Chapter 7, Problem 11PE

(a)

Interpretation Introduction

Interpretation:

The number of atoms in $\text{25}$ molecules of ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ has to be given.

Answer to Problem 11PE

The number of atoms in $\text{25}$ molecules of ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ is $\text{175}\text{atoms}\text{.}$

Explanation of Solution

Given,

The number of molecules of ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ is $\text{25}\text{.}$

There are seven atoms in ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ (two phosphorus and five oxygen atoms).

The number of atoms in $\text{25}$ molecules of ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ can be calculated as,

  $\left(\text{25}\text{molecules}\right)\text{×}\left(\frac{\text{7}\text{atoms}}{\text{1}\text{molcule}}\right)\text{=175}\text{atoms}$

The number of atoms in $\text{25}$ molecules of ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ is $\text{175}\text{atoms}\text{.}$

(b)

Interpretation Introduction

Interpretation:

The number of atoms in $\text{3}\text{.62}\text{mol}$ of ${\text{O}}_{\text{2}}$ has to be given.

Answer to Problem 11PE

The number of atoms in $\text{3}\text{.62}\text{mol}$ of ${\text{O}}_{\text{2}}$ is $\text{43}{\text{.59×10}}^{\text{23}}\text{atoms}\text{.}$

Explanation of Solution

Given,

The number of moles of ${\text{O}}_{\text{2}}$ is $\text{3}\text{.62}\text{mol}\text{.}$

The Avogadro’s number is $\text{6}{\text{.022×10}}^{\text{23}}\text{molecules}\text{.}$

There are two atoms in ${\text{O}}_{\text{2}}\text{.}$

The number of atoms in $\text{3}\text{.62}\text{mol}$ of ${\text{O}}_{\text{2}}$ can be calculated as,

  $\left(\text{3}\text{.62}\text{moles}\right)\text{×}\left(\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules}}{\text{1}\text{mol}}\right)\left(\frac{\text{2}\text{atoms}}{\text{1}\text{molcule}}\right)\text{=43}{\text{.59×10}}^{\text{23}}\text{atoms}$

The number of atoms in $\text{3}\text{.62}\text{mol}$ of ${\text{O}}_{\text{2}}$ is $\text{43}{\text{.59×10}}^{\text{23}}\text{atoms}\text{.}$

(c)

Interpretation Introduction

Interpretation:

The number of atoms in $\text{12}\text{.2}\text{mol}$ of ${\text{CS}}_{\text{2}}$ has to be given.

Answer to Problem 11PE

The number of atoms in $\text{12}\text{.2}\text{mol}$ of ${\text{CS}}_{\text{2}}$ is $\text{2}{\text{.20×10}}^{\text{25}}\text{atoms}\text{.}$

Explanation of Solution

Given,

The number of moles of ${\text{CS}}_{\text{2}}$ is $\text{12}\text{.2}\text{mol}\text{.}$

The Avogadro’s number is $\text{6}{\text{.022×10}}^{\text{23}}\text{molecules}\text{.}$

There are three atoms in ${\text{CS}}_{\text{2}}$ (one carbon atom and two sulfur atom).

The number of atoms in $\text{12}\text{.2}\text{mol}$ of ${\text{CS}}_{\text{2}}$ can be calculated as,

$\left(12.2\text{moles}\right)\text{×}\left(\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules}}{\text{1}\text{mol}}\right)\left(\frac{3\text{atoms}}{\text{1}\text{molcule}}\right)\text{=220}{\text{.40×10}}^{\text{23}}\text{atoms}=\text{2}{\text{.20×10}}^{\text{25}}\text{atoms}$

The number of atoms in $\text{12}\text{.2}\text{mol}$ of ${\text{CS}}_{\text{2}}$ is $\text{2}{\text{.20×10}}^{\text{25}}\text{atoms}\text{.}$

(d)

Interpretation Introduction

Interpretation:

The number of atoms in $\text{1}\text{.25}\text{g}$ of $\text{Na}$ has to be given.

Answer to Problem 11PE

The number of atoms in $\text{1}\text{.25}\text{g}$ of $\text{Na}$ is $\text{0}{\text{.327×10}}^{\text{23}}\text{ atoms}\text{.}$

Explanation of Solution

Given,

The molar mass of $\text{Na}$ is $\text{23}\text{g/mol}\text{.}$

The mass of sodium is $1.25\text{g}\text{.}$

The Avogadro’s number is $\text{6}{\text{.022×10}}^{\text{23}}\text{atoms}\text{.}$

The number of atoms in $\text{1}\text{.25}\text{g}$ of $\text{Na}$ can be calculated as,

  $\text{1}\text{.25}\text{g×}\left(\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{atoms}}{\text{23}\text{g}}\right)\text{=0}{\text{.327×10}}^{\text{23}}\text{atoms}$

The number of atoms in $\text{1}\text{.25}\text{g}$ of $\text{Na}$ is $\text{0}{\text{.327×10}}^{\text{23}}\text{ atoms}\text{.}$

(e)

Interpretation Introduction

Interpretation:

The number of atoms in $2.7\text{g}$ of ${\text{CO}}_{\text{2}}$ has to be given.

Answer to Problem 11PE

The number of atoms in $2.7\text{g}$ of ${\text{CO}}_{\text{2}}$ is $\text{1}{\text{.1×10}}^{\text{23}}\text{ atoms}\text{.}$

Explanation of Solution

Given,

The molar mass of ${\text{CO}}_{\text{2}}$ is $44.01\text{g/mol}\text{.}$

The mass of ${\text{CO}}_{\text{2}}$ is $2.7\text{g}\text{.}$

The Avogadro’s number is $\text{6}{\text{.022×10}}^{\text{23}}\text{atoms}\text{.}$

The number of atoms in $2.7\text{g}$ of ${\text{CO}}_{\text{2}}$ can be calculated as,

  $2.7\text{g×}\left(\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{atoms}\times \text{3}}{44.01\text{g}}\right)\text{=1}{\text{.1×10}}^{\text{23}}\text{atoms}$

The number of atoms in $2.7\text{g}$ of ${\text{CO}}_{\text{2}}$ is $\text{1}{\text{.1×10}}^{\text{23}}\text{ atoms}\text{.}$

(f)

Interpretation Introduction

Interpretation:

The number of atoms in $0.25\text{g}$ of ${\text{CH}}_{\text{4}}$ has to be given.

Answer to Problem 11PE

The number of atoms in $0.25\text{g}$ of ${\text{CH}}_{\text{4}}$ is $\text{0}{\text{.469×10}}^{\text{23}}\text{ atoms}\text{.}$

Explanation of Solution

Given,

The molar mass of ${\text{CH}}_{\text{4}}$ is $16.04\text{g/mol}\text{.}$

The mass of ${\text{CH}}_{\text{4}}$ is $0.25\text{g}\text{.}$

The Avogadro’s number is $\text{6}{\text{.022×10}}^{\text{23}}\text{atoms}\text{.}$

The number of atoms in $0.25\text{g}$ of ${\text{CH}}_{\text{4}}$ can be calculated as,

  $\text{0}\text{.25}\text{g×}\left(\frac{\text{6}{\text{.022×10}}^{\text{23}}\text{atoms×5}}{\text{16}\text{.04}\text{g}}\right)\text{=0}{\text{.469×10}}^{\text{23}}\text{atoms}$

The number of atoms in $0.25\text{g}$ of ${\text{CH}}_{\text{4}}$ is $\text{0}{\text{.469×10}}^{\text{23}}\text{ atoms}\text{.}$