On June 1, 2014, about 1315 Alaska daylight time, a Cessna 182K airplane, N2631R, sustained substantial damage when it was involved in an accident near Galena, Alaska. The pilot and one passenger sustained minor injuries, and two passengers were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 flight. The pilot reported that the purpose of the flight was to pick up three employees from two remote locations to transport them to Fairbanks, Alaska, so they could attend a training class. After departing Fairbanks International Airport (FAI), Fairbanks, he flew to the two locations and picked up the three employees uneventfully. The flight then departed Kaltag, Alaska, destined for Edward G. Pitka Sr. Airport (GAL), Galena, Alaska, for a planned fuel stop before returning to FAI. The pilot reported that, as the airplane approached GAL and while flying level at 1,500 ft mean sea level, the engine began to run roughly and lose power. The pilot applied carburetor heat, but it had no effect. He then confirmed that the fuel selector was set to both and saw that the fuel totalizer indicated that about 22.8 gallons of fuel were remaining. However, both fuel gauges were indicating near empty with little or no movement of the needles. Shortly thereafter, the engine lost all power, so he chose to conduct a forced landing on a lake shoreline, during which the airplane flipped over, became partially submerged in water, and sustained substantial damage to the fuselage and wings. The wreckage was recovered about 1.5 months after the accident. Examination of the wing fuel bladders revealed that at least five bladder fastening snaps in the left wing and three snaps in the right wing were unfastened; however, it could not be determined if the bladder fastening snaps became unfastened before or during the accident or during the wreckage recovery. Examination of the airplane revealed no other evidence of any mechanical malfunctions or failures that would have precluded normal operation.  According to the Federal Aviation Administration carburetor icing probability chart, the temperature and dew point when the engine lost power, were conducive to the accumulation of serious icing at cruise power settings.