Dr. Couch, it seems as if the book of Romans is written to believers, but then chapter 2 appears to be addressing the unbelievers. Is this true?
Yes, you have it correct. The book in the larger sense is addressed to those who have trusted Christ but Paul has several segments that are aimed at the lost. There is nothing wrong with this. We just have to observe carefully when he makes the shift in context. Notice in 2:3 he writes "O man" and then reminds humanity in general of the wrath that they will have to face from the righteous judgment of God (v. 5). 2:17-29 is aimed at the Jews. Paul begins here by writing "But if you bear the name 'Jew' …" (v. 17). In 3:9-20 the apostle puts all of humanity, both Jew and Gentile, under sin and condemned. Only Christ, and justification by faith, can get us out of the mess of sin!
As Paul gets into chapter 3 he starts applying the salvation process to his readers and shows that by faith we are saved and have a new position in Christ. I would say then that the rest of the book goes back and is aimed at his audience, the believers who are residing in Rome.
Thanks for asking.
Dr. Mal Couch