C182 ENRTE FWA-ARB NOTICED L AND R FUEL GAUGE INDICATING ZERO. SUSPECTED HAD LOST FUEL CAP. CONTINUED TO DEST OK. FOUND 20 GALLONS FUEL IN L TANK; ZERO IN THE R AND R FUEL CAP MISSING.

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IFR FLT FROM FWA TO ARB. FWA 2 MI 9 OVCST; ARB 11 BROKEN; 10 MI. DTW TAF JUST AMENDED FROM 40 OVCST TO 14 OVCST. DEPARTED FWA 30 MINS BEFORE SUNSET. ESTIMATED TIME ENRTE 60 MINS. HAD ACFT TOPPED PRIOR TO DEP. I DIPPED TANKS TO CHK LEVEL BEFORE DEP (HIGH WING C182). TRIP WAS UNEVENTFUL UNTIL LAST 20 MINS -- BECAME VERY R WING HVY. I THEN NOTICED BOTH FUEL GAUGES SHOWED EMPTY. I THEN SUSPECTED LOSS OF FUEL CAP. I WAS IMC AND IT WAS NOW DARK! I SWITCHED TO L TANK SO I WOULD NOT EXHAUST BOTH AT ONCE. I ALSO DELAYED MY DSCNT TO MDA UNTIL THE LAST MIN. I FOUND ABOUT 20 GALLONS IN MY L TANK AND 0 GALLONS IN THE R TANK. THE R GAS CAP WAS GONE. I MUST NOT HAVE TIGHTENED IT SECURELY WHEN I CHKED IT. I ALSO FOUND AN ACCUMULATION OF ICE ON THE TOP OF THE WING AFT OF THE FUEL CAP; WHICH MAY EXPLAIN THE R WING BEING HVY EVEN THOUGH IT WAS THE L TANK THAT HAD FUEL. ALSO THE FLAP MOTOR IS IN THE R WING AFT OF THE FUEL TANK. I SUPPOSED THAT COULD HAVE STARTED A FIRE. THE MORAL OF THE STORY IS ALWAYS GET A LADDER WHEN YOU CHK THE TANKS ON A HIGH WING AIRPLANE! EVEN THOUGH I WALKED AROUND AND LOOKED AT IT FROM BEHIND. I DID NOT NOTICE IT BEING LOOSE.