on account of faith. Faith is never represented as the ground of our justification--if it was it would be a meritorious work of man (Romans 3:21, 27, 28; 4:3-4, Galatians 2:16, 21, 3:21, etc).

Probably a better name than instrument would be appropriating organ. Thus, by faith the sinner appropriates the righteousness of Christ and establishes union between himself and Christ. The merits of Christ constitute the dikaioma, the legal basis on which the formal declaration of God in justification rests. By faith the sinner appropriates the righteousness of the Mediator already imputed to him ideally in the practum salutis; and on the basis of this he is now formally justified before God. The phrase appropriating organ includes the instrumental idea and is therefore perfectly in harmony with the statements found in our confessional standards. It has an advantage over the phrase instrumental cause because it excludes the idea that faith is in any sense the basis for justification. See Hodge (attachment) for more....

There are some excellent articles here (select: Sola Fide) (Berkhof's is there also)

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