An apparatus (2, 20, 200) for separating CO2 from a mixture of gases includes CO2 and a second gas, the apparatus (2, 20, 200) includes an active heat exchanger (216) and a regenerating heat exchanger (221). The active heat exchanger (216) includes a heat exchange surface in contact with the mixture of gases. The mixture of gases is present in the active heat exchanger (216) at a predetermined pressure which is chosen such that CO2 freezes on the heat exchange surface when the surface is cooled by a refrigerant having a temperature below that at which CO2 freezes at the predetermined pressure. The regenerating heat exchanger (221) includes a heat exchange surface in contact with the refrigerant and also in contact with a layer of frozen CO2. The refrigerant enters the regenerating heat exchanger (221) at a temperature above that at which the CO2 in the frozen layer of CO2 sublimates. The sublimation of the solid CO2 cools the refrigerant prior to the refrigerant being expanded through an expansion valve (215), which reduces the temperature of the refrigerant to a point below the freezing point of CO2 at the predetermined pressure. The refrigerant is re-compressed by a compressor (60, 160, 218) after leaving the active heat exchanger (216). In the preferred embodiment of the present invention, the gaseous CO2 released by the regenerating heat exchanger (221) is used to precool the incoming gas mixture. A second precooling heat exchanger (167) precools the compressed refrigerant by providing thermal contact with the refrigerant leaving the active heat exchanger (216).