ON DEP FREQ AFTER TKOF; A B737 CREW ARE INSTRUCTED TO CONTACT ANOTHER DEP SECTOR; BUT THEY CHANGED TO THE WRONG FREQ.

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TOOK OFF RWY 31 WITH A R TURN EBOUND AND A CLB TO 3000 FT. WE WERE TALKING TO DEP CTL ON 118.4; WHO GAVE US A CLB TO 4000 FT WITH A FREQ CHANGE. WE INADVERTENTLY WENT TO THE WRONG FREQ; WHICH TURNED OUT TO BE CHICAGO CTR ON 120.35. CTR ACKNOWLEDGED US AND GAVE US A CLB TO FLT LEVEL 210. WE DID NOT KNOW WE HAD GONE TO THE WRONG FREQ; BECAUSE CTR PICKED US UP AND GAVE US CLB INSTRUCTIONS. PASSING AROUND 7000 FT; WE NOTICED TFC ON OUR TCASII THAT APPEARED TO BE DSNDING OUT IN OUR DIRECTION. WE ASKED CTR ABOUT THE TFC AND WERE TOLD THEY WERE DSNDING INTO O'HARE. HE DIDN'T SEEM CONCERNED ABOUT THE SEPARATION. THE TFC PASSED WITHIN 2 1/2 MI; BUT AT ITS CLOSET POINT; WAS MORE THAN 1000 FT BELOW US. WE ALSO RECEIVED A TA ON TCASII. A COUPLE OF MINS LATER; CTR ASKED US IF WE HAD BEEN CLRED BY DEP CTL TO 13000 FT BEFORE THE HDOF. I TOLD THEM WE HAD BEEN CLRED TO 4000 FT. AFTER A LONG PAUSE; CTR SAID THERE WAS SOME CONFUSION AND TO GIVE THEM A CALL UPON LNDG. I CALLED AND TALKED TO A CTR SUPVR. I RELAYED THE STORY TO HIM; AND HE SAID TO CALL BACK LATER AFTER HE DID SOME CHKING. I CONTACTED HIM LATER AND WAS TOLD CTR ASSUMED WE HAD BEEN CLRED BY DEP CTL TO 13000 FT; AND HE AUTOMATICALLY CLRED US TO FL210; APPARENTLY WITHOUT HEARING MY 4000 FT CALL OR OBSERVING OUR ALT READOUT. AFTER REMINDING ME TO LISTEN CAREFULLY ON THE RADIO; HE SAID THERE WOULD BE NO FURTHER ACTION; BECAUSE NO ACFT SEPARATION CRITERIA WAS VIOLATED. WE ALMOST DID NOT SUBMIT THIS RPT; BECAUSE EVEN THOUGH WE WENT TO THE WRONG FREQ; CTR PICKED US UP AND APPEARED TO BE CTLING US NORMALLY. THE CTR SUPVR SAID THERE WAS NOTHING TO RPT. SUPPLEMENTAL INFO FROM ACN 574967: CLBING THROUGH ABOUT 7000 FT; WE SAW SOME DSNDING TFC ON OUR TCASII AND ASKED THE CTLR ABOUT IT. HE SAID THAT IT WAS TFC FOR O'HARE AND IT WAS NOT A FACTOR WE CLBED THROUGH ITS ALT AT ABOUT 8000 FT AND WERE ABOUT 3-5 MI AWAY FROM IT AND AT LEAST 1000 FT CLR OF IT AT ALL TIMES. WE DID NOT RECEIVE ANY TA'S AND NEITHER DID THE CTR. AFTER TFC PASSED; THE CTLR ASKED US ABOUT OUR LAST ALT CLRNC AND WHAT THE PREVIOUS CTLR HAD CLRED US TO. WE COULD TELL THAT THE CTLR WAS CONFUSED/CONCERNED ABOUT THE ALT CLRNC WE HAD BEEN GIVEN BEFORE CHKING ON WITH HIM. CTR SUPVR HE REVIEWED THE TAPES AND DETERMINED THAT WE HAD SKIPPED A FREQ. WE SHOULD HAVE GONE TO 125.00. SINCE HE ACCEPTED US AND GAVE US AN ALT CLRNC WE THOUGHT WE WERE ON THE CORRECT FREQ FOR OUR PHASE OF FLT.