A process is disclosed for making CF3CF═CHF or a mixture thereof with CF2═CFCHF2. The process involves (i) contacting CH2ClCF2CF3, and optionally CH2FCF2CClF2, in a reaction zone in the presence of a catalytically effective amount of dehydrofluorination catalyst to produce CHCl═CFCF3, and, if CH2FCF2CClF2 is present, CHF═CFCClF2; (ii) contacting CHCl═CFCF3, and CHF═CFCClF2, if any, formed in (i) with hydrogen fluoride (HF) in a reaction zone, optionally in the presence of a fluorination catalyst, to produce a product mixture comprising CHF═CFCF3, and, if CHF═CFCClF2 is present, CF2═CFCHF2; and (iii) recovering CF3CF═CHF, or a mixture thereof with CF2═CFCHF2, from the product mixture formed in (ii); and optionally (iv) separating at least a portion of any CF3CF═CHF in the product mixture formed in (ii) from the CF2═CFCHF2 in the product mixture formed in (ii). Also disclosed is an azeotropic composition involving CHCl═CFCF3, CHF═CFCClF2 and HF.