AN EMB170 CREW FLIES HDG 238 DEGS WHILE DEP CYUL RWY 28 INSTEAD OF HDG 283 DEGS. HDG 238 DEGS APPLIES TO RWY 24.

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WE TAXIED OUT THE GATE IN CYUL TO RWY 28. THE FO WAS ASSIGNED AS THE PF. DURING THE TAXI; HE BRIEFED THE DORVAL 6 OFF RWY 28; WHICH INITIALLY CALLED FOR A HDG OF 238 DEGS. HE BRIEFED EVERYTHING; WE COMPLETED THE TAXI CHK; TAXIED TO RWY 28 AND TOOK OFF. AT 400 FT AGL HE ASKED FOR 'HDG.' I PUSHED THE 'HDG' BUTTON THEN REACHED DOWN TO FLIP THE RADIO TO DEP CTL. I CALLED DEP CTL AND THERE WAS NO ANSWER. ABOUT THIS TIME I NOTED THAT WE WERE TURNING L MORE THAN I THOUGHT WE SHOULD BE. I MADE ANOTHER CALL TO DEP AND ALSO I TURNED TO THE SID TO MAKE SURE WE HAD THE RIGHT FREQ AND TO DOUBLE CHK TO MAKE SURE WE WERE ON THE RIGHT HDG. DEP ANSWERED US AND ASKED OUR HDG. I LOOKED AT THE BUG AND REPLIED '238 DEGS.' ATC ASKED IF WE WERE ON THE DORVAL 6 AND I REPLIED 'AFFIRMATIVE.' JUST THEN I LOOKED AT THE DEP PROC AND REALIZED OUR MISTAKE. INSTEAD OF HDG 283 DEGS WE WERE HDG 238 DEGS. ATC THEN JUST ADVISED US THAT WAS THE HDG FOR RWY 24 DEPS AND I APOLOGIZED AT OUR MISTAKE. HE TOLD US TO TURN TO 300 DEG HDG AFTER PASSING 4000 FT AND THE FLT RESUMED NORMALLY. AFTER DISCUSSING WHAT WENT WRONG; WE DIDN'T KNOW IF THE FO READING THE DEP HDG FOR RWY 24 R/L; 238 DEGS; WHICH WAS LOCATED ABOVE THE DEP HDG FOR RWY 28; OR IF HE READ THE CORRECT HDG FOR DEPARTING RWY 28 AND SIMPLY SWITCHED THE LAST 8 AND 3 WHEN HE SET THE HDG BUG TO 238 DEGS. USUALLY THESE TYPES OF ERRORS I CATCH BUT UNFORTUNATELY THIS TIME I DIDN'T. ONE POSSIBLE FACTOR IS A LARGE AMOUNT OF INACTIVITY PRIOR TO WORK. WE HAD BEEN SITTING AT THE HOTEL ALL DAY. I'VE NOTICED IN THESE CASES; I'M NOT AS SHARP AS I USUALLY AM WHEN I RPT TO THE ARPT EARLIER. ANOTHER FACTOR WAS; DUE TO CONSTRUCTION ON THE N RAMP WE HAD TO TAXI IN THE CTR RAMP WHERE IT IS A BIT TIGHTER AND I WAS PAYING CLOSE ATTENTION TO CLRING EVERYTHING. DUE TO THIS I MAY HAVE MISHEARD THE FO'S HDG AND HIS TAKEOFF BRIEFING.