The airplane departed with 24 gallons of usable fuel, which normally allows for 4.5 hours of flight. Two and half hours into the flight, the engine started running rough. The pilot confirmed the mixture was rich and the carburetor heat was on. About 5 minutes later the engine quit and the pilot executed a forced landing to an area of tundra-covered terrain, substantially damaging the undercarriage, fuselage, and left wing strut. A postaccident examination by a Federal Aviation Administration Inspector revealed that the carburetor had separated from the engine during the forced landing, and the gascolator drain had tundra embedded in it. The pilot stated that he had turned the fuel selector to the OFF position about 30 minutes after the landing. The carburetor icing chart indicated the possibility of serious carburetor icing at the reported atmospheric conditions. The Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25A) states that first indication of carburetor ice in an airplane with a fixed-pitch propeller is a decrease in engine rpm. Additionally, it states that when conditions are conductive to carburetor icing that carburetor heat should be applied immediately and should be left ON until the pilot is certain all the ice has been removed. If ice is present applying partial heat or leaving heat on for an insufficient time might aggravate the situation. Postaccident examination of the airframe and engine revealed no preimpact mechanical malfunctions or failure that would have precluded normal operation.