B737 Next Generation Undifferentiated
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 150; Flight Crew Type 15000
Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Wake Vortex Encounter
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Airport; Environment - Non Weather Related; Human Factors
An aircraft was on a three-mile final for our Runway 31C. Aircraft Y was cleared for takeoff on 31C. Immediately after that; while Aircraft Y was barely moving; we where cleared for takeoff with a heading of 010 degrees that we both heard and confirmed with each other. The heading seemed odd at the time; but we where both distracted by checking to see if Aircraft Y was wheels up yet on 31C. He was not by the time we were in position for takeoff and we delayed a few seconds until he lifted off. Once airborne; the First Officer (FO) turned to 010 heading and I contacted Departure. We did hit prior aircraft's wake turbulence that was an additive. When I contacted Departure; the FO stated my comment panel was still on intercoms. Once I changed over; Departure asked what heading we were assigned. I told him 010; which again felt weird. Departure told us to turn to 110 and we complied.
We were cleared into position 31C with an aircraft on 2.5 to 3 mile final.  Aircraft Y had just taken off; and we were cleared for takeoff with Aircraft Y still on takeoff roll; this surprised us. We were given a heading of 010 as we lined up on runway and exchanged controls.  Shortly after starting the turn; we hit wake off of Aircraft Y close ahead of us. It was a flaps 25 takeoff so we were also busy with cleaning the configuration; turning; leveling off and contacting Departure.  In the turn we contacted Departure.  As we rolled out I realized something was wrong. In my head I heard 010; and 010 was set and confirmed; but mentally I was thinking we were turning to 110 per normal operations.  I was surprised when we reached the heading bug so quickly; and knew something was off.  Departure gave us the 110 heading and we complied.
B737 flight crew reported a track deviation occurred following a misunderstood ATC clearance.