EMER DECLARED UNNECESSARILY.

Narrative

WE SWITCHED TO THE AUX FUEL TANKS APPROX 1 HR 30 MINS AFTER TKOF. APPROX 50 MINS AFTER SWITCHING TANKS; THE L ENG FAILED. THE L AUX FUEL TANK HAD EXHAUSTED ITS FUEL SUPPLY. AFTER TROUBLESHOOTING THE CAUSE OF THE ENG FAILURE; THE FUEL SELECTORS WERE PLACED BACK ON THE MAIN TANKS. THE L ENG CAME BACK ON LINE; BUT THERE WAS SIGNIFICANT 'COUGHING AND SPUTTERING.' WE DECLARED AN EMER AND RECEIVED VECTORS TO FOX FIELD. I THEN ACTIVATED THE AUX FUEL PUMP ON HIGH; WHICH SUBSEQUENTLY CLRED THE VAPOR FROM THE LINE AND THE ENG RESUMED NORMAL OPS. WE DECIDED TO LAND ANYWAY AND CONFIRM THAT; INDEED; VAPOR WAS THE PROB. IT WAS; AND AFTER REFUELING THE AUX TANKS; WE RESUMED OUR TRIP. WE WERE PROBABLY A LITTLE HASTY IN DECLARING THE EMER; HOWEVER; AND I SINCERELY HOPE THAT NO ONE WAS INCONVENIENCED AS A RESULT. WE ADVISED ATC THAT EMER ASSISTANCE WAS NO LONGER NEEDED ONCE THE ENG RESUMED NORMAL OP. IN THE FUTURE; I WILL TEACH STUDENTS TO TIME THE OPS ON THE AUX TANKS RATHER THAN USE THE GAUGES. IT WILL ALSO BE ADVISABLE THAT ONLY 45 MINS OF TIME BE SPENT USING THESE TANKS. ALSO; IT IS NOT A GOOD IDEA TO RUN A TANK DRY EVEN IF YOU HAVE MORE FUEL IN ANOTHER TANK. VAPOR LOCK CAN CAUSE A LOSS OF THE ENG. I VIEW THIS AS A LEARNING EXPERIENCE.