# Find the number of waters of hydration (x) in this sample of Epsom salts?

## Epsom salts is a hydrated ionic compound with e formula MgSO4 · xH2O. A 9.86g sample of Epsom salts was heated to drive off the water of hydration. The mass of the sample after complete dehydration was 4.82g.

Jun 17, 2017

$\text{MgSO"_4 * 7"H"_2"O}$

#### Explanation:

The idea here is that heating the hydrate will drive off the water of evaporation and leave behind the anhydrous salt.

In your case, the anhydrous salt is magnesium sulfate, ${\text{MgSO}}_{4}$. Since you know that after complete dehydration the mass of the sample is equal to $\text{4.82 g}$, you can say that the hydrate contained

${\text{4.82 g " -> " MgSO}}_{4}$

Use the molar mass of the compound to convert this to moles

4.82 color(red)(cancel(color(black)("g"))) * "1 mole MgSO"_4/(120.37color(red)(cancel(color(black)("g")))) = "0.04004 moles MgSO"_4

Now, the difference between the mass of the hydrate and the mass of the anhydrous salt will be equal to the mass of water of hydration.

You can thus say that the hydrate contained

overbrace("9.86 g")^(color(blue)("mass of hydrate")) - overbrace("4.82 g")^(color(blue)("mass of anhydrous salt")) = overbrace("5.04 g")^(color(blue)("mass of water of hydration"))

Use the molar mass of water to convert this to moles

5.04 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "0.2798 moles H"_2"O"

The number of waters of hydration is given by the number of moles of water present for every $1$ mole of anhydrous salt.

In your case, you know that

$\text{0.04004 moles MgSO"_4 " " ->" " "0.2798 moles H"_2"O}$

This means that $1$ mole of magnesium sulfate will have

1 color(red)(cancel(color(black)("moles MgSO"_4))) * ("0.2798 moles H"_2"O")/(0.04004color(red)(cancel(color(black)("moles MgSO"_4)))) = 6.988 ~~ 7

Therefore, you can say that the chemical formula of the hydrate is

$\text{MgSO"_4 * 7"H"_2"O} \to$ magnesium sulfate heptahydrate