A process for purifying a crude furan 2,5-dicarboxylic acid composition (cFDCA) by hydrogenation of a FDCA composition dissolved in a hydrogenation solvent such as water, and hydrogenating under mild conditions, such as at a temperature within a range of 130° C. to 225° C. by contacting the solvated FDCA composition with hydrogen in the presence of a hydrogenation catalyst under a hydrogen partial pressure within a range of 10 psi to 900 psi. A product FDCA composition is produced having a low amount of tetrahydrofuran dicarboxylic acid, a low b*, and a low amount of 5-formyl furan-2-carboxylic acid (FFCA).