Chapter 10, Problem 199A

Interpretation Introduction

Interpretation:

Molecular formula of the two given rock samples containing lead and sulfur must be found.

Concept introduction:

Empirical formula of a molecule is the smallest unit which is repeated in the molecule.

Molecular formula ${\text{=(empirical formula)}}_{\text{n}}$ where n is the number of times the empirical formula is present in the molecular formula, n can be 1, 2, 3 etc.

Answer to Problem 199A

The empirical formulas are Pb₂Sand PbS.

Explanation of Solution

For rock sample 1

% of Pb and S are 86.6 and 13.4 respectively.

Thus, this is equal to the mass of Pb and S present in 100 g of the sample.

The number of moles can be calculated using the molar mass. The molar mass of pb and S is 107 g/mol and 32 g/mol respectively.

Therefore,

Moles of Pb $\text{=}\frac{86.6}{\text{107}}\text{=0}\text{.81}\text{.}$

Moles of S $=\frac{13.4}{32}=\mathrm{0.42.}$

Smallest mole ratio Pb: S

$\begin{array}{l}=\frac{0.81}{0.42}:\frac{0.42}{0.42}\\ =1.93:1\approx 2:1.\end{array}$

Thus empirical formula is Pb₂S.

For rock sample 2

% of Pb and S are 76.4 and 23.6 respectively.

Here, mass of Pb and S is 76.4 g and 23.6 g respectively.

The number of moles can be calculated as follows:

Moles of Pb $\text{=}\frac{76.4}{\text{107}}\text{=0}\text{.71}\text{.}$

Moles of S $\text{=}\frac{23.6}{32}\text{=0}\text{.74}\text{.}$

Smallest mole ratio Pb: S

$\begin{array}{l}=\frac{0.71}{0.71}:\frac{0.74}{0.71}\\ =1:1.04\approx 1:1.\end{array}$

Thus empirical formula is PbS.

Conclusion

Empirical formula of rock salt 1 and 2 are Pb₂S and PbS respectively.