Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Confusion; Situational Awareness; Communication Breakdown
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Executed Go Around / Missed Approach
Human Factors
We were arriving into DEN on the Molten3. When we checked on with Approach they told us Runway 35L. We had initially planned for Runway 34R. We then re-briefed Runway 35L. I was happy when I heard this as it would be a short taxi to the gate. We when checked on with the next Approach Controller; on check on I stated our clearance to descend via and for stated for Runway 35L. Controller said roger; 35L. On that frequency we heard [another] flight changed from Runway 35L to Runway 34R. We were not given a Runway change.We were then switched to final Controller. On check in I advised our descend via and for Runway 35L. Controller said;Runway 35L. On downwind were given descend to 9000 ft. and turn to heading 080. In the turn [Controller asked] 'advise the airport in sight'. I said it was in sight. Controller cleared us for what we thought was the visual for Runway 35L on heading of 020 to join the final approach course.At this point I am unclear if the Controller said Runway 34R or Runway 35L visual as both pilots still thought Runway 35L as it had not been changed for 3 Approach Controllers. I am not even sure if I read back Runway 34R or Runway 35L. On the heading of 020 we were on a heading to join the final approach course just over the final approach fix. While on the 020 heading the Approach Controller said traffic 3 o-clock and you are going through the course. I responded we have not intercepted the course for Runway 35L. The Controller said I have you down for Runway 34R.At that point he said 'traffic Alert; turn left 260 and climb 9000 ft.'. We executed the instructions and completed a missed approach. Once on the downwind I advised the Controller that we had been told Runway 35L from our first check on with approach. He said we will figure it out and turn left to 180 and expect visual Runway 34R. I loaded up the FMS for Runway 34R ILS and re-briefed the visual. We then received vectors for the visual Runway 34R and landed the aircraft on Runway 34R without further incident and taxied to gate. I believe the main cause was the conflicting clearance from the first check on with Denver Approach. I was completely confused and startled when the Approach Controller called the traffic and said we were going through the course and we had not even joined the course yet.    I think I could have verified the clearance one more time. I thought I had verified we were on the correct runway 3 times. I am not sure what else I could have done but I am more than open to suggestions.
Captain reported executing an ATC-commanded go-around after lining up for the wrong runway at DEN following a communication breakdown.