Processes for separating a di-carboxylic acid or salt thereof from a mixture containing the di-carboxylic acid or salt thereof and one or more other components are provided. Also separation media useful for these separation processes is provided. In particular, processes for preparing an aldaric acid are described, such as glucaric acid from glucose, which includes separating the aldaric acid from the reaction product. Also, various glucaric acid products are described.