Chapter 3, Problem 3.20QP

(a)

Interpretation Introduction

Interpretation: The number of moles of each gas in the sample is to be calculated.

Concept introduction: A mole of a substance is the quantity of a substance which contains the same number of particles as the number of carbon atoms in exactly 12 grams for the carbon-12 isotopes. A mole of particles contains Avogadro’s number $\left(6.022\times {10}^{23}\right)$ of particles.

To determine: The number of moles of the given gas in the sample.

Answer to Problem 3.20QP

Solution

The number of moles of ${\text{H}}_2\left(g\right)$ is $\underset{\_}{2.3\times 10^{-11}mol}$.

Explanation of Solution

Explanation

Given

The number of molecules of ${\text{H}}_2\left(g\right)$ is $1.4\times {10}^{13}$ molecules.

Also, $1\text{mol}=6.022\times {10}^{23}\text{molecules}$.

The number of moles is calculated by using the formula,

$\text{Number}\text{of}\text{moles}=\frac{N}{N_A}$

Where,

• $N$ is the number of atoms.
• $N_A$ is the Avogadro’s number of atoms.

Substitute the value of $N$ and $N_A$ in the above formula to calculate the number of moles.

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{of}{\text{H}}_2\left(g\right)=\frac{\text{1}{\text{.4×10}}^{\text{13}}\text{molecules}}{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules/mol}}\\ =\underset{\_}{2.3\times 10^{-11}mol}\end{array}$

Hence, the number of moles of ${\text{H}}_2\left(g\right)$ is $\underset{\_}{2.3\times 10^{-11}mol}$.

(b)

Interpretation Introduction

To determine: The number of moles of the given gas in the sample.

Answer to Problem 3.20QP

Solution

The number of moles of $\text{He}\left(g\right)$ is $\underset{\_}{2.5\times 10^{-8}mol}$.

Explanation of Solution

Explanation

Given

The number of molecules of $\text{He}\left(g\right)$ is $1.5\times {10}^{14}$ molecules.

Also, $1\text{mol}=6.022\times {10}^{23}\text{molecules}$.

The number of moles is calculated by using the formula,

$\text{Number}\text{of}\text{moles}=\frac{N}{N_A}$

Where,

• $N$ is the number of atoms.
• $N_A$ is the Avogadro’s number of atoms.

Substitute the value of $N$ and $N_A$ in the above formula to calculate the number of moles.

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{of}\text{He}\left(g\right)=\frac{\text{1}{\text{.5×10}}^{\text{14}}\text{molecules}}{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules/mol}}\\ =\underset{\_}{2.5\times 10^{-8}mol}\end{array}$

Hence, the number of moles of $\text{He}\left(g\right)$ is $\underset{\_}{2.5\times 10^{-8}mol}$.

(c)

Interpretation Introduction

To determine: The number of moles of the given gas in the sample.

Answer to Problem 3.20QP

Solution

The number of moles of ${\text{N}}_2\text{O}\left(g\right)$ is $\underset{\_}{1.3\times 10^{-11}mol}$.

Explanation of Solution

Explanation

Given

The number of molecules of ${\text{N}}_2\text{O}\left(g\right)$ is $7.7\times {10}^{12}$ molecules

Also, $1\text{mol}=6.022\times {10}^{23}\text{molecules}$.

The number of moles is calculated by using the formula,

$\text{Number}\text{of}\text{moles}=\frac{N}{N_A}$

Where,

• $N$ is the number of atoms.
• $N_A$ is the Avogadro’s number of atoms.

Substitute the value of $N$ and $N_A$ in the above formula to calculate the number of moles.

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{of}{\text{N}}_{\text{2}}\text{O}\left(g\right)=\frac{\text{7}{\text{.7×10}}^{\text{12}}\text{molecules}}{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules/mol}}\\ =\underset{\_}{1.3\times 10^{-11}mol}\end{array}$

Hence, the number of moles of ${\text{N}}_2\text{O}\left(g\right)$ is $\underset{\_}{1.3\times 10^{-11}mol}$.

(d)

Interpretation Introduction

To determine: The number of moles of the given gas in the sample.

Answer to Problem 3.20QP

Solution

The number of moles of $\text{CO}\left(g\right)$ is $\underset{\_}{5.0\times 10^{-12}mol}$.

Explanation of Solution

Explanation

Given

The number of molecules of $\text{CO}\left(g\right)$ is $3.0\times {10}^{12}$ molecules

Also, $1\text{mol}=6.022\times {10}^{23}\text{molecules}$

The number of moles is calculated by using the formula,

$\text{Number}\text{of}\text{moles}=\frac{N}{N_A}$

Where,

• $N$ is the number of atoms.
• $N_A$ is the Avogadro’s number of atoms.

Substitute the value of $N$ and $N_A$ in the above formula to calculate the number of moles.

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{of}\text{CO}\left(g\right)=\frac{\text{3}{\text{.0×10}}^{13}\text{molecules}}{\text{6}{\text{.022×10}}^{\text{23}}\text{molecules/mol}}\\ =\underset{\_}{5.0\times 10^{-12}mol}\end{array}$

Hence, the number of moles of $\text{CO}\left(g\right)$ is $\underset{\_}{5.0\times 10^{-12}mol}$.

Conclusion

1. a. The number of moles of ${\text{H}}_2\left(g\right)$ in a sample of air is $\underset{\_}{2.3\times 10^{-11}mol}$.
2. b. The number of moles of $\text{He}\left(g\right)$ in a sample of air is $\underset{\_}{2.5\times 10^{-8}mol}$.
3. c. The number of moles of ${\text{N}}_2\text{O}\left(g\right)$ in a sample of air is $\underset{\_}{1.3\times 10^{-11}mol}$.
4. d. The number of moles of $\text{CO}\left(g\right)$ in a sample of air is $\underset{\_}{5.0\times 10^{-12}mol}$