Chapter 10, Problem 186A

A 1.628-g sample of a hydrate of magnesium iodide is heated until its mass is reduced to 1.072 g and all water has been removed. What is the formula of the hydrate?

Interpretation Introduction

Interpretation:

Formula of the hydrated magnesium iodide needs to be determined for which 1.628 g hydrated sample gives 1.027 g anhydrous salt.

Concept introduction:

Hydrated salts are those which contain certain molecules of water as water of crystallization.

Answer to Problem 186A

Formula of the hydrate is MgI₂.9H₂O.

Explanation of Solution

Mass of hydrated magnesium iodide is 1.628 g.

Mass of anhydrous magnesium iodide is 1.027 g.

Thus,

Mass of water $\text{=(1}\text{.628-1}\text{.027) g =0}\text{.601 g}\text{.}$

Molar mass of MgI₂ is 278 g/mol.

Molar mass of H₂O is 18 g/mol.

Thus, number of moles of MgI₂ and H₂O can be calculated as follows:

$n=\frac{m}{M}$

Putting the values,

Mole of MgI₂$=\frac{1.027\text{ g}}{278\text{ g/mol}}=0.0037\text{ mol}$

Mole of H₂O $=\frac{0.601\text{ g}}{18\text{ g/mol}}=0.0333\text{ mol}$

Mole ratio of MgI₂: H₂O $=0.0037:0.033=1:9.$

So, the formula is MgI₂.9H₂O.

Conclusion

Formula of the given hydrate is MgI₂.9H₂O.