Processes and apparatus for isomerizing hydrocarbons are provided. The process comprises isomerizing at least a portion of the hydrocarbon feed stream comprising at least one of C4 to C7 hydrocarbons in the presence of an isomerization catalyst and hydrogen under isomerization conditions to produce a isomerized stream. The isomerized stream is stabilized in a stabilizer to provide a stabilizer off-gas stream comprising chlorides and a liquid isomerate stream. At least a portion of the stabilizer off-gas stream is contacted with an exchange stream to provide an absorber overhead stream and absorber bottoms stream comprising chlorides. The absorber bottoms stream is passed to the isomerization reactor. The liquid isomerate stream is passed to a deisohexanizer column to provide an isomerate product and deisohexanizer side stream.