C-172 Flight Instructor reported fuel leak inflight. Post flight it was discovered a fuel cap was missing.

Narrative

We noticed an unusually low fuel reading on our left tank for the duration we had flown. Our fuel was topped off prior to flight. Approximately one hour into the flight we were showing half a tank on the left (~13 gallons missing) and a full tank on the right; we would have expected closer to ~5 gallons missing from each tank. We were able to see fuel leaking from the right tank while in flight; so we diverted to ZZZ and requested priority sequencing due to our fuel loss. We were able to see the fuel gauge dropping in level. We landed at ZZZ with an indication of 5 gallons on the left tank and full on the right tank; the both tanks hold 26 gallons. After landing; we inspected the aircraft and discovered our right tank fuel cap missing; it was present during our preflight. At our sister flight school at ZZZ; we were able to obtain a temporary replacement fuel cap so that we could return to ZZZ1. We topped off with fuel; taxied to the run-up; and departed for ZZZ1 and returned to ZZZ1 without incident. Prior to our flight; we had called for a fuel truck and had the tanks filled to full. The student noticed the fuel was very high; to the very top; of the fuel necks after the fueling was completed. Our run-up; departure; and flight were without incident until we discovered the fuel leak. After returning to ZZZ1; we had learned that Airport Ops had been notified of FOD on taxiway C; which was a fuel cap; we had taxied down taxiway C. Ops returned the fuel cap to our front desk and it looks like it was from our aircraft.