A 2.500 gram sample of hydrate of calcium sulfate loses 0.532 grams of water when heated. Determine the mass percent of water in the hydrate and the formula of the hydrate.

Answer 1

It lost 0.532 g H2O out of a 2.500 g sample.
%H2O = (mass water lost/mass sample) x 100 = approximately 22 but you need to go through it to do it more exacting than that.

Now take 100 g sample. That will give you
22% H2O (or the value you recalculate)
78% CaSO4 (found by 100%-% water)

22/molar mass H2O = moles H2O
78/molar mass CaSO4 = moles CaSO4.

Now find the ratio of the two numbers in small whole numbers. The easy way to do this is to divide the small number by itself give 1.000 for that. Then divide the other number by the same small number. Round to whole numbers and you have the formula written this way.
CaSO4.xH2O where x is what you find.

Answer 2

20.92 %