Chapter 6, Problem 6A

(a)

Interpretation Introduction

Interpretation:The number of atoms in 40.08 amu of calcium needs to be determined.

Concept Introduction: The molecular mass of a compound is the sum of the atomic mass of all the atoms present in the given chemical compound. Mole concept is used to calculate the moles, mass, number of atoms and moles of a compound. The relation between these values can be shown as:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ {\text{1 mole = N}}_{\text{a}}\text{ atoms}\\ {\text{N}}_{\text{a}}\text{ = 6}\text{.022 }\times {\text{ 10}}^{\text{23}}\end{array}$

Answer to Problem 6A

1 atom.

Explanation of Solution

Mass of Ca = 40.08 amu

The conversion of amu to grams is done as follows:

  $1\text{ amu}=\text{1}\text{.6605}\times {10}^{\text{-24}}\text{ g}$

Thus, the mass of Ca in grams will be:

  $40.08\text{ amu}=\text{6}\text{.65544}\times {\text{10}}^{\text{-23}}\text{ g}$

Molar mass of Ca = 40.08 g/mol

Calculate moles of Ca-

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{6}\text{.65544}\times {\text{10}}^{\text{-23}}\text{ g}}{\text{40}\text{.08 g/mol }}\text{= 0}\text{.166}\times {\text{10}}^{\text{-23}}\text{ moles}\end{array}$

Calculate number of atoms:

  $\text{0}\text{.166}\times {\text{10}}^{\text{-23}}\text{ moles }\times \frac{\text{6}\text{.022}\times {\text{ 10}}^{\text{23}}\text{ atoms}}{\text{1}\text{.0 moles }}=0.9\text{ atom}\approx 1\text{ atom}$

(b)

Interpretation Introduction

Interpretation:The number of atoms in 919.5 amu of tungsten needs to be determined.

Concept Introduction: The molecular mass of a compound is the sum of the atomic mass of all the atoms present in the given chemical compound. Mole concept is used to calculate the moles, mass, number of atoms and moles of a compound. The relation between these values can be shown as:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ {\text{1 mole = N}}_{\text{a}}\text{ atoms}\\ {\text{N}}_{\text{a}}\text{ = 6}\text{.022 }\times {\text{ 10}}^{\text{23}}\end{array}$

Answer to Problem 6A

5 atoms.

Explanation of Solution

Mass of W = 919.5 amu

The conversion of amu to grams is done as follows:

  $1\text{ amu}=\text{1}\text{.6605}\times {10}^{\text{-24}}\text{ g}$

Thus, the mass of W in grams will be:

  $919.5\text{ amu}=\text{1}\text{.526}\times {\text{10}}^{\text{-21}}\text{ g}$

Molar mass of W = 183.9 g/mol

Calculate moles of W-

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{1}\text{.526}\times {\text{10}}^{\text{-21}}}{\text{183}\text{.9 g/mol }}\text{= 0}\text{.0083}\times {\text{10}}^{\text{-21}}\text{moles}\end{array}$

Calculate number of atoms:

  $\text{ 0}\text{.0083}\times {\text{10}}^{\text{-21}}\text{ moles }\times \frac{\text{6}\text{.022}\times {\text{ 10}}^{\text{23}}\text{ atoms}}{\text{1}\text{.0 moles }}=5\text{ atoms}$

(c)

Interpretation Introduction

Interpretation:The number of atoms in 549.4 amu of manganese needs to be determined.

Concept Introduction: The molecular mass of a compound is the sum of the atomic mass of all the atoms present in the given chemical compound. Mole concept is used to calculate the moles, mass, number of atoms and moles of a compound. The relation between these values can be shown as:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ {\text{1 mole = N}}_{\text{a}}\text{ atoms}\\ {\text{N}}_{\text{a}}\text{ = 6}\text{.022 }\times {\text{ 10}}^{\text{23}}\end{array}$

Answer to Problem 6A

10 atoms.

Explanation of Solution

Mass of Mn = 549.4 amu

The conversion of amu to grams is done as follows:

  $1\text{ amu}=\text{1}\text{.6605}\times {10}^{\text{-24}}\text{ g}$

Thus, the mass of Mn in grams will be:

  $549.4\text{ amu}=9.123001\times {10}^{-22}\text{g}$

Molar mass of Mn = 54.94 g/mol

Calculate moles of Mn-

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{9.123001\times {10}^{-22}\text{g}}{\text{54}\text{.94 g/mol }}\text{= 0}\text{.167}\times {10}^{-22}\text{ moles}\end{array}$

Calculate number of atoms:

  $\text{0}\text{.167}\times {10}^{-22}\text{ moles }\times \frac{\text{6}\text{.022}\times {\text{ 10}}^{\text{23}}\text{ atoms}}{\text{1}\text{.0 moles }}=10\text{ atoms}$

(d)

Interpretation Introduction

Interpretation:The number of atoms in 6345 amu of iodine needs to be determined.

Concept Introduction: The molecular mass of a compound is the sum of the atomic mass of all the atoms present in the given chemical compound. Mole concept is used to calculate the moles, mass, number of atoms and moles of a compound. The relation between these values can be shown as:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ {\text{1 mole = N}}_{\text{a}}\text{ atoms}\\ {\text{N}}_{\text{a}}\text{ = 6}\text{.022 }\times {\text{ 10}}^{\text{23}}\end{array}$

Answer to Problem 6A

50 atoms.

Explanation of Solution

Mass of I = 6345 amu

The given mass can be converted into grams as follows:

  $1\text{ amu}=\text{1}\text{.6605}\times {10}^{\text{-24}}\text{ g}$

Thus, the mass of I will be:

  $\text{6345 amu=1}\text{.05361}\times {\text{10}}^{\text{-20}}\text{ g}$

Molar mass of I = 126.9 g/mol

Calculate moles of I-

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{1}\text{.05361}\times {\text{10}}^{\text{-20}}\text{ g}}{\text{126}\text{.9 g/mol }}\text{= 8}\text{.3}\times {\text{10}}^{-23}\text{ moles}\end{array}$

Calculate number of atoms:

  $\text{ 8}\text{.3}\times {\text{10}}^{-23}\text{ moles}\times \frac{\text{6}\text{.022}\times {\text{ 10}}^{\text{23}}\text{ atoms}}{\text{1}\text{.0 moles }}=50\text{ atoms}$

(e)

Interpretation Introduction

Interpretation:The number of atoms in 2072 amu of lead needs to be determined.

Concept Introduction: The molecular mass of a compound is the sum of the atomic mass of all the atoms present in the given chemical compound. Mole concept is used to calculate the moles, mass, number of atoms and moles of a compound. The relation between these values can be shown as:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ {\text{1 mole = N}}_{\text{a}}\text{ atoms}\\ {\text{N}}_{\text{a}}\text{ = 6}\text{.022 }\times {\text{ 10}}^{\text{23}}\end{array}$

Answer to Problem 6A

10 atoms.

Explanation of Solution

Mass of Pb = 2072 amu

The given mass can be converted into grams as follows:

  $1\text{ amu}=\text{1}\text{.6605}\times {10}^{\text{-24}}\text{ g}$

Thus, the mass of Pb will be:

  $\text{2072 amu=3}\text{.44064}\times {\text{10}}^{\text{-21}}\text{g}$

Molar mass of Pb = 207.2 g/mol

Calculate moles of Pb -

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{3}\text{.44064}\times {\text{10}}^{\text{-21}}}{\text{207}\text{.2 g/mol }}\text{= 1}\text{.67}\times {\text{10}}^{-23}\text{ moles}\end{array}$

Calculate number of atoms:

  $\text{1}\text{.67}\times {\text{10}}^{-23}\text{ moles }\times \frac{\text{6}\text{.022}\times {\text{ 10}}^{\text{23}}\text{ atoms}}{\text{1}\text{.0 moles }}=10\text{ atoms}$