Chapter 10.5, Problem 75PP

Interpretation Introduction

Interpretation:

The formula and the name of this hydrate needs to be determined.

Concept introduction:

The relation between number of moles, mass and molar mass of a substance is represented as follows:

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

Here, m is mass and M is molar mass.

Answer to Problem 75PP

The chemical formula of the hydrate is ${\text{CoCl}}_{\text{2}}{\text{.2H}}_{\text{2}}\text{O}$.

The name of the hydrate is Cobalt $(II)$ chloride dihydrate.

Explanation of Solution

Given information:

The mass of hydrate of cobalt (II) chloride is 11.75 g. The number of anhydrous cobalt chloride remains after heating is 0.0712 mol.

Here, total mass of hydrated compound $=11.75\text{ g}\text{.}$

Moles of Cobalt Chloride (anhydrous remaining) $=0.0712\text{ mol}\text{.}$

Atomic mass of cobalt $=58.93\text{ amu}$

Atomic mass of chlorine $=35.45\text{ amu}$

Thus, molar mass of cobalt chloride will be:

${\text{M}}_{{\text{CoCl}}_{\text{2}}}=58.93+{(35.45)}^2=129.83\text{ g/mol}$

Moles of Cobalt Chloride (anhydrous remaining) $=0.0712\text{ mol}\text{.}$

Now, mass of $0.0712\text{ mol}$ of $CoC{l}_2$ will be:

$m=n\times M=0.0712\text{ mol}\times 129.83\text{ g/mol}=9.25\text{ g}$

Total mass of hydrated compound $=11.75\text{ g}\text{.}$

Also, mass of anhydrous compound $=9.25\text{ g}\text{.}$

Therefore, amount of water in hydrate $=11.75-9.25=2.5\text{ g}$

Now, the number of moles of $CoC{l}_2$ and water can be calculated as follows:

$\begin{array}{l}{\text{Moles of CoCl}}_2=\frac{9.24\text{ g}}{129.84\text{ g/mol}}\\ =0.0712\text{ mol}\\ \text{Moles of water = }\frac{2.5\text{ g}}{18\text{ g/mol}}\\ =\text{ 0}\text{.139 mol}\end{array}$

Dividing by smallest number of moles,

$\begin{array}{l}{\text{CoCl}}_2\text{ = }\frac{0.0712}{0.0712}=1\\ H_{2}O=\frac{0.139}{0.0712}=1.95\approx 2\end{array}$

Thus, the chemical formula is ${\text{CoCl}}_{\text{2}}{\text{.2H}}_{\text{2}}\text{O}$ and the name of hydrate is Cobalt $(II)$ chloride dihydrate.

Conclusion

Thus, the chemical formula of the hydrate is $CoC{l}_2.2H_{2}O$ and the name of the hydrate is Cobalt $(II)$ chloride dihydrate.