Chapter 3, Problem 3.22QP

(a)

Interpretation Introduction

Interpretation: The atoms of iron in $2.5\text{moles}$ of each of the given compound are 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. The number of atoms in a substance is equal to the product of moles and Avogadro’s number.

To determine: The atoms of iron in $2.5\text{mole}$ of ${\text{FeWO}}_{\text{4}}$.

Answer to Problem 3.22QP

Solution

The number of iron atoms in $2.5\text{mole}$ of ${\text{FeWO}}_{\text{4}}$ is $\underset{\_}{1.5\times 10^{24}atoms}$.

Explanation of Solution

Explanation

Given

One mole of wolframite contains Avogadro’s number of molecules of wolframite. Therefore, one mole of wolframite is equivalent to $6.022\times {10}^{23}$ molecules of wolframite.

So, $1\text{mol}{\text{FeWO}}_4=6.022\times {10}^{23}\text{molecules}{\text{FeWO}}_4$.

One molecule of ${\text{FeWO}}_{\text{4}}$ contains one atom of $\text{Fe}$, one atom of $\text{W}$ and 4 atoms of $\text{O}$

The number of iron atoms in $2.5\text{mole}$ of ${\text{FeWO}}_4$ is calculated by using the formula,

$N=n\times N_A\times \text{number}\text{of}\text{Fe}\text{atoms}\text{in}\text{a}\text{molecule}$

Where,

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

Substitute the values of $n$ and $N_A$ in the above formula to calculate the number of iron atoms.

$\begin{array}{c}N=2.5\text{mole}\times 6.022\times {10}^{23}\text{molecules/mole}\times \frac{1\text{Fe}\text{atom}}{\text{1}\text{molecule}{\text{FeWO}}_4}\\ =2.5\times 6.022\times {10}^{23}\times 1\text{atoms}\\ =\underset{\_}{1.5\times 10^{24}atoms}\end{array}$

Hence, the number of iron atoms in $2.5\text{mole}$ of ${\text{FeWO}}_{\text{4}}$ is $\underset{\_}{1.5\times 10^{24}atoms}$.

(b)

Interpretation Introduction

To determine: The atoms of iron in $2.5\text{mole}$ of ${\text{FeS}}_{\text{2}}$.

Answer to Problem 3.22QP

Solution

The number of iron atoms in $2.5\text{mole}$ of ${\text{FeS}}_2$ is $\underset{\_}{1.5\times 10^{24}atoms}$.

Explanation of Solution

Explanation

Given

One mole of ${\text{FeS}}_{\text{2}}$ contains Avogadro’s number of molecules of ${\text{FeS}}_{\text{2}}$. Therefore, one mole of ${\text{FeS}}_{\text{2}}$ is equivalent to $6.022\times {10}^{23}$ molecules of ${\text{FeS}}_{\text{2}}$.

So, $1\text{mol}{\text{FeS}}_2=6.022\times {10}^{23}\text{molecules}{\text{FeS}}_2$.

One molecule of ${\text{FeS}}_{\text{2}}$ contains one atom of $\text{Fe}$ and two atoms of $\text{S}$.

The number of iron atoms in $2.5\text{mole}$ of ${\text{FeS}}_{\text{2}}$ is calculated by using the formula,

$N=n\times N_A\times \text{number}\text{of}\text{Fe}\text{atoms}\text{in}\text{a}\text{molecule}$

Where,

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

Substitute the values of $n$ and $N_A$ in the above formula to calculate the number of iron atoms.

$\begin{array}{c}N=2.5\text{mole}\times 6.022\times {10}^{23}\text{molecules/mole}\times \frac{1\text{Fe}\text{atom}}{\text{1}\text{molecule}{\text{FeS}}_2}\\ =2.5\times 6.022\times {10}^{23}\times 1\text{atoms}\\ =\underset{\_}{1.5\times 10^{24}atoms}\end{array}$

Hence, the number of iron atoms in $2.5\text{mole}$ of ${\text{FeS}}_2$ is $\underset{\_}{1.5\times 10^{24}atoms}$.

(c)

Interpretation Introduction

To determine: The atoms of iron in $2.5\text{mole}$ of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$.

Answer to Problem 3.22QP

Solution

The number of iron atoms in $2.5\text{mole}$ of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$ is $\underset{\_}{4.5\times 10^{24}atoms}$.

Explanation of Solution

Explanation

Given

One mole of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$ contains Avogadro’s number of molecules of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$. Therefore, one mole of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$ is equivalent to $6.022\times {10}^{23}$ molecules of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$.

So, $1\text{mol}{\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}=6.022\times {10}^{23}\text{molecules}{\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$.

One molecule of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$ contains three atoms of $\text{Fe}$ and four atoms of $\text{O}$.

The number of iron atoms in $2.5\text{mole}$ of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$ is calculated by using the formula,

$N=n\times N_A\times \text{number}\text{of}\text{Fe}\text{atoms}\text{in}\text{a}\text{molecule}$

Where,

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

Substitute the values of $n$ and $N_A$ in the above formula to calculate the number of iron atoms.

$\begin{array}{c}N=2.5\text{mole}\times 6.022\times {10}^{23}\text{molecules/mole}\times \frac{3\text{Fe}\text{atom}}{\text{1}\text{molecule}{\text{Fe}}_3{\text{O}}_{\text{4}}}\\ =2.5\times 6.022\times {10}^{23}\times 3\text{atoms}\\ =\underset{\_}{4.5\times 10^{24}atoms}\end{array}$

Hence, the number of iron atoms in $2.5\text{mole}$ of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$ is $\underset{\_}{4.5\times 10^{24}atoms}$.

(d)

Interpretation Introduction

To determine: The atoms of iron in $2.5\text{mole}$ of ${\text{Fe}}_2{\text{O}}_3$.

Answer to Problem 3.22QP

Solution

The number of iron atoms in $2.5\text{mole}$ of ${\text{Fe}}_2{\text{O}}_3$ is $\underset{\_}{3.0\times 10^{24}atoms}$.

Explanation of Solution

Explanation

Given

One mole of ${\text{Fe}}_2{\text{O}}_3$ contains Avogadro’s number of molecules of ${\text{Fe}}_2{\text{O}}_3$. Therefore, one mole of ${\text{Fe}}_2{\text{O}}_3$ is equivalent to $6.022\times {10}^{23}$ molecules of ${\text{Fe}}_2{\text{O}}_3$.

So, $1\text{mol}{\text{Fe}}_2{\text{O}}_3=6.022\times {10}^{23}\text{molecules}{\text{Fe}}_2{\text{O}}_3$.

One molecule of ${\text{Fe}}_2{\text{O}}_3$ contains two atoms of $\text{Fe}$ and three atoms of $\text{O}$.

The number of iron atoms in $2.5\text{mole}$ of ${\text{Fe}}_2{\text{O}}_3$ is calculated by using the formula,

$N=n\times N_A\times \text{number}\text{of}\text{Fe}\text{atoms}\text{in}\text{a}\text{molecule}$

Where,

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

Substitute the values of $n$ and $N_A$ in the above formula to calculate the number of iron atoms.

$\begin{array}{c}N=2.5\text{mole}\times 6.022\times {10}^{23}\text{molecules/mole}\times \frac{2\text{Fe}\text{atom}}{\text{1}\text{molecule}{\text{Fe}}_2{\text{O}}_3}\\ =2.5\times 6.022\times {10}^{23}\times 2\text{atoms}\\ =\underset{\_}{3.0\times 10^{24}atoms}\end{array}$

Hence, the number of iron atoms in $2.5\text{mole}$ of ${\text{Fe}}_2{\text{O}}_3$ is $\underset{\_}{3.0\times 10^{24}atoms}$.

Conclusion

1. a. The number of iron atoms in $2.5\text{mole}$ of ${\text{FeWO}}_{\text{4}}$ is $\underset{\_}{1.5\times 10^{24}atoms}$.
2. b. The number of iron atoms in $2.5\text{mole}$ of ${\text{FeS}}_2$ is $\underset{\_}{1.5\times 10^{24}atoms}$.
3. c. The number of iron atoms in $2.5\text{mole}$ of ${\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}$ is $\underset{\_}{4.5\times 10^{24}atoms}$.
4. d. The number of iron atoms in $2.5\text{mole}$ of ${\text{Fe}}_2{\text{O}}_3$ is $\underset{\_}{3.0\times 10^{24}atoms}$