Chapter 3, Problem 3.30P

(a)

Interpretation Introduction

Interpretation:

The number of moles of lead (II) sulfide in $1.00{\text{ ft}}^3$ of galena is to be calculated.

Concept Introduction:

Molar mass is defined as the mass of $1\text{ mol}$ of a chemical substance in grams. The molar mass of a compound is calculated by the addition of the molar mass of each element multiplied by its number of atoms present in the chemical formula.

The expression that relates volume and density with the mass of a chemical substance is as follows:

$\text{Mass }\left(\text{g}\right)=\left(\text{Volume }\left({\text{cm}}^3\right)\right)\left(\text{Density }\left({\text{g/cm}}^3\right)\right)$                                                    (1)

The SI unit for amount of substance is $\text{mol}$. The mass and molar mass of a substance are used to calculate the amount of substance. The formula to calculate moles from the mass is as follows:

$\text{Amount}\left(\text{mol}\right)=\left(\text{Mass}\left(\text{g}\right)\right)\left(\frac{1\text{ mol}}{\text{No}\text{. of grams}}\right)$                                                          (2)

(b)

Interpretation Introduction

Interpretation:

The number of lead atoms in $1.00{\text{ dm}}^3$ of galena is to be calculated.

Concept introduction:

One mole is defined as the amount of substance that contains the same number of entities such as molecules, ions, atoms as the number of atoms in $12\text{ g}$ of $\text{C-12}$. This number is called Avogadro’s number. The value of Avogadro’s number is $\text{6}\text{.022}\times {\text{10}}^{23}\left(\text{entitites/mol}\right)$.

Molar mass is defined as the mass of $1\text{ mol}$ of a chemical substance in grams. The molar mass of a compound is calculated by the addition of the molar mass of each element multiplied by its number of atoms present in the chemical formula.

The molecular formula of a compound tells the number of atoms/ions of each element present in the compound.

Following are the steps to calculate the number of atoms of an element in a compound when the volume and density of the compound are given.

Step 1: Convert the volume of the compound to ${\text{cm}}^3$ by using the conversion factors and calculate the mass of the compound. The expression that relates volume and density with the mass of a chemical substance is as follows:

$\text{Mass }\left(\text{g}\right)=\left(\text{Volume }\left({\text{cm}}^3\right)\right)\left(\text{Density }\left({\text{g/cm}}^3\right)\right)$                                                     (1)

Step 2: Convert the mass of the compound to moles by using the molar mass of that compound as follows:

$\text{Amount}\left(\text{mol}\right)=\left(\text{Given mass}\left(\text{g}\right)\right)\left(\frac{1\text{ mol}}{\text{No}\text{. of grams}}\right)$                                                 (2)

Step 3: Determine the number of moles of atoms of an element from the molecular formula of the compound. The formula to calculate the moles of atoms is as follows:

$\text{Amount of element}\left(\text{mol}\right)=\left(\begin{array}{l}\text{amount of}\\ \text{compound}\\ \left(\text{mol}\right)\end{array}\right)\left(\frac{\begin{array}{l}\text{moles of atoms in}\\ \text{molecular formula}\end{array}}{1\text{ mol compound}}\right)$                              (4)

Step 4: Determine the number of atoms by multiplying the moles of the element with the Avogadro’s number. The expression to calculate the number of atoms of an element is as follows:

$\text{Number of atoms}=\left(\text{Amount of element }\left(\text{mol}\right)\right)\left(\frac{6.022\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)$                   (5)