Chapter 15, Problem 21E

Interpretation Introduction

(a)

Interpretation:

The mole concept map is to be drawn. The volume of hydrogen sulfide $\left({\text{H}}_{\text{2}}\text{S}\right)$ gas dissolved in $\text{450}\text{.0}\text{mL}$ of solution is to be stated.

Concept introduction:

A mole of a substance is defined as the same number of particles of the substance as present in $12\text{g}$ of $\text{C}-12$. The number of particles present in one mole of a substance is $6.023\times {10}^{23}$ particle. The concept map of a mole is a diagram used to relate the different concepts of mole chemistry. The unit of the mole is denoted as $\text{mol}$.

Answer to Problem 21E

The mole concept map is shown below.

The volume of ${\text{H}}_{\text{2}}\text{S}$ gas at $\text{STP}$ dissolved in $\text{450}\text{.0}\text{mL}$ of solution is $\text{0}\text{.826}\text{L}$.

Explanation of Solution

It is given that the number of molecules of ${\text{H}}_{\text{2}}\text{S}$ is $2.22\times {10}^{22}$ which are dissolved in $450.0\text{mL}$ of solution.

The mole concept map is shown below.

Figure 1

The Figure 1 shows that the number of moles should be calculated first, to calculate other parameters.

The number of moles is calculated from the relation shown below.

$\begin{array}{rll}1\text{mol}& =& 6.022\times {10}^{23}\text{molecules}\\ \frac{\text{1}}{6.022\times {10}^{23}}\text{mol}& =& 1\text{molecule}\end{array}$

Therefore, the number of moles for $\text{2}{\text{.22×10}}^{\text{22}}\text{molecules}$ is calculated as shown below.

$\begin{array}{rll}\text{The}\text{number}\text{of}\text{moles}\text{of}{\text{H}}_{\text{2}}\text{S}& =& \frac{\text{1}\text{mol}}{6.022\times {10}^{23}\text{molecules}}\times \left(2.22\times {10}^{22}\right)\text{molecules}\\ & =& \text{0}\text{.0369}\text{mol}\end{array}$

The volume of ${\text{H}}_{\text{2}}\text{S}$ gas is calculated from the relation as shown below.

$1\text{mol}=\text{2}\text{.24}\text{L}\text{of}{\text{H}}_2\text{S}$

The number of moles of ${\text{H}}_{\text{2}}\text{S}$ gas is $\text{0}\text{.0369}\text{mol}$.

The volume for $\text{0}\text{.0369}\text{mol}$ of ${\text{H}}_{\text{2}}\text{S}$ is calculated as shown below

$\begin{array}{rll}\text{Volume}\text{of}{\text{H}}_{\text{2}}\text{S}& =& 0.0369\text{mol×}\frac{\text{22}\text{.4}\text{L}}{\text{1}\text{mol}}\\ & =& \text{0}\text{.826}\text{L}\end{array}$

Therefore, the volume of ${\text{H}}_{\text{2}}\text{S}$ gas at $\text{STP}$ is $\text{0}\text{.826}\text{L}$.

Conclusion

The mole concept map is shown in Figure 1. The volume of ${\text{H}}_{\text{2}}\text{S}$ gas dissolved at $\text{STP}$ is $\text{0}\text{.826}\text{L}$.

Interpretation Introduction

(b)

Interpretation:

The mole concept map is to be drawn. The mass of ${\text{H}}_{\text{2}}\text{S}$ gas dissolved in the solution is to be calculated.

Concept introduction:

A mole of a substance is defined as the same number of particles of the substance as present in $12\text{g}$ of $\text{C}-12$. The number of particles present in one mole of a substance is $6.023\times {10}^{23}$ particle. The concept map of a mole is a diagram used to relate the different concepts of mole chemistry. The unit of the mole is denoted as $\text{mol}$.

Answer to Problem 21E

The grams of ${\text{H}}_{\text{2}}\text{S}$ gas dissolved in $\text{450}\text{.0}\text{mL}$ of solution is $\text{1}\text{.26}\text{g}$.

Explanation of Solution

It is given that the number of molecules of ${\text{H}}_{\text{2}}\text{S}$ is $2.22\times {10}^{22}$ which are dissolved in $450.0\text{mL}$ of solution.

The mole concept map is shown below.

Figure 1

The Figure 1 shows that the number of moles should be calculated first, to calculate other parameters.

The number of moles is calculated from the relation shown below.

$\begin{array}{rll}1\text{mol}& =& 6.022\times {10}^{23}\text{molecules}\\ \frac{\text{1}}{6.022\times {10}^{23}}\text{mol}& =& 1\text{molecule}\end{array}$

Therefore, the number of moles for $\text{2}{\text{.22×10}}^{\text{22}}\text{molecules}$ is calculated as shown below.

$\begin{array}{rll}\text{The}\text{number}\text{of}\text{moles}\text{of}{\text{H}}_{\text{2}}\text{S}& =& \frac{\text{1}\text{mol}}{6.022\times {10}^{23}\text{molecules}}\times \left(2.22\times {10}^{22}\right)\text{molecules}\\ & =& \text{0}\text{.0369}\text{mol}\end{array}$

The molar mass of hydrogen is $\text{1}\text{.01}\text{g}{\text{mol}}^{-\text{1}}$.

The molar mass of sulfur is $\text{32}\text{.07}\text{g}{\text{mol}}^{-\text{1}}$

$\begin{array}{rll}\text{Molar}\text{mass}\text{of}{\text{H}}_{\text{2}}\text{S}\text{gas}& =& \left(\text{2}\times \text{Mass}\text{of}\text{H}\right)+\text{Mass}\text{of}\text{S}\\ & =& \text{2}\times 1.01\text{g}{\text{mol}}^{-\text{1}}+32.07\text{g}{\text{mol}}^{-\text{1}}\\ & =& 2.02\text{g}{\text{mol}}^{-\text{1}}+32.07\text{g}{\text{mol}}^{-\text{1}}\\ & =& 34.09\text{g}{\text{mol}}^{-\text{1}}\end{array}$

The mass of ${\text{H}}_{\text{2}}\text{S}$ gas is calculated from the relation as shown below.

$\begin{array}{l}1\text{mol}=\text{Molar}\text{mass}\text{of}{\text{H}}_{\text{2}}\text{S}\\ 1\text{mol}=34.09\text{g}\text{of}{\text{H}}_2\text{S}\end{array}$

The number of moles of ${\text{H}}_{\text{2}}\text{S}$ gas is $\text{0}\text{.0369}\text{mol}$.

The mass for $\text{0}\text{.0369}\text{mol}$ of ${\text{H}}_{\text{2}}\text{S}$ is calculated as shown below.

$\begin{array}{rll}\text{Mass}\text{of}{\text{H}}_{\text{2}}\text{S}& =& \text{0}\text{.0369}\text{mol}\times \frac{34.09\text{g}{\text{H}}_{\text{2}}\text{S}}{\text{1}\text{mol}{\text{H}}_{\text{2}}\text{S}}\\ & =& \text{1}\text{.26}\text{g}{\text{H}}_{\text{2}}\text{S}\end{array}$

Therefore, the mass of ${\text{H}}_{\text{2}}\text{S}$ gas is $\text{1}\text{.26}\text{g}$.

Conclusion

The mass of ${\text{H}}_{\text{2}}\text{S}$ gas dissolved in $\text{450}\text{.0}\text{mL}$ of solution is. $\text{1}\text{.26}\text{g}$.

Interpretation Introduction

(c)

Interpretation:

The mole concept map is to be drawn and the molar concentration of ${\text{H}}_{\text{2}}\text{S}$ solution dissolved in the solution is to be calculated.

Concept introduction:

A mole of a substance is defined as the same number of particles of the substance as present in $12\text{g}$ of $\text{C}-12$. The number of particles present in one mole of a substance is $6.023\times {10}^{23}$ particle. The concept map of a mole is a diagram used to relate the different concepts of mole chemistry. The unit of the mole is denoted as $\text{mol}$. The unit of the mole is denoted as mol. Molarity is defined as the number of moles in $\text{1000}\text{mL}$ of solution. Molarity is denoted by $M$.

Answer to Problem 21E

The molar concentration of ${\text{H}}_{\text{2}}\text{S}$ gas dissolved in $\text{450}\text{.0}\text{mL}$ of solution is $0.0819M$.

Explanation of Solution

It is given that the number of molecules of ${\text{H}}_{\text{2}}\text{S}$ is $\text{2}{\text{.22×10}}^{\text{22}}$ which are dissolved in $450.0\text{mL}$ of solution.

The mole concept map is shown below.

Figure 1

The Figure 1 shows that the number of moles should be calculated first, to calculate other parameters.

The number of moles is calculated from the relation shown below.

$\begin{array}{rll}1\text{mol}& =& 6.022\times {10}^{23}\text{molecules}\\ \frac{\text{1}}{6.022\times {10}^{23}}\text{mol}& =& 1\text{molecule}\end{array}$

Therefore, the number of moles for $\text{2}{\text{.22×10}}^{\text{22}}\text{molecules}$ is calculated as shown below.

$\begin{array}{rll}\text{The}\text{number}\text{of}\text{moles}\text{of}{\text{H}}_{\text{2}}\text{S}& =& \frac{\text{1}\text{mol}}{6.022\times {10}^{23}\text{molecules}}\times \left(2.22\times {10}^{22}\right)\text{molecules}\\ & =& \text{0}\text{.03686}\text{mol}\end{array}$

The number of moles of ${\text{H}}_{\text{2}}\text{S}$ in $\text{450}\text{.0}\text{mL}$ of solution is $\text{0}\text{.03686}\text{mol}$.

The formula to determine molarity is shown below.

$M=\frac{n}{V}$ …(1)

Where

• $M$ is the molarity of a solution.

• $n$ is the number of moles of solute.

• $V$ is the volume of the solution.

The relation between $\text{L}$ and $\text{mL}$ is shown below.

$\text{1}\text{L}=\text{1000}\text{mL}$

The probable unit factors are given below.

$\frac{\text{1}\text{L}}{\text{1000}\text{mL}}\text{and}\frac{\text{1000}\text{mL}}{\text{1}\text{L}}$

The unit factor to determine $\text{L}$ from $\text{mL}$ is given below.

$\frac{\text{1L}}{\text{1000}\text{mL}}$

Therefore, the volume in $\text{L}$ is calculated below.

$\begin{array}{rll}\text{Volume}& =& 450.0\text{ mL}\times \frac{\text{1 L}}{\text{1000}\text{mL}}\\ & =& 0.45\text{L}\end{array}$

Substitute the value of number of moles as $\text{0}\text{.03686}\text{mol}$ and volume as $\text{0}\text{.45}\text{L}$ in equation (1).

$\begin{array}{rll}\text{Molar}\text{concentration}\text{of}{\text{H}}_{\text{2}}\text{S}& =& \frac{\text{0}\text{.03686}\text{mol}}{\text{0}\text{.45}\text{L}}\\ & =& \left(0.0819\text{mol}/\text{L}\right)\left(\frac{1M}{\text{1 mol}/\text{L}}\right)\\ & =& 0.0819M\end{array}$

Therefore, the molar concentration of ${\text{H}}_{\text{2}}\text{S}$ gas is $0.0819M$.

Conclusion

The molar concentration of ${\text{H}}_{\text{2}}\text{S}$ gas dissolved in $\text{450}\text{.0}\text{mL}$ of solution is. $0.0819M$.