Method and apparatus for purifying and cooling a gas mixture

In a process for cooling and purifying a gaseous mixture (1) containing at least one impurity, cooled gas mixture containing at least one impurity until a temperature at or below that at which the at least one impurity solidifies in a heat exchanger (3,3A) having cooling passages, the cooling passages being at least partially covered with a coating and / or treated physically and / or chemically treated, coating and / or treatment serving to limit or even prevent the formation and / or adherence of the solidified impurity on a surface of the passages, are collected at least a portion (5B, 19) of the outgoing solidified impurity cooling passages of heat exchanger and / or at an intermediate level of the heat exchanger and is taken off the gas mixture of the heat exchanger.