Problem: Epsom salts is a hydrated ionic compound with the following formula: MgSO4 • xH2 O. A 4.93 g sample of Epsom salts is heated to drive off the water of hydration. The mass of the sample after complete dehydration was 2.41 g.Find the number of waters of hydration (x) in Epsom salts.

Step 1: Calculate the mass and moles of MgSO₄ and H₂O in the compound.

The problem states that the sample of Epsom salt is heated to drive off the water of hydration:

mass of hydrated (with water) Epsom salt = 4.93 g

mass of dehydrated (without water) Epsom salt = 2.41 g MgSO₄

Therefore, the mass of water is then the difference in mass:

mass of water = mass of hydrated Epsom salt – mass of dehydrated Epsom salt

mass of water = 4.93 g – 2.41 g

mass of water = 2.52 g H₂O

Now, we need to get the moles of each MgSO₄ and H₂O compound. We will need their molar mass for the calculation:

molar mass MgSO₄:

MgSO₄           1 Mg x 24.3 g/mol = 24.3 g/mol
                       1 S x 32.07 g/mol = 32.07 g/mol            
                       4 O x 16.00 g/mol = 64.00 g/mol
                     _____________________________
                                            Sum = 120.37 g/mol

molar mass H₂O:

H₂O                 2 H x 1.008 g/mol = 2.016 g/mol
                        1 O x 16.00 g/mol = 16.00 g/mol
                       ____________________________
                                            Sum = 18.016 g/mol

mass (molar mass) → moles

$\mathbf{moles}\mathbf{ }{\mathbf{MgSO}}_{\mathbf{4}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{41}\mathbf{ }\cancel{\mathbf{g}\mathbf{ }{\mathbf{MgSO}}_{\mathbf{4}}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\mathbf{mol}\mathbf{ }{\mathbf{MgSO}}_{\mathbf{4}}}{\mathbf{120}\mathbf{.}\mathbf{37}\mathbf{ }\cancel{\mathbf{g}\mathbf{ }{\mathbf{MgSO}}_{\mathbf{4}}}}$

moles MgSO₄ = 0.0200 mol

$\mathbf{moles}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{52}\mathbf{ }\cancel{\mathbf{g}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\mathbf{mol}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}{\mathbf{18}\mathbf{.}\mathbf{016}\mathbf{ }\cancel{\mathbf{g}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}}$

moles H₂O = 0.1399 mol

Step 2: Determine the lowest whole number ratio of MgSO₄ and H₂O to get the formula of the compound.