ACR MLG MADE A TKOF FROM THE WRONG RWY AT ORD.

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I WAS FLYING AS FO ON A SCHEDULED FLT. TAXI INSTRUCTIONS WERE TO PROCEED BY THE OUTER AND CARGO TAXIWAYS TO RWY 22L. THE CAPT SEEMED FAMILIAR WITH THE TAXI RTE; SO I JUST MADE A QUICK GLANCE AT THE ARPT DIAGRAM. WHILE TAXIING WE WERE TOLD TO MONITOR THE TWR. WE TAXIED UP BEHIND WDB THAT WAS TURNING L INTO THE CARGO AREA AND WE MADE A R TURN INTO A RUNUP PAD AHEAD AND CAME TO A STOP. I SAW RWY 27L AHEAD OF US AND THOUGHT THE THRESHOLDS OF 22L AND 27L WERE IN THE SAME AREA AND THAT WE WOULD CROSS 27L TO GET TO 22L. AS THERE WAS NO TFC; I THOUGHT IT WAS ODD THAT THE TWR HAD NOT CALLED US; SO I CALLED THE TWR AND TOLD THEM WE WERE READY FOR TKOF. THERE WAS A PAUSE AND THE TWR SAID CLRED FOR TKOF BUT DIDN'T GIVE A RWY NUMBER. MY RESPONSE WAS CLRED FOR TKOF; BUT I ALSO DIDN'T GIVE A RWY NUMBER. AS WE STARTED TAXIING MY ATTN WENT TO THE CHKLIST AND I DIDN'T REALIZE THAT WE TURNED ON RWY 27L AND THAT IS WHERE WE TOOK OFF. I SHOULD HAVE REALIZED THAT SOMETHING WAS NOT QUITE RIGHT BY THE WAY THE TKOF CLRNC WAS ISSUED BY THE TWR AND I SHOULD HAVE LOOKED AT THE ARPT DIAGRAM MORE CLOSELY IN THE AREAS OF RWYS 22L AND 27L.