Identification of both minerals is usually not easy one. I remember I used to put the cuttings in a sample tray with HCl and after few hours I could see the emerging yellow circle on the tray hole top, I think it was due to the slow sulfur reaction. But again since both Gypsum and Anhydrite contain sulfur it was yet difficult to distinguish between these two minerals..

Both minerals, Gypsum and Anhydrite are Calcium Sulphate; gypsum has water molecule attached to it whereas there is no water (H2O) with anhydrite. Both look same except few physical properties that are distinguishable. One is that Gypsum is softer than Anhydrite. At Moh's hardness scale Gypsum is 2 and Anhydrite is about 3 to 3.5. Density of Gypsum is 2.33 g/cc and Anhydrite 2.9 to 3.2 g/cc. Try this simple experiment as well by scratching rock cutting with your finger nail if the rock sample is big enough.

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