Epsom salts is a hydrated ionic compound with the following formula: MgSO4⋅xH2O A sample of Epsom salts with a mass of 4.93 g is heated to drive off the water of hydration. The mass of the sample after complete dehydration is 2.41 g. Find the number of waters of hydration (x) in Epsom salts

Let´s calculate this in moles. To do that we may know the molecular weight of water, so, we add the atomics wheights´ contributions of its components:

[tex]MW (H_{2}O) = 2.1\frac{g}{mol}+16\frac{g}{mol} =18\frac{g}{mol}[/tex]

Then, the number of water moles in the sample is:

[tex]moles of water in the sample = \frac{2.52 g}{18\frac{g}{mol}}=0.14 mol H_{2}O[/tex]

Now, to know hoy many moles are 2.41 g of [tex]MgSO_{4}[/tex] we may use the molecular weight of [tex]MgSO_{4}[/tex].

[tex]MW (MgSO_{4}) = 24\frac{g}{mol}+32\frac{g}{mol}+4.16\frac{g}{mol} = 120\frac{g}{mol}[/tex]

[tex]moles of MgSO_{4} in the sample = \frac{2.41 g}{120\frac{g}{mol}}=0.02 mol MgSO_{4}[/tex]

Hydrated ionic compounds´ formulas are normally written for 1 mol of the salt (in our case [tex]MgSO_{4}[/tex]), and the corresponding number of water molecules.

So, we have a sample with 0.02 mol of [tex]MgSO_{4}[/tex] and 0.14 mol [tex]H_{2}O[/tex]. Let´s find the multiplying factor to obtain the forula for 1 mol of [tex]MgSO_{4}[/tex]:

[tex]Factor=\frac{1 mol}{0.02 mol} =50[/tex]

Finally, we must multiply the number of water moles in the sample with this factor to obtain x, as well:

x = 50 x 0.14 mol = 7 mol

Then, the complete formula for Epson salt is [tex]MgSO_{4} .7H_{2}O[/tex]