Disclosed herein are azeotrope and near-azeotrope compositions comprising 1,1,1,2,2,4,5,5,6,6,7,7,7-tridecafluoro-3-heptene (HFC-162-13mczy, CF.sub.3CF.sub.2CH.dbd.CFCF.sub.2CF.sub.2CF.sub.3) and 1,1,1,2,2,3,5,5,6,6,7,7,7-tridecafluoro-3-heptene (HFC-162-13mcyz, CF.sub.3CF.sub.2CF.dbd.CHCF.sub.2CF.sub.2CF.sub.3) and hydrogen fluoride (HF) and to azeotrope and near-azeotrope compositions comprising 1,1,1,2,2,3,4,5,5,6,6,7,7,7-tetradecafluoroheptane and hydrogen fluoride (HF). These compositions are useful in processes to produce and purify HFC-162-13mcyz, HFC-162-13mczy and HFC-63-14mee.