Chapter 8, Problem 23QAP

Using the average atomic masses given inside the front cover of this book, calculate the number of atoms present in each of the following samples.

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1.50 g of silver, Ag

0.0015 moIe of copper, Cu

0.0015 g of copper, Cu

2.00 kg of magnesium, Mg

2.34 oz of calcium, Ca

2.34 g of calcium, Ca

2.34 moles of calcium, Ca

Interpretation Introduction

(a)

Interpretation:

The number of atoms present in the given sample should be calculated.

Concept Introduction:

Number of moles is related to mass and molar mass as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Here, m is mass and M is molar mass.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. This is known as Avogadro’s number and denoted by symbol${\text{N}}_{\text{A}}$.

Thus, number of molecules can be calculated from number of moles using the following conversion factor:

$\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)$.

Answer to Problem 23QAP

$8.375\times {10}^{21}\text{ atoms}$.

Explanation of Solution

Mass of silver is 1.50 g

First calculate the number of moles as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Molar mass of silver is 107.8682 g/mol thus,

$\begin{array}{c}\text{n}=\frac{\text{1}\text{.50 g}}{\text{107}\text{.8682 g/mol}}\\ =0.014\text{ mol}\end{array}$

Therefore, number of moles of silver is$0.014\text{ mol}$.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. The following conversion factor is used to calculate number of atoms:

$\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)$

Number of atoms in 0.014 mol will be:

$\begin{array}{c}\text{N}=0.014\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)\\ =8.375\times {10}^{21}\text{ atoms}\end{array}$

Thus, number of atoms in silver is$8.375\times {10}^{21}\text{ atoms}$.

Interpretation Introduction

(b)

Interpretation:

The number of atoms present in the given sample should be calculated.

Concept Introduction:

Number of moles is related to mass and molar mass as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Here, m is mass and M is molar mass.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. This is known as Avogadro’s number and denoted by symbol${\text{N}}_{\text{A}}$.

Thus, number of molecules can be calculated from number of moles using the following conversion factor:

$\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)$.

Answer to Problem 23QAP

$9.03\times {10}^{20}\text{ atoms}$.

Explanation of Solution

Number of moles of copper is 0.0015 mol.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. The following conversion factor is used to calculate number of atoms:

$\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)$

Number of atoms in 0.0015 mol will be:

$\begin{array}{c}\text{N}=0.0015\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)\\ =9.03\times {10}^{20}\text{ atoms}\end{array}$

Thus, number of atoms in copper is$9.03\times {10}^{20}\text{ atoms}$.

Interpretation Introduction

(c)

Interpretation:

The number of atoms present in the given sample should be calculated.

Concept Introduction:

Number of moles is related to mass and molar mass as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Here, m is mass and M is molar mass.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. This is known as Avogadro’s number and denoted by symbol${\text{N}}_{\text{A}}$.

Thus, number of molecules can be calculated from number of moles using the following conversion factor:

$\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)$.

Answer to Problem 23QAP

$1.421\times {10}^{19}\text{ atoms}$.

Explanation of Solution

Mass of copper is 0.0015 g

First calculate the number of moles as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Molar mass of copper is 63.546 g/mol thus,

$\begin{array}{c}\text{n}=\frac{\text{0}\text{.0015 g}}{\text{63}\text{.546 g/mol}}\\ =2.36\times {10}^{-5}\text{ mol}\end{array}$

The number of copper atoms is$2.36\times {10}^{-5}\text{ mol}$.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. The following conversion factor is used to calculate number of atoms:

$\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)$

Number of atoms in$2.36\times {10}^{-5}\text{ mol}$ will be:

$\begin{array}{c}\text{N}=2.36\times {10}^{-5}\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)\\ =1.421\times {10}^{19}\text{ atoms}\end{array}$

Thus, number of atoms of copper is$1.421\times {10}^{19}\text{ atoms}$.

Interpretation Introduction

(d)

Interpretation:

The number of atoms present in the given sample should be calculated.

Concept Introduction:

Number of moles is related to mass and molar mass as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Here, m is mass and M is molar mass.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. This is known as Avogadro’s number and denoted by symbol${\text{N}}_{\text{A}}$.

Thus, number of molecules can be calculated from number of moles using the following conversion factor:

$\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)$.

Answer to Problem 23QAP

$4.95\times {10}^{25}\text{ atoms}$.

Explanation of Solution

Mass of magnesium is 2.00 kg

First calculate the number of moles of magnesium as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Molar mass of magnesium is 24.305 g/mol thus,

$\begin{array}{c}\text{n}=\frac{\text{2}\text{.00 kg}\left(\frac{1000\text{ g}}{1\text{ kg}}\right)}{\text{24}\text{.305 g/mol}}\\ =82.28\text{ mol}\end{array}$

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. The following conversion factor is used to calculate number of atoms:

$\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)$

Number of atoms in$82.28\text{ mol}$ will be:

$\begin{array}{c}\text{N}=82.28\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)\\ =4.95\times {10}^{25}\text{ atoms}\end{array}$

Thus, number of atoms of magnesium is$4.95\times {10}^{25}\text{ atoms}$.

Interpretation Introduction

(e)

Interpretation:

The number of atoms present in the given sample should be calculated.

Concept Introduction:

Number of moles is related to mass and molar mass as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Here, m is mass and M is molar mass.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. This is known as Avogadro’s number and denoted by symbol${\text{N}}_{\text{A}}$.

Thus, number of molecules can be calculated from number of moles using the following conversion factor:

$\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)$.

Answer to Problem 23QAP

$9.97\times {10}^{23}\text{ atoms}$.

Explanation of Solution

Mass of calcium is 2.34 oz

Convert it into grams as using the following conversion factor:

$\left(\frac{28.35\text{ g}}{1\text{ oz}}\right)$

Mass in grams will be:

$\begin{array}{c}\text{m}=2.34\text{ oz}\left(\frac{28.35\text{ g}}{1\text{ oz}}\right)\\ =66.34\text{ g}\end{array}$

First calculate the number of moles as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Molar mass of calcium is 40.078 g/mol thus,

$\begin{array}{c}\text{n}=\frac{\text{66}\text{.34 g}}{\text{40}\text{.078 g/mol}}\\ =1.655\text{ mol}\end{array}$

Number of moles of calcium is$1.655\text{ mol}$.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. The following conversion factor is used to calculate number of atoms:

$\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)$

Number of atoms in1.655 mol will be:

$\begin{array}{c}\text{N}=1.655\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)\\ =9.97\times {10}^{23}\text{ atoms}\end{array}$

Thus, number of atoms of calcium is$9.97\times {10}^{23}\text{ atoms}$.

Interpretation Introduction

(f)

Interpretation:

The number of atoms present in the given sample should be calculated.

Concept Introduction:

Number of moles is related to mass and molar mass as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Here, m is mass and M is molar mass.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. This is known as Avogadro’s number and denoted by symbol${\text{N}}_{\text{A}}$.

Thus, number of molecules can be calculated from number of moles using the following conversion factor:

$\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)$.

Answer to Problem 23QAP

$3.516\times {10}^{22}\text{ atoms}$.

Explanation of Solution

Mass of calcium is 2.34 g

First calculate the number of moles of calcium as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Molar mass of calcium is 40.078 g/mol thus,

$\begin{array}{c}\text{n}=\frac{\text{2}\text{.34 g}}{\text{40}\text{.078 g/mol}}\\ =0.058\text{ mol}\end{array}$

Number of moles of calcium is$0.058\text{ mol}$.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. The following conversion factor is used to calculate number of atoms:

$\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)$

Number of atoms in$0.058\text{ mol}$ will be:

$\begin{array}{c}\text{N}=0.058\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)\\ =3.516\times {10}^{22}\text{ atoms}\end{array}$

Thus, number of atoms of calcium is$3.516\times {10}^{22}\text{ atoms}$.

Interpretation Introduction

(g)

Interpretation:

The number of atoms present in the given sample should be calculated.

Concept Introduction:

Number of moles is related to mass and molar mass as follows:

$\text{n}=\frac{\text{m}}{\text{M}}$

Here, m is mass and M is molar mass.

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. This is known as Avogadro’s number and denoted by symbol${\text{N}}_{\text{A}}$.

Thus, number of molecules can be calculated from number of moles using the following conversion factor:

$\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)$.

Answer to Problem 23QAP

$1.41\times {10}^{24}\text{ atoms}$.

Explanation of Solution

Number of moles of calcium is 2.34 mol

According to Avogadro’s law, 1 mole of a substance contains$6.023\times {10}^{23}$ atoms. The following conversion factor is used to calculate number of atoms:

$\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)$

Number of atoms in 2.34 mol will be:

$\begin{array}{c}\text{N}=2.34\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)\\ =1.41\times {10}^{24}\text{ atoms}\end{array}$

Thus, number of atoms in calcium is$1.41\times {10}^{24}\text{ atoms}$.