Chapter 11, Problem 11.1P

(a)

Interpretation Introduction

Interpretation:

The number of moles in $\text{52 g}$ calcium carbonate has to be determined.

Concept Introduction:

Mole is S.I. unit. The number of moles is calculated as ratio of mass of compound to molar mass of compound.

Molar mass is sum of the total mass in grams of all atoms that make up mole of particular molecule that is mass of 1 mole of compound. The S.I unit is $\text{g/mol}$.

The expression to relate number of moles, mass and molar mass of compound is as follows:

  $\text{Number of moles}=\frac{\text{mass of the compound}}{\text{molar mass of the compound}}$

Answer to Problem 11.1P

The number of moles in $\text{52 g}$ calcium carbonate is $\text{0}\text{.51954 mol}$.

Explanation of Solution

The formula to calculate number of moles of calcium carbonate is as follows:

  ${\text{Number of moles of CaCO}}_3=\frac{{\text{Given mass of CaCO}}_3}{{\text{molar mass of CaCO}}_3}$        (1)

Substitute $\text{52 g}$ for given mass of ${\text{CaCO}}_3$ and $\text{100}\text{.0869 g/mol}$ for molar mass of ${\text{CaCO}}_3$ in equation (1).

  $\begin{array}{c}{\text{number of moles of CaCO}}_3=\frac{\text{52 g}}{\text{100}\text{.0869 g/mol}}\\ =\text{0}\text{.51954 mol}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The number of moles in ethanol has to be determined

Concept Introduction:

Density is characteristic property of a substance. It is defined as mass per unit volume. It is represented by $\rho$.

The formula to calculate the density is as follows:

  $\text{Density}\left(\rho \right)=\frac{\text{Mass}\left(\text{M}\right)}{\text{Volume}\left(\text{V}\right)}$

Answer to Problem 11.1P

The number of moles in ethanol is $\text{4}\text{.1241 mol}$.

Explanation of Solution

The formula to calculate the density is as follows:

  $\text{Density}\left(\rho \right)=\frac{\text{Mass}\left(\text{M}\right)}{\text{Volume}\left(\text{V}\right)}$        (2)

Rearrange equation (2) to calculate the mass of solution.

  $\text{Mass}\left(\text{ethanol}\right)=\left(\text{density}\right)\left(\text{volume}\right)$

Substitute $\text{250 mL}$ for volume of ethanol and $\text{0}\text{.76 g/mL}$ for density of ethanol in equation (2).

    $\begin{array}{c}\text{Mass}\left(\text{ethanol}\right)=\left(\text{0}\text{.76 g/mL}\right)\left(\text{250 mL}\right)\\ =\text{190 g}\end{array}$

The formula to calculate number of moles of ethanol is as follows:

  $\text{Number of moles of ethanol}=\frac{\text{Given mass of ethanol}}{\text{molar mass of ethanol}}$        (3)

Substitute $\text{190 g}$ for given mass of ethanol and $\text{46}\text{.07 g/mol}$ for molar mass of ethanol in equation (3).

  $\begin{array}{c}\text{number of moles of ethanol}=\frac{\text{190 g}}{\text{46}\text{.07 g/mol}}\\ =\text{4}\text{.1241 mol}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The number of moles in $\text{28}\text{.1 g}$ carbon dioxide has to be determined.

Concept Introduction:

Refer to part (a)

Answer to Problem 11.1P

The number of moles in $\text{28}\text{.1 g}$ carbon dioxide is $\text{0}\text{.63849 mol}$.

Explanation of Solution

The formula to calculate number of moles of carbon dioxide is as follows:

  $\text{Number of moles of carbon dioxide}=\frac{\text{Given mass of carbon dioxide}}{\text{molar mass of carbon dioxide}}$        (4)

Substitute $\text{28}\text{.1 g}$ for given mass of carbon dioxide and $\text{44}\text{.01 g/mol}$ for molar mass of carbon dioxide in equation (4).

  $\begin{array}{c}\text{number of moles of carbon dioxide}=\frac{\text{28}\text{.1 g}}{\text{44}\text{.01 g/mol}}\\ =\text{0}\text{.63849 mol}\end{array}$

(d)

Interpretation Introduction

Interpretation:

The number of moles in $5.5\times {10}^{22}\text{ molecules}$ of sulfur hexafluoride gas has to be determined.

Concept Introduction:

One mole of any substance contains $6.022\times {10}^{23}$ formula units. This number is called Avogadro’s number.

The expression is as follows:

    $1\text{ mole}=6.022\times {10}^{23}\text{ molecules}$

Answer to Problem 11.1P

The number of moles in $5.55\times {10}^{22}\text{ molecules}$ of sulfur hexafluoride gas is $\text{0}\text{.09216 mol}$.

Explanation of Solution

The number of molecules of sulfur hexafluoride gas is $5.55\times {10}^{22}\text{ molecules}$.

The formula to calculate number of moles is as follows:

  $\text{Number of moles}=\left(\text{number of molecules}\right)\left(\frac{\text{1 mol}}{6.022\times {10}^{23}\text{ molecules}}\right)$

Substitute $5.55\times {10}^{22}\text{ molecules}$ for number of molecules.

  $\begin{array}{c}\text{Number of moles}=\left(5.55\times {10}^{22}\text{ molecules}\right)\left(\frac{\text{1 mol}}{6.022\times {10}^{23}\text{ molecules}}\right)\\ =\text{0}\text{.09216 mol}\end{array}$