Chapter 10, Problem 182A

Chromium(lll) nitrate forms a hydrate that is 40.50% water by mass. What is its chemical formula?

Interpretation Introduction

Interpretation:

Formula of the hydrate of chromium (III) nitrate needs to be determined in which there is 40.50 % water by mass.

Concept introduction:

Number of water molecules present per molecule of a compound is known as water of crystallization.

Answer to Problem 182A

Formula is Cr (NO₃)₃.9H₂O.

Explanation of Solution

Molar mass of Cr (NO₃)₃ is 238 g/mol.

Molar mass of H₂O is 18 g/mol.

Water is 40.50 % by mass which means 40.50 g water is there in 59.5 g Cr (NO₃)_3. The number of moles of Cr (NO₃)₃and H₂O can be calculated as follows:

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

Putting the values,

Moles of Cr (NO₃)₃$=\frac{59.5\text{ g}}{238\text{ g/mol}}=0.25\text{ mol}$

Moles of H₂O $=\frac{40.5\text{ g}}{18\text{ g/mol}}=2.25\text{ mol}$

Thus,

Moles ratio of Cr (NO₃)₃:H₂O $=0.25:2.25=1:9.$

Formula is Cr (NO₃)₃ .9H₂O.

Conclusion

Formula of the hydrate is Cr (NO₃)₃ .9H₂O.