The carbon-free gas turbine is a power-producing turbine driven by the combustion of hydrocarbon fuels with oxygen. The carbon-free gas turbine includes at least one combustor for combusting gaseous fuel with oxygen. The at least one combustor includes a housing containing at least one oxygen transport reactor. The oxygen transport reactor includes an outer wall and an inner cylindrical ion transport membrane. The membrane receives pressurized air and separates gaseous oxygen therefrom, transporting the oxygen into a central region thereof for combustion with the gaseous hydrocarbon fuel, producing gaseous carbon dioxide and water vapor. A first turbine is driven by the gaseous carbon dioxide and water vapor produced by the at least one combustor and drives a first compressor. The first compressor provides the pressurized air supplied to the at least one combustor. A second turbine is driven by pressurized nitrogen gas resulting from the combustion.