Chapter 6, Problem 52A

(a)

Interpretation Introduction

Interpretation: The number of moles and atoms in 5.00 g of Aluminium 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 52A

  $1.12{\text{ ×10}}^{\text{23}}\text{ atoms}$ and 0.185 moles

Explanation of Solution

Molar mass of Al = 27.0 g/mol

Mass of Al given = 5.00 g

1 mole = 6.022 x 10²³atoms

Calculate moles of Al:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{5}\text{.0 g }}{\text{27}\text{.0 g/mol }}\text{= 0}\text{.185moles}\end{array}$

Calculate number of atoms:

  $\text{0}\text{.185 moles ×}\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{atoms}}{\text{1 mole}}=1.12{\text{ ×10}}^{\text{23}}\text{ atoms}$

(b)

Interpretation Introduction

Interpretation: The mass and atoms in 0.00250 moles of iron 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 52A

  $1.50{\text{ ×10}}^{\text{21}}\text{ atoms}$ and 0.1395 g

Explanation of Solution

Molar mass of Fe = 55.8 g/mol

Moles of Fe given = 0.00250 g

1 mole = 6.022 x 10²³atoms

Calculate mass of Fe:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Mass=Moles×molar mass}\\ \text{Mass=0}\text{.00250 moles × 55}\text{.8 g/mol }\\ \text{Mass=0}\text{.1395g}\end{array}$

Calculate number of atoms:

  $\text{0}\text{.00250 moles ×}\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{atoms}}{\text{1 mole}}=1.50{\text{ ×10}}^{\text{21}}\text{ atoms}$

(c)

Interpretation Introduction

Interpretation: The number of moles and mass in $2.6\times {10}^{24}$ atoms of Cu 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 52A

273 g and 4.3 moles

Explanation of Solution

Molar mass of Cu = 63.5 g/mol

Number of atoms of Cu = 2.6 x 10²⁴atoms

1 mole = 6.022 x 10²³atoms

Calculate moles:

  $\text{2}{\text{.6 ×10}}^{\text{24}}\text{atoms ×}\frac{\text{1 mole }}{\text{6}{\text{.022×10}}^{\text{23}}\text{atoms}}\text{ = 4}\text{.3 moles }$

Calculate mass of Fe:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Mass= moles s×molar mass}\\ \text{Mass= 4}\text{.3 moles × 63}\text{.5 g/mol }\\ \text{Mass= 273 g}\end{array}$

(c)

Interpretation Introduction

Interpretation: The number of moles and atoms in 0.002500 g of Mg 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 52A

  $6.269{\text{×10}}^{\text{19}}\text{ atoms}$ and $\text{1}\text{.041}\times {\text{10}}^{\text{-4 }}\text{moles}$

Explanation of Solution

Molar mass of Mg = 24.0 g/mol

Mass of Mg given = 0.00250 g

1 mole = 6.022 x 10²³atoms

Calculate moles of Mg:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{0}\text{.00250 g }}{\text{24}\text{.0 g/mol }}\text{= 1}\text{.041}\times {\text{10}}^{\text{-4 }}\text{moles}\end{array}$

Calculate number of atoms:

  $\text{1}\text{.041}\times {\text{10}}^{\text{-4 }}\text{moles ×}\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{atoms}}{\text{1 mole}}=6.269{\text{×10}}^{\text{19}}\text{ atoms}$

(e)

Interpretation Introduction

Interpretation: The number of moles and number of atoms in 2.7 x 10-3 moles of Na 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 52A

  ${\text{ 62× 10}}^{\text{-3}}\text{g}$ and $\text{16}{\text{.3 ×10}}^{\text{20}}\text{atoms}$

Explanation of Solution

Molar mass of Na = 23.0 g/mol

Moles of Na = 2.7 x 10-3 moles

1 mole = 6.022 x 10²³atoms

Calculate mass of Na:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Mass= moles ×molar mass}\\ \text{Mass= 2}{\text{.7 × 10}}^{\text{-3}}\text{moles × 23}\text{.0 g/mol }\\ {\text{Mass = 62× 10}}^{\text{-3}}\text{g}\end{array}$

Calculate moles:

  $\text{2}{\text{.7× 10}}^{\text{-3}}\text{moles ×}\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{atom}}{\text{1 mole}}\text{ = 16}{\text{.3 ×10}}^{\text{20}}\text{atoms}$

(f)

Interpretation Introduction

Interpretation: The number of moles and mass of 1.00 x 10⁴atoms of U 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 52A

  ${\text{ 395× 10}}^{\text{-20}}\text{g}$ and $\text{1}{\text{.66 ×10}}^{\text{-20}}\text{ moles}$

Explanation of Solution

Molar mass of U = 238 g/mol

Number of atoms = 1.00 x 10⁴ atoms

1 mole = 6.022 x 10²³atoms

Calculate moles:

  $\text{1}{\text{.00 ×10}}^{\text{4}}\text{atoms ×}\frac{\text{1 mole}}{\text{6}{\text{.022×10}}^{\text{23}}\text{atom}}\text{ = 1}{\text{.66 ×10}}^{\text{-20}}\text{ moles}$

Calculate mass of U:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Mass= moles ×molar mass}\\ \text{Mass= 1}{\text{.66 ×10}}^{\text{-20}}\text{ moles × 238 g/mol }\\ {\text{Mass = 395× 10}}^{\text{-20}}\text{g}\end{array}$