For the law causeth wrath, etc. This is a confirmation of the last verse, derived from the contrary effect of the law; for as the law generates nothing but vengeance, it cannot bring grace. It can indeed show to the good and the perfect the way of life: but as it prescribes to the sinful and corrupt what they ought to do, and supplies them with no power for doing, it exhibits them as guilty before the tribunal of God. For such is the viciousness of our nature, that the more we are taught what is right and just, the more openly is our iniquity discovered, and especially our contumacy, and thus a heavier judgment is incurred. By wrath, understand God's judgment, which meaning it has everywhere. They who explain it of the wrath of the sinner, excited by the law, inasmuch as he hates and execrates the Lawgiver, whom he finds to be opposed to his lusts, say what is ingenious, but not suitable to this passage; for Paul meant no other thing, than that condemnation only is what is brought on us all by the law, as it is evident from the common use of the expression, and also from the reason which he immediately adds. Where there is no law, etc. This is the proof, by which he confirms what he had said; for it would have been difficult to see how God's wrath is kindled against us through the law, unless it had been made more apparent. And the reason is, that as the knowledge of God's justice is discovered by the law, the less excuse we have, and hence the more grievously we offend against God; for they who despise the known will of God, justly deserve to sustain a heavier punishment, than those who offend through ignorance. But the Apostle speaks not of the mere transgression of what is right, from which no man is exempt; but he calls that a transgression, when man, having been taught what pleases and displeases God, knowingly and willfully passes over the boundaries fixed by God's word; or, in other words, transgression here is not a mere act of sin, but a willful determination to violate what is right. [1] The particle, ou, where, which I take as an adverb, some consider to be a relative, of which; but the former reading is the most suitable, and the most commonly received. Whichever reading you may follow, the meaning will be the same, -- that he who is not instructed by the written law, when he sins, is not guilty of so great a transgression, as he is who knowingly breaks and transgresses the law of God.

Footnotes

1 - It is better to take this sentence, "Where there is no law, there is no transgression," according to its obvious meaning; as it comports better with the former clause. The reasoning seems to be this, -- "The promise is by faith, and not by the law; for the law brings wrath or condemnation: but where there is no law, there is no transgression to occasion wrath." The same idea is essentially conveyed in verse Romans 4:16, where it is said, that the promise is sure, because it is through faith and by grace. Had it been by the law, there would have been transgression and wrath, and hence the loss of the promise. This verse is connected with the Romans 4:13 rather than with the 14th. It contains another reason, besides what Romans 4:14 gives, in confirmation of what is said in Romans 4:13. Hence Macknight renders gar, in this verse, "farther," which renders the connection more evident. "Where no law is, there is no transgression, and therefore no wrath or punishment; but where law is, there is transgression, wrath, and punishment." -- Pareus

Because the law - All law. It is the tendency of law.
Worketh wrath - Produces or causes wrath. While man is fallen, and a sinner, its tendency, so far from justifying him, and producing peace, is just the reverse. It condemns, denounces wrath, and produces suffering. The word "wrath" here is to be taken in the sense of punishment. Romans 2:8. And the meaning is, that the Law of God, demanding perfect purity, and denouncing every sin condemns the sinner, and consigns him to punishment. As the apostle had proved Romans. 1; 2; 3 that all were sinners, so it followed that if any attempted to be justified by the Law, they would be involved only in condemnation and wrath.
For where no law is - This is a general principle; a maxim of common justice and of common sense. Law is a rule of conduct. If no such rule is given and known, there can be no crime. Law expresses what may be done, and what may not be done. If there is no command to pursue a certain course, no injunction to forbid certain conduct, actions will be innocent. The connection in which this declaration is made here, seems to imply that as the Jews had a multitude of clear laws, and as the Gentiles had the laws of nature, there could be no hope of escape from the charge of their violation. Since human nature was depraved, and people were prone to sin, the more just and reasonable the laws, the less hope was there of being justified by the Law, and the more certainty was there that the Law would produce wrath and condemnation.

Because the law worketh wrath - For law νομος, any law, or rule of duty. No law makes provision for the exercise of mercy, for it worketh wrath, οργην, punishment, for the disobedient. Law necessarily subjects the transgressor to punishment; for where no law is - where no rule of duty is enacted and acknowledged, there is no transgression; and where there is no transgression there can be no punishment, for there is no law to enforce it. But the Jews have a law, which they have broken; and now they are exposed to the penal sanctions of that law; and, if the promises of pardon without the works of the law, do not extend to them, they must be finally miserable, because they have all broken the law, and the law exacts punishment. This was a home stroke, and the argument is unanswerable.

(13) Because the law worketh wrath: for where no law is, [there is] no transgression.
(13) A reason of the first confirmation, why the promise cannot be apprehended by the law: because the law does not reconcile God and us, but rather proclaims his anger against us, because no man can fully keep it.

Because the law worketh wrath,.... Not the wrath of man, though that is sometimes stirred up through the prohibitions of the law, to which the carnal mind of man is enmity, but the wrath of God the law is so far from justifying sinners, that it curses and condemns them; and when it comes into the heart and is let into the conscience of a sinner, it fills with terrible apprehensions of the wrath of God, and a fearful looking for of his judgment and fiery indignation:
for where no law is, there is no transgression; (r); a sort of a proverbial expression: had the law of Moses not been given, there was the law of nature which sin is a transgression of; but the law of Moses was added for the better discovery and detection of sin, which would not have been so manifest without it, and which may be the apostle's sense; that where there is no law, there is no knowledge of any transgression; and so the Ethiopic version reads the words, "if the law had not come, there would have been none who would have known sin"; but the law is come, and there is a law by which is the knowledge of sin, and therefore no man can be justified by it; since that convinces him of sin, and fills him with a sense of divine wrath on account of it.
(r) Caphtor, fol. 10. 1.

Because the law worketh wrath--has nothing to give to those who break is but condemnation and vengeance.
for where there is no law, there is no transgression--It is just the law that makes transgression, in the case of those who break it; nor can the one exist without the other.

Because the law - Considered apart from that grace, which though it was in fact mingled with it, yet is no part of the legal dispensation, is so difficult, and we so weak and sinful, that, instead of bringing us a blessing, it only worketh wrath; it becomes to us an occasion of wrath, and exposes us to punishment as transgressors. Where there is no law in force, there can be no transgression of it.