Chapter 8, Problem 39QAP

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

l type="a">

4.75 mmol of phosphine, ${\text{PH}}_3$

i>4.75 g of phosphine, ${\text{PH}}_3$

i> $1.25\times {10}^{-2}$ g of lead(II) acetate, $\text{Pb}{\left({\text{CH}}_3{\text{CO}}_2\right)}_2$

i>1.25 X 10 2 moles of lead(II) acetate, $\text{Pb}{\left({\text{CH}}_3{\text{CO}}_2\right)}_2$

i>a sample of benzene, ${\text{C}}_6{\text{H}}_6$

1. , which contains a total of 5.40 moles of carbon

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 39QAP

$2.86\times {10}^{21}\text{ molecules}$.

Explanation of Solution

Number of moles of phosphine ${\text{PH}}_{\text{3}}$ is 4.75 mmol.

First convert mmol into mol as follows:

$\left(\frac{{10}^{-3}\text{ mol}}{1\text{ mmol}}\right)$

Thus, number of moles will be:

$\begin{array}{c}\text{n}=4.75\text{ mmol}\left(\frac{{10}^{-3}\text{ mol}}{1\text{ mmol}}\right)\\ =4.75\times {10}^{-3}\text{ mol}\end{array}$

Since, 1 mole of phosphine contains $6.023\times {10}^{23}$ molecules thus, $4.75\times {10}^{-3}\text{ mol}$ of phosphine will have following molecules:

$4.75\times {10}^{-3}\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=2.86\times {10}^{21}\text{ molecules}$

Therefore, number of molecules in phosphine is $2.86\times {10}^{21}\text{ molecules}$.

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 39QAP

$8.432\times {10}^{22}\text{ molecules}$.

Explanation of Solution

Mass of posphine is 4.75 g.

Calculate number of moles as follows:

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

Molar mass of phosphine is 34 g/mol, putting the values,

$\text{n}=\frac{4.75\text{ g}}{34\text{ g/mol}}=0.14\text{ mol}$

Since, 1 mole of phosphine contains $6.023\times {10}^{23}$ molecules thus, 0.14 mol of phosphine will have following molecules:

$0.14\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=8.432\times {10}^{22}\text{ molecules}$

Therefore, number of molecules in phosphine is $8.432\times {10}^{22}\text{ molecules}$.

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 39QAP

$2.32\times {10}^{19}\text{ molecules}$.

Explanation of Solution

Mass of lead (II) acetate is $1.25\times {10}^{-2}\text{ g}$.

Calculate number of moles as follows:

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

Molar mass of lead (II) acetate is 325.3 g/mol, putting the values,

$\text{n}=\frac{1.25\times {10}^{-2}\text{ g}}{324.3\text{ g/mol}}=3.85\times {10}^{-5}\text{ mol}$

Since, 1 mole of lead (II) acetate contains $6.023\times {10}^{23}$ molecules thus, $3.85\times {10}^{-5}\text{ mol}$ of lead (II) acetate will have following molecules:

$3.85\times {10}^{-5}\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=2.32\times {10}^{19}\text{ molecules}$

Therefore, number of molecules in lead (II) acetate is $2.32\times {10}^{19}\text{ molecules}$.

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 39QAP

$7.53\times {10}^{21}\text{ molecules}$.

Explanation of Solution

Number of moles of lead (II) acetate is $1.25\times {10}^{-2}\text{ mol}$.

Since, 1 mole of lead (II) acetate contains $6.023\times {10}^{23}$ molecules thus, $1.25\times {10}^{-2}\text{ mol}$ of lead (II) acetate will have following molecules:

$1.25\times {10}^{-2}\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=7.53\times {10}^{21}\text{ molecules}$

Therefore, number of molecules in lead (II) acetate is $7.53\times {10}^{21}\text{ molecules}$.

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 39QAP

$5.42\times {10}^{23}\text{ molecules}$.

Explanation of Solution

Total number of moles of carbon is 5.40 mol.

From the formula of benzene ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}$, 1 mol of benzene contains 6 mol of carbon thus, 1 mol of carbon will be present in 1/6 moles of benzene and 5.40 mol will be present in $\frac{1}{6}\times 5.40\text{ mol=0}\text{.9 mol}$

Since, 1 mole of benzene contains $6.023\times {10}^{23}$ molecules thus, 0.9 mol of benzene will have following molecules:

$0.9\text{ mol}\left(\frac{6.023\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)=5.42\times {10}^{23}\text{ molecules}$

Therefore, number of molecules in benzene is $5.42\times {10}^{23}\text{ molecules}$.