Chapter 10, Problem 57A

(a)

Interpretation Introduction

Interpretation: The representative particle needs to be determined in 3.00 mol Sn.

Concept Introduction: In a substance, a representative particle is the smallest unit of the substance in which it naturally exists. For example, for elements, the representative particle is an atom.

The four types of representative particles are as follows:

1. Atom is the smallest particle of an element.
2. Ions are atoms with positive or negative charges.
3. Molecules are formed when two or more atoms are covalently bonded.
4. Formula units are the simplest ratio of ions to form an ionic compound.

Explanation of Solution

The given substance is 3.0 mol of Sn. The smallest unit of the substance in which it naturally exists is an element. Thus, the representative element is the atom. According to Avogadro’s law, 1 mol of a substance contains $6.022\times {10}^{23}$ atoms. Thus, the number of atoms in 3.0 mol of Sn is calculated as follows:

  $\begin{array}{c}N=3.0\text{ mol}\left(\frac{6.022\times {10}^{23}\text{ atoms}}{1.0\text{ mol}}\right)\\ =1.806\times {10}^{24}\text{ atoms}\end{array}$

Therefore, the number of atoms in 3.0 mol of Sn is $1.806\times {10}^{24}\text{ atoms}$ .

(b)

Interpretation Introduction

Interpretation: The representative particle needs to be determined in 0.400 mol KCl.

Concept Introduction: In a substance, a representative particle is the smallest unit of the substance in which it naturally exists. For example, for elements, the representative particle is an atom.

The four types of representative particles are as follows:

1. Atom is the smallest particle of an element.
2. Ions are atoms with positive or negative charges.
3. Molecules are formed when two or more atoms are covalently bonded.
4. Formula units are the simplest ratio of ions to form an ionic compound.

Explanation of Solution

The given substance is 0.40 mol of KCl. The smallest unit of the substance in which it naturally exists is the formula unit because it is an ionic compound. Thus, the representative element is the formula unit. According to Avogadro’s law, 1 mol of a substance contains $6.022\times {10}^{23}$ formula unit. Thus, the number of formula unit in 0.40 mol of KCl is calculated as follows:

  $\begin{array}{c}N=0.40\text{ mol}\left(\frac{6.022\times {10}^{23}\text{ Formula units}}{1.0\text{ mol}}\right)\\ =2.41\times {10}^{23}\text{ Formula units}\end{array}$

Therefore, the number of formula units in 0.40 mol of KCl is $2.41\times {10}^{23}\text{ Formula units}$ .

(c)

Interpretation Introduction

Interpretation: The representative particle needs to be determined in 7.50 mol of ${\text{SO}}_{\text{2}}$

Concept Introduction: In a substance, a representative particle is the smallest unit of the substance in which it naturally exists. For example, for elements, the representative particle is an atom.

The four types of representative particles are as follows:

1. Atom is the smallest particle of an element.
2. Ions are atoms with positive or negative charges.
3. Molecules are formed when two or more atoms are covalently bonded.
4. Formula units are the simplest ratio of ions to form an ionic compound.

Explanation of Solution

The given substance is 7.50 mol of ${\text{SO}}_{\text{2}}$ . The smallest unit of the substance in which it naturally exists is a molecule because it is a covalent compound. Thus, the representative element is a molecule. According to Avogadro’s law, 1 mol of a substance contains $6.022\times {10}^{23}$ molecule. Thus, the number of molecules in 7.50 mol of ${\text{SO}}_{\text{2}}$ is calculated as follows:

  $\begin{array}{c}N=7.50\text{ mol}\left(\frac{6.022\times {10}^{23}\text{ molecules}}{1.0\text{ mol}}\right)\\ =4.52\times {10}^{24}\text{ molecules}\end{array}$

Therefore, the number of molecules in 7.50 mol of ${\text{SO}}_{\text{2}}$ is $4.52\times {10}^{24}\text{ molecules}$ .

(d)

Interpretation Introduction

Interpretation: The representative particle needs to be determined in $4.80\times {10}^{-3}\text{ mol}$ of NaI.

Concept Introduction: In a substance, a representative particle is the smallest unit of the substance in which it naturally exists. For example, for elements, the representative particle is an atom.

Explanation of Solution

The given substance is $4.80\times {10}^{-3}\text{ mol}$ of NaI. The smallest unit of the substance in which it naturally exists is the formula unit because it is an ionic compound. Thus, the representative element is the formula unit. According to Avogadro’s law, 1 mol of a substance contains $6.022\times {10}^{23}$ formula unit. Thus, the number of formula unit in $4.80\times {10}^{-3}\text{ mol}$ of NaI is calculated as follows:

  $\begin{array}{c}N=4.80\times {10}^{-3}\text{ mol}\left(\frac{6.022\times {10}^{23}\text{ Formula units}}{1.0\text{ mol}}\right)\\ =2.90\times {10}^{21}\text{ Formula units}\end{array}$

Therefore, the number of formula units in $4.80\times {10}^{-3}\text{ mol}$ of NaI is $2.90\times {10}^{21}\text{ Formula units}$ .