Chapter 6, Problem 53A

(a)

Interpretation Introduction

Interpretation: The moles and number of molecules and atoms in 4.24 g of ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}$ needs to be determined.

Concept Introduction: The molecular mass of compound is the sum of 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 53A

  $3.25{\text{ ×10}}^{\text{22}}\text{ molecules}$

  ${\text{ 39×10}}^{\text{22}}\text{atoms}$

  $\text{0}\text{.054 moles}$

Explanation of Solution

Molar mass of ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}$ = 78.0 g/mol

Mass of ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}$ given = 4.24 g

1 mole = 6.022 x 10²³ atoms

Calculate moles of ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}$ :

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{4}\text{.24 g }}{\text{78}\text{.0 g/mol }}\text{= 0}\text{.054 moles}\end{array}$

Calculate number of molecules:

  $\text{0}\text{.054 moles ×}\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules}}{\text{1 mole}}=3.25{\text{ ×10}}^{\text{22}}\text{ molecules}$

Calculate number of atoms:

1 molecule of ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}$ = 12 atoms

  $\text{3}{\text{.25 ×10}}^{\text{22}}\text{ molecules× }\frac{\text{12 atoms }}{\text{1 molecule}}{\text{= 39×10}}^{\text{22}}\text{atoms}$

(b)

Interpretation Introduction

Interpretation: The mass and number of molecules and atoms in 0.224 moles of ${\text{H}}_{\text{2}}\text{O}$ needs to be determined.

Concept Introduction: The molecular mass of compound is the sum of 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 53A

  $1.35{\text{×10}}^{\text{23}}\text{molecules}$

  $\text{4}{\text{.05×10}}^{\text{23}}\text{atoms}$

  $\text{4}\text{.032 g}$

Explanation of Solution

Molar mass of ${\text{H}}_{\text{2}}\text{O}$ = 18.0 g/mol

Moles of ${\text{H}}_{\text{2}}\text{O}$ given = 0.224 moles

1 mole = 6.022 x 10²³ atoms

Calculate mass of ${\text{H}}_{\text{2}}\text{O}$ :

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Mass=Moles×molar mass}\\ \text{Mass=0}\text{.224 moles × 18}\text{.0 g/mol }\\ \text{Mass= 4}\text{.032 g}\end{array}$

Calculate number of atoms:

  $\text{0}\text{.224 moles ×}\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules}}{\text{1 mole}}=1.35{\text{×10}}^{\text{23}}\text{molecules}$

Calculate number of atoms:

1 molecule of ${\text{H}}_{\text{2}}\text{O}$ = 3 atoms

  $1.35{\text{×10}}^{\text{23}}\text{molecules× }\frac{\text{3 atoms }}{\text{1 molecule}}\text{= 4}{\text{.05×10}}^{\text{23}}\text{atoms}$

(c)

Interpretation Introduction

Interpretation: The mass, moles and number of atoms in 2.71 x 10²² molecules of ${\text{CO}}_{\text{2}}$ needs to be determined.

Concept Introduction: The molecular mass of compound is the sum of 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 53A

  $\text{ 8}{\text{.13×10}}^{\text{22}}\text{atoms}$

  $\text{Mass= 1}\text{.98 g}$

  $\text{0}\text{.045 moles }$

Explanation of Solution

Molar mass of ${\text{CO}}_{\text{2}}$ = 44.0 g/mol

Number of atoms of ${\text{CO}}_{\text{2}}$ = 2.71 x 10²²molecule

1 mole = 6.022 x 10²³ atoms

Calculate moles:

  $\text{2}{\text{.71× 10}}^{\text{22}}\text{molecule×}\frac{\text{1 mole }}{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules}}\text{ = 0}\text{.045 moles }$

Calculate mass of ${\text{CO}}_{\text{2}}$ :

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Mass= moles ×molar mass}\\ \text{Mass= 0}\text{.045 moles × 44}\text{.0 g/mol }\\ \text{Mass= 1}\text{.98 g}\end{array}$

Calculate number of atoms:

1 molecule of ${\text{CO}}_{\text{2}}$ = 3 atoms

  $\text{2}{\text{.71 ×10}}^{\text{22}}\text{molecule× }\frac{\text{3 atoms }}{\text{1 molecule}}\text{= 8}{\text{.13×10}}^{\text{22}}\text{atoms}$

(d)

Interpretation Introduction

Interpretation: The mass and number of atoms, molecules in 1.26 moles of $\text{HCl}$ needs to be determined.

Concept Introduction: The molecular mass of compound is the sum of 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 53A

  $\text{Mass= 46}\text{.0 g}$

  $7.59{\text{×10}}^{\text{23}}\text{ molecules}$

  $\text{15}{\text{.2×10}}^{\text{23}}\text{atom}$

Explanation of Solution

Molar mass of $\text{HCl}$ = 36.5 g/mol

Moles of $\text{HCl}$ given = 1.26 moles

1 mole = 6.022 x 10²³ atoms

Calculate mass of $\text{HCl}$ :

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Mass=Moles×molar mass}\\ \text{Mass= 1}\text{.26 moles × 36}\text{.5 g/mol }\\ \text{Mass= 46}\text{.0 g}\end{array}$

Calculate number of atoms:

  $\text{1}\text{.26 moles ×}\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules}}{\text{1 mole}}=7.59{\text{×10}}^{\text{23}}\text{ molecules}$

Calculate number of atoms:

1 molecule of $\text{HCl}$ = 2 atoms

  $7.59{\text{×10}}^{\text{23}}\text{ molecules× }\frac{\text{2 atoms }}{\text{1 molecule}}\text{= 15}{\text{.2×10}}^{\text{23}}\text{atoms}$

(e)

Interpretation Introduction

Interpretation: The mass, moles and number of atoms in 4.12 x 10²⁴ molecules of ${\text{H}}_{\text{2}}\text{O}$ needs to be determined.

Concept Introduction: The molecular mass of compound is the sum of 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 53A

  $\text{6}\text{.84 moles }$

  $\text{Mass = 123 g}$

  $\text{12}{\text{.4×10}}^{\text{24}}\text{atoms}$

Explanation of Solution

Molar mass of ${\text{H}}_{\text{2}}\text{O}$ = 18.0 g/mol

Number of molecules = 4.12 x 10²⁴ molecules

1 mole = 6.022 x 10²³ atoms

Calculate moles:

  $\text{ 4}{\text{.12×10}}^{\text{24}}\text{molecules×}\frac{\text{1 mole}}{\text{6}{\text{.022×10}}^{\text{23}}\text{ molecules}}\text{ = 6}\text{.84 moles }$

Calculate mass of H₂O:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Mass= moles ×molar mass}\\ \text{Mass= 6}\text{.84 moles × 18}\text{.0 g/mol }\\ \text{Mass = 123 g}\end{array}$

Calculate number of atoms:

1 molecule of ${\text{H}}_{\text{2}}\text{O}$ = 3 atoms

  $4.12\times {10}^{24}\text{ molecules× }\frac{\text{3 atoms }}{\text{1 molecule}}\text{= 12}{\text{.4×10}}^{\text{24}}\text{atoms}$

(f)

Interpretation Introduction

Interpretation: The moles and number of atoms, molecules in 0.297 g of ${\text{CH}}_{\text{3}}\text{OH}$ needs to be determined.

Concept Introduction: The molecular mass of compound is the sum of 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 53A

  $\text{0}\text{.0093 moles}$

  $5.60{\text{ ×10}}^{\text{21}}\text{molecules}$

  $\text{ 33}{\text{.6×10}}^{\text{21}}\text{atoms}$

Explanation of Solution

Molar mass of ${\text{CH}}_{\text{3}}\text{OH}$ = 32.0 g/mol

Mass of ${\text{CH}}_{\text{3}}\text{OH}$ given = 0.297 g

1 mole = 6.022 x 10²³ atoms

Calculate moles of ${\text{CH}}_{\text{3}}\text{OH}$ :

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{0}\text{.297 g }}{\text{32}\text{.0 g/mol }}\text{= 0}\text{.0093 moles}\end{array}$

Calculate number of atoms:

  $\text{0}\text{.0093 moles ×}\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules }}{\text{1 mole}}=5.60{\text{ ×10}}^{\text{21}}\text{molecules}$

Calculate number of atoms:

1 molecule of ${\text{CH}}_{\text{3}}\text{OH}$ = 6 atoms

  $5.60{\text{ ×10}}^{\text{21}}\text{molecules× }\frac{\text{6 atoms }}{\text{1 molecule}}\text{= 33}{\text{.6×10}}^{\text{21}}\text{atoms}$