The words of the chapter refute your argument that it was - "to show God chose Israel".
Israel sought God not by faith; the chapter points that out.
(Please read) :
[SUP]23 [/SUP]And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory,
[SUP]24 [/SUP]Even us, whom he hath called, not of the Jews only, but also of the Gentiles?
[SUP]25 [/SUP]As he saith also in Osee, I will call them my people, which were not my people; and her beloved, which was not beloved. - (Who is this addressing E.G? Israel or the church?)
[SUP]26 [/SUP]And it shall come to pass, that in the place where it was said unto them, Ye are not my people; there shall they be called the children of the living God. - (Again....the ekklesia, and not the physical nation of Israel)
[SUP]27 [/SUP]Esaias also crieth concerning Israel, Though the number of the children of Israel be as the sand of the sea, a remnant shall be saved: - (How much more plain can it be,.....that Paul is talking about believers and not the physical nation?)
[SUP]28 [/SUP]For he will finish the work, and cut it short in righteousness: because a short work will the Lord make upon the earth.
[SUP]29 [/SUP]And as Esaias said before, Except the Lord of Sabaoth had left us a seed, we had been as Sodoma, and been made like unto Gomorrha.
[SUP]30 [/SUP]What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith.
[SUP]31 [/SUP]But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.
[SUP]32 [/SUP]Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
[SUP]33 [/SUP]As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed.
The very words of the Apostle refute your contention - that Romans 9 was written to show God chose the physical nation
of Israel. He is clearly addressing those of the household of faith - (Who's faith is a gift from God - lest any man should boast)