Mount Hopeful is a peak standing 1.5 nautical miles (2.8 km) north of the head of King George Bay

King George Bay

King George Bay is a large bay on the coast of West Falkland in the Falkland Islands, facing westwards. There are three settlements on the bay Chartres, Dunnose Head and Roy Cove. Storm Mountain is on the north coast. it contains numerous islands, including the Passage Islands....

 and 1.5 nautical miles (2.8 km) southeast of Rea Peak

Rea Peak

Rea Peak is a peak, 590 m, lying nearly 2 nautical miles northeast of Rose Peak and 1.5 nautical miles northwest of Mount Hopeful in the central part of King George Island, in the South Shetland Islands...

 on King George Island, in the South Shetland Islands

South Shetland Islands

The South Shetland Islands are a group of Antarctic islands, lying about north of the Antarctic Peninsula, with a total area of . By the Antarctic Treaty of 1959, the Islands' sovereignty is neither recognized nor disputed by the signatories and they are free for use by any signatory for...

. Named by the United Kingdom Antarctic Place-Names Committee (UK-APC) in 1960 for the Enderby Brothers' schooner Hopeful (Captain Henry Rea), which sailed from London in 1833 in company with the tender Rose in order to continue John Biscoe

John Biscoe

John Biscoe was an English mariner and explorer who commanded the first expedition known to have sighted the areas named Enderby Land and Graham Land along the coast of Antarctica...

's Antarctic researches. The Antarctic voyage was abandoned after the Rose had been crushed in the pack ice at 6017S, 5326W, December 1833 or January 1834.