Chapter 6, Problem 40A

Interpretation Introduction

Interpretation: The empirical formula of the sulfide needs to be determined.

Concept Introduction: The empirical formula is the simplest ratio of atoms of elements present in the compound. It does not tell about the actual number of atoms present in it. Some molecules have empirical formulas equal to their molecular formula.

Answer to Problem 40A

  ${\text{Co}}_{\text{2}}{\text{S}}_{\text{3}}$

Explanation of Solution

Cobalt metal is mixed with sulfur in excess and results in the formation of cobalt sulfide. The mass percent of cobalt present in it is 55.06%.

Let the mass of cobalt sulfide formed be 100 g thus, the mass of cobalt in will be 55.06 g and that of sulfur will be $100-55.06=44.94\text{ g}$ .

The number of moles of cobalt and sulfur can be calculated as follows:

  $n=\frac{m}{M}$

The molar mass of Co and S is 58.93 g/mol and 32.065 g/mol respectively.

The number of moles of Co and S can be calculated as follows:

  $\begin{array}{l}{n}_{Co}=\frac{m}{M}=\frac{55.06\text{ g}}{58.93\text{ g/mol}}=0.934\text{ mol}\\ n_S=\frac{44.94\text{ g}}{32.065\text{ g/mol}}=1.40\text{ mol}\end{array}$

The ratio of the number of moles of Co and S will be 0.934:1.40 or 2:3.

Thus, the empirical formula will be ${\text{Co}}_{\text{2}}{\text{S}}_{\text{3}}$ .

Conclusion

Therefore, the empirical formula will be ${\text{Co}}_{\text{2}}{\text{S}}_{\text{3}}$ .