Find the formulas for the following hydrate?

Question

Ca= 21.05%
S=16.84%
O= 58.95%
H= 3.16%
H20= 28.42%

Answer 1

If these are wt% then you need to divide each one by it's respective molar mass to get % by numbers of atoms/molecules.

21.05/40.08 = 0.525
16.84/32.06 = 0.525
58.95/16.00 = 3.68
3.16/1.01 = 3.13
28.42/18.03 = 1.58

These numbers are in the proper ratio for the empirical formula but they are not in whole numbers so, we will divide everything by 0.525 and see if we get whole (or nearly whole) numbers:

0.525/0.525 = 1.00
0.525/0.525 =1.00
3.68/0.525 = 7.01
3.13/0.525 = 5.96
1.58/0.525 = 3.01

We can see that the empirical formula for the compound hydrate is CaSO7H6 and that the 28.42 % water by weight in the hydrate corresponds to 3 molecules of water so the material is : CaSO4*3H2O

Check the answer:

[3 x (16.00 + (2 x 1.01))]/[40.08 + 32.06 + (7 x 16.00) + (6 x 1.01)] X 100% = 54.06/190.2 x 100% = 28.42% water

Added:

Note: the the first 4 entries for the data total 100%; the last entry (for water) tells you how much of the hydrogen and oxygen (from the other entries) are in the form of water of hydration, as opposed to some other group, ion, etc.