Chapter 2, Problem 2.43E

Write three relationships (equalities) based on the mole concept for each of the following elements:

a. beryllium

b. lead

c. sodium

Interpretation Introduction

(a)

Interpretation:

The three relationships (equalities) based on the mole concept for the given elements are to be stated.

Concept introduction:

Molar mass is the sum of the atomic masses of all the atoms present in the chemical formula of any compound. One mole of substance contains $6.02\times {10}^{23}$ atoms or molecules. This number is known as the Avogadro number.

Answer to Problem 2.43E

The three relationships (equalities) based on the mole concept for given element are,

$9.012\text{g}\text{Be}=1\text{mol}\text{Be}$ … (1)

$1\text{mol}\text{Be}=6.02\times {10}^{23}\text{Be}\text{atoms}$ … (2)

$6.02\times {10}^{23}\text{Be}\text{atoms}=9.012\text{g}\text{Be}$ … (3)

Explanation of Solution

The molar mass of beryllium is $9.012\text{g}/\text{mol}$. This is the mass of one mole of beryllium. The relationship between the molar mass and moles is shown below.

$9.012\text{g}\text{Be}=1\text{mol}\text{Be}$ … (1)

The conversion factor corresponding to the given relationship is,

$\frac{9.012\text{g}\text{Be}}{1\text{mol}}$ and $\frac{1\text{mol}}{9.012\text{g}\text{Be}}$

One mole of beryllium contains $6.02\times {10}^{23}$ atoms. The relationship between the number of atoms and moles is shown below.

$1\text{mol}\text{Be}=6.02\times {10}^{23}\text{Be}\text{atoms}$ … (2)

The conversion factor corresponding to the given relationship is,

$\frac{6.02\times {10}^{23}\text{atoms}}{1\text{mol}}$ and $\frac{1\text{mol}}{6.02\times {10}^{23}\text{atoms}}$

From the equalities (1) and (2), the mass of $6.02\times {10}^{23}$ atoms of beryllium is $9.012\text{g}$. The relationship between molar mass and number of atoms is shown below.

$6.02\times {10}^{23}\text{Be}\text{atoms}=9.012\text{g}\text{Be}$ … (3)

The conversion factor corresponding to the given relationship is,

$\frac{6.02\times {10}^{23}\text{atoms}}{9.012\text{g}\text{Be}}$ and $\frac{9.012\text{g}\text{Be}}{6.02\times {10}^{23}\text{atoms}}$

Conclusion

The three relationships (equalities) based on the mole concept for given element are,

$9.012\text{g}\text{Be}=1\text{mol}\text{Be}$ …(1)

$1\text{mol}\text{Be}=6.02\times {10}^{23}\text{Be}\text{atoms}$…(2)

$6.02\times {10}^{23}\text{Be}\text{atoms}=9.012\text{g}\text{Be}$ …(3)

Interpretation Introduction

(b)

Interpretation:

The three relationships (equalities) based on the mole concept for given element are to be stated.

Concept introduction:

Molar mass is the sum of the atomic masses of all the atoms present in the chemical formula of any compound. One mole of substance contains $6.02\times {10}^{23}$ atoms or molecules. This number is known as the Avogadro number.

Answer to Problem 2.43E

The three relationships (equalities) based on the mole concept for given element are,

$207.2\text{g}\text{Pb}=1\text{mol}\text{Pb}$ … (1)

$1\text{mol}\text{Pb}=6.02\times {10}^{23}\text{Pb}\text{atoms}$ … (2)

$6.02\times {10}^{23}\text{Pb}\text{atoms}=207.2\text{g}\text{Pb}$ … (3)

Explanation of Solution

The molar mass of lead is $207.2\text{g}/\text{mol}$. This is the mass of one mole of lead. The relationship between the molar mass and moles is as follows:

$207.2\text{g}\text{Pb}=1\text{mol}\text{Pb}$…(1)

The conversion factor corresponding to the given relationship is,

$\frac{207.2\text{g}\text{Pb}}{1\text{mol}}$ and $\frac{1\text{mol}}{207.2\text{g}\text{Pb}}$

One mole of lead contains $6.02\times {10}^{23}$ atoms. The relationship between the number of atoms and moles is shown below.

$1\text{mol}\text{Pb}=6.02\times {10}^{23}\text{Pb}\text{atoms}$…(2)

The conversion factor corresponding to the given relationship is,

$\frac{6.02\times {10}^{23}\text{atoms}}{1\text{mol}}$ and $\frac{1\text{mol}}{6.02\times {10}^{23}\text{atoms}}$

From the equalities (1) and (2), the mass of $6.02\times {10}^{23}$ atoms of lead is $207.2\text{g}$. The relationship between molar mass and number of atoms is shown below.

$6.02\times {10}^{23}\text{Pb}\text{atoms}=207.2\text{g}\text{Pb}$…(3)

The conversion factor corresponding to the given relationship is,

$\frac{6.02\times {10}^{23}\text{atoms}}{207.2\text{g}\text{Pb}}$ and $\frac{207.2\text{g}\text{Pb}}{6.02\times {10}^{23}\text{atoms}}$

Conclusion

The three relationships (equalities) based on the mole concept for given element are,

$207.2\text{g}\text{Pb}=1\text{mol}\text{Pb}$…(1)

$1\text{mol}\text{Pb}=6.02\times {10}^{23}\text{Pb}\text{atoms}$…(2)

$6.02\times {10}^{23}\text{Pb}\text{atoms}=207.2\text{g}\text{Pb}$…(3)

Interpretation Introduction

(c)

Interpretation:

The three relationships (equalities) based on the mole concept for given element are to be stated.

Concept introduction:

Molar mass is the sum of the atomic masses of all the atoms present in the chemical formula of any compound. One mole of substance contains $6.02\times {10}^{23}$ atoms or molecules. This number is known as the Avogadro number.

Answer to Problem 2.43E

The three relationships (equalities) based on the mole concept for given element are,

$23.00\text{g}\text{Na}=1\text{mol}\text{Na}$…(1)

$1\text{mol}\text{Na}=6.02\times {10}^{23}\text{Na}\text{atoms}$…(2)

$6.02\times {10}^{23}\text{Na}\text{atoms}=23.00\text{g}\text{Na}$…(3)

Explanation of Solution

The molar mass of sodium is $23.00\text{g}/\text{mol}$. This is the mass of one mole of sodium. The relationship between the molar mass and moles is shown below.

$23.00\text{g}\text{Na}=1\text{mol}\text{Na}$…(1)

The conversion factor corresponding to the given relationship is,

$\frac{23.00\text{g}\text{Na}}{1\text{mol}}$ and $\frac{1\text{mol}}{23.00\text{g}\text{Na}}$

One mole of sodium contains $6.02\times {10}^{23}$ atoms. The relationship between the number of atoms and moles is shown below.

$1\text{mol}\text{Na}=6.02\times {10}^{23}\text{Na}\text{atoms}$…(2)

The conversion factor corresponding to the given relationship is,

$\frac{6.02\times {10}^{23}\text{atoms}}{1\text{mol}}$ and $\frac{1\text{mol}}{6.02\times {10}^{23}\text{atoms}}$

From the equalities (1) and (2), the mass of $6.02\times {10}^{23}$ atoms of sodium is $23.00\text{g}$. The relationship between molar mass and number of atoms is shown below.

$6.02\times {10}^{23}\text{Na}\text{atoms}=23.00\text{g}\text{Na}$…(3)

The conversion factor corresponding to the given relationship is,

$\frac{6.02\times {10}^{23}\text{atoms}}{23.00\text{g}\text{Na}}$ and $\frac{23.00\text{g}\text{Na}}{6.02\times {10}^{23}\text{atoms}}$

Conclusion

The three relationships (equalities) based on the mole concept for given element are,

$23.00\text{g}\text{Na}=1\text{mol}\text{Na}$…(1)

$1\text{mol}\text{Na}=6.02\times {10}^{23}\text{Na}\text{atoms}$…(2)

$6.02\times {10}^{23}\text{Na}\text{atoms}=23.00\text{g}\text{Na}$…(3)