FLC OF AN EMBRAER 145 FOLLOWED THE HEADING GIVEN BY THE ORD TWR CTLR AFTER TKOF AND WAS SUBSEQUENTLY GIVEN A 180 DEG TURN BY THE DEP CTLR SINCE THEY WERE HEADING TOWARD ARR TFC.

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WHILE AWAITING DEP FOR RWY 27L AT ORD; TWR XMISSIONS WERE NUMEROUS AND FAST. ORD TWR WAS CTLING ARRS ON RWY 22L AND DEPS ON BOTH RWYS 22L AND 27L. WE WERE CLRED BEHIND ACR AB INTO POS AND HOLD ON RWY 27L. AFTER RESPONDING; WE REVERIFIED OUR CLRNC. TWR CONFIRMED POS AND HOLD RWY 27L; HOWEVER HIS RESPONSE WAS SHORT AND HIS VOICE IRRITATED. WE RAN THE CHKLIST (BEFORE TKOF). WE THEN HEARD CLRNC FOR ACR CD (OUR FLT); 'CLRED FOR TKOF TURN R HDG 320 DEGS.' I READ THE CLRNC BACK; AND ALTHOUGH WE BOTH THOUGHT THE HEADING/TURN SOUNDED INCORRECT; THE CTLR DID NOT RESPOND. AFTER BEING REBUKED FOR VERIFYING OUR POS AND HOLD CLRNC; THE CTLR ALSO NOT RESPONDING OR CORRECTING OUR HEADING READBACK AND DUE TO THE BUSY OPS AT THE TIME; WE DID NOT REVERIFY THE 320 DEG HDG AND TOOK OFF; (ALT CLRED US TO WAS 5000 FT MSL). UPON CONTACTING DEP AT APPROX 2500 FT MSL AND ON A 320 DEG HDG; WE RECEIVED NO RESPONSE INITIALLY. WE CALLED AGAIN AND BLOCKED PARTIALLY DEP'S XMISSION. WE THEN RECEIVED 'ACR CD TURN IMMEDIATELY TO 180 DEG HDG; LEVEL AT 4000 FT.' WE COMPLIED. THE 320 DEG HDG WAS TAKING US TOWARDS ARRS ON RWY 14R AND CONFLICTING TFC. NO TCASII WARNINGS WERE OBSERVED AND TFC CONFLICTS WERE AVOIDED. BOTH THE CAPT AND MYSELF HEARD 'R TURN; HDG 320 DEGS.' IT WAS EITHER BROADCAST IN ERROR; OR RECEIVED IN ERROR; WE COULD NOT DETERMINE WHICH.