AN ACR MLG CREW TOOK OFF WITHOUT AN AIRWAYS CLRNC THROUGH THEIR ACARS.

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WE HAD JUST FLOWN ACR FLT X FROM SYR TO PIT AND WERE ON THE GND IN PIT WITH 1 HR BEFORE CONTINUING TO LAN ON THE SAME FLT. SINCE IT WAS TOO EARLY TO GET OUR ATC CLRNC TO LAN; I INITIATED THE ACARS FOR THE NEXT LEG AND LEFT THE ACFT. UPON ARR BACK AT THE ACFT; SOME 45 MINS LATER; THE CAPT AND I PERFORMED OUR REQUIRED CHKLISTS AND ENGAGED IN SOME CONVERSATION. DEP TIME CAME. THE PUSHBACK AND TAXI OUT WAS PERFORMED AND WHEN WE REACHED THE END OF THE RWY; OUR TKOF CLRNC WAS GIVEN AND WE DEPARTED. ONCE AIRBORNE; WE CONTACTED DEP CTL. WHEN WE CHKED IN WITH THE CTLR; WE WERE TOLD TO SQUAWK A DIFFERENT CODE THAN THE ONE WHICH WAS SET IN. IT WAS THEN WHEN I REALIZED THAT WE HAD NOT RECEIVED OUR CLRNC OVER THE ACARS (PRE-DEP CLRNC). WE THEN SET IN THE NEW XPONDER CODE AND PROCEEDED TO LAN AS FILED AND WITHOUT FURTHER QUESTIONS OR COMMENTS FROM ATC. I BELIEVE THAT THIS PROB WILL BE AND IS A COMMON OCCURRENCE WHEN USING ACARS (PRE-DEP CLRNC). I ALSO BELIEVE THIS PROB CAN BE SOLVED BY OBTAINING CONFIRMATION OF YOUR CLRNC RECEIVED BY GND CTL ON TAXI OUT.