The natural gas arriving through pipe 1 is deacidified by being brought
into contact with a solvent in column C2. The solvent charged with acid
compounds is regenerated in zone R. The purified gas evacuated by pipe 9
includes some of the solvent. The method enables the solvent contained in
the purified gas to be extracted. In zone ZA, the purified gas is brought
into contact with a non-aqueous ionic liquid whose general formula is
Q.sup.+ A.sup.-, where Q.sup.+ designates an ammonium, phosphonium,
and/or sulfonium cation, and A.sup.- designates an anion able to form a
liquid salt. The solvent-impoverished purified gas is evacuated through
pipe 17. The ionic liquid charged with solvent is regenerated by heating
in an evaporator DE. The solvents separated from the ionic liquid in
evaporator DE are recycled.