Chapter 8, Problem 40QAP

Calculate the number of molecules present in each of the following samples.

oles of sulfur dioxide, ${\text{SO}}_2$

of sulfur dioxide, ${\text{SO}}_2$

:math> 4.46 × 10 − 5 g of ammonia, ${\text{NH}}_3$

:math> 4.46 × 10 − 5 moles of ammonia, ${\text{NH}}_3$

g of ethane, ${\text{C}}_2{\text{H}}_6$

Interpretation Introduction

(a)

Interpretation:

The number of molecules of substance 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 40QAP

$2.132\times {10}^{24}\text{ molecules}$.

Explanation of Solution

Number of moles of sulfur dioxide, ${\text{SO}}_{\text{2}}$ is 3.54 moles.

Since, 1 mole of sulfur dioxxide contains $6.023\times {10}^{23}$ molecules thus, 3.54 mol of sulfur dioxide will have following molecules:

$3.54\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=2.132\times {10}^{24}\text{ molecules}$

Therefore, number of molecules in sulfur dioxide is $2.132\times {10}^{24}\text{ molecules}$.

Interpretation Introduction

(b)

Interpretation:

The number of molecules of substance 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 40QAP

$3.33\times {10}^{22}\text{ molecules}$.

Explanation of Solution

Mass of sulfur dioxide is 3.54 g.

Calculate number of moles as follows:

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

Molar mass of sulfur dioxide is 64.066 g/mol, putting the values,

$\text{n}=\frac{\text{3}\text{.54 g}}{\text{64}\text{.066 g/mol}}=0.055\text{ mol}$

Since, 1 mole of sulfur dioxide contains $6.023\times {10}^{23}$ molecules thus, 0.055 mol of sulfur dioxide will have following molecules:

$0.055\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=3.33\times {10}^{22}\text{ molecules}$

Therefore, number of molecules in sulfur dioxide is $3.33\times {10}^{22}\text{ molecules}$.

Interpretation Introduction

(c)

Interpretation:

The number of molecules of substance 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 40QAP

$1.58\times {10}^{18}\text{ molecules}$.

Explanation of Solution

Mass of ammonia is $4.46\times {10}^{-5}\text{ g}$.

Calculate number of moles as follows:

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

Molar mass of ammonia is 17.031 g/mol, putting the values,

$\text{n}=\frac{4.46\times {10}^{-5}\text{ g}}{17.031\text{ g/mol}}=2.62\times {10}^{-6}\text{ mol}$

Since, 1 mole of ammonia contains $6.023\times {10}^{23}$ molecules thus, $2.62\times {10}^{-6}\text{ mol}$ of ammonia will have following molecules:

$2.62\times {10}^{-6}\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=1.58\times {10}^{18}\text{ molecules}$

Therefore, number of molecules in ammonia is $1.58\times {10}^{18}\text{ molecules}$.

Interpretation Introduction

(d)

Interpretation:

The number of molecules of substance 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 40QAP

$2.686\times {10}^{19}\text{ molecules}$.

Explanation of Solution

Number of moles of ammonia is $4.46\times {10}^{-5}\text{ mol}$.

Since, 1 mole of ammonia contains $6.023\times {10}^{23}$ molecules thus, $4.46\times {10}^{-5}\text{ mol}$ of ammonia will have following molecules:

$4.46\times {10}^{-5}\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=2.686\times {10}^{19}\text{ molecules}$

Therefore, number of molecules in ammonia is $2.686\times {10}^{19}\text{ molecules}$.

Interpretation Introduction

(e)

Interpretation:

The number of molecules of substance 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 40QAP

$3.93\times {10}^{19}\text{ molecules}$.

Explanation of Solution

Mass of ethane is 1.96 mg.

Convert mass from mg to g as follows:

$\left(\frac{{10}^{-3}\text{ g}}{1\text{ mg}}\right)$

Molar mass of ethane is 30.07 g/mol. Calculate number of moles of ethane as follows:

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

Putting the values,

$\text{n}=\frac{1.96\text{ mg}\left(\frac{{10}^{-3}\text{ g}}{1\text{ mg}}\right)}{30.07\text{ g/mol}}=6.52\times {10}^{-5}\text{ mol}$

Since, 1 mole of ethane contains $6.023\times {10}^{23}$ molecules thus, $6.52\times {10}^{-5}\text{ mol}$ of ethane will have following molecules:

$6.52\times {10}^{-5}\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=3.93\times {10}^{19}\text{ molecules}$

Therefore, number of molecules in ethane is $3.93\times {10}^{19}\text{ molecules}$.