Question

Epsom salt is commonly purchased in the pharmacy for a variety of uses, anti-inflammatory, laxative, and cosmetic. epsom salt is a hydrated salt of magnesium sulfate. if 2.000 g of epsom salt are heated to remove the waters of hydration, 0.977 g of the anhydrous (without water) magnesium sulfate, mgso4, were obtained. calculate the number of waters of hydration, and write the chemical formula of the epsom salt.

Answer 1

Epsom salt is MgSO4.
We assume x water of hydration in the crystalline form.

Molecular mass of MgSO4 = 24+32+4*16=120
Molecular mass of MgSO4.xH2O = 120+18x

By proportion, 
2.000/0.977 = (120+18x)/120
Cross multiply
0.977(120+18x) = 120*2.000
from which we solve for x
17.586x+117.24 = 240
x=122.78/17.586
=6.980

Answer: there are 7 water of hydration in Epsom salt, according to the experiment.

Note: more accurate (proper) results may be obtained by using exact values (3-4 significant figures) in the molecular masses.  However, since water of hydration is the nearest integer, using approximate values (to at least two significant figures) suffice.

Answer 2

The total weight (MgSO₄ + xH₂O) = 2.000 g

Weight of anhydrous, that is, without water magnesium sulfate = 0.977 g

Weight of xH₂O = 2.000 - 0.977 = 1.023 g

Moles of water = Weight / molecular mass

= 1.023 / 18 = 0.057  

Moles of MgSO₄ = 0.977 / 120.366 = 0.0081

0.0081 mole (0.977) MgSO₄ hydrated with = 0.057 mol of water

1 mole will react with = 7 mol of water

Chemical formula of the Epsom salt = MgSO₄.7H₂O