Chapter 3, Problem 3.1P

Interpretation Introduction

Interpretation:

The masses of $3\text{ mol}$ of $\text{Al}$ atoms and $\text{2 mol}$ of $\text{Cl}$ atoms in grams are to be calculated.

Concept introduction:

The atomic mass of an element is expressed in $\text{amu}$ which is numerically equivalent to the mass of $\text{1 mol}$ of that element expressed in grams.

The mass of each element in grams can be calculated from the given moles and the molar mass of the element. The road map to calculate the mass of an element in grams is as follows:

The expression to calculate the mass of an element in grams is as follows:

$\text{Mass }\left(\text{g}\right)=\left(\text{amount}\left(\text{mol}\right)\right)\left(\frac{\text{no}\text{. of grams}}{1\text{ mol}}\right)$

Answer to Problem 3.1P

The mass of $3\text{ mol}$ of $\text{Al}$ atoms in grams is $80.94\text{ g}$ and the mass of $\text{2 mol}$ of $\text{Cl}$ atoms in grams is $70.90\text{ g}$.

Explanation of Solution

The atomic mass of $\text{Al}$ is $26.98\text{ amu}$ and the mass of $1\text{ mol}$ of $\text{Al}$ is $26.98\text{ g}$. The atomic mass of $\text{Al}$ is numerically equivalent to the mass of $\text{1 mol}$ of $\text{Al}$ expressed in grams. Therefore, the relation between $\text{amu}$ and $\text{g/mol}$ for $\text{Al}$ atoms is as follows:

$26.98\text{ amu}\equiv 26.98\text{ g/mol}$

The expression to calculate the mass of $\text{Al}$ is as follows:

$\begin{array}{c}\text{Mass of Al}\left(\text{g}\right)=\left(3\text{ mol Al}\right)\left(\frac{26.98\text{ g Al}}{1\text{ mol Al}}\right)\\ =80.94\text{ g Al}\end{array}$

The atomic mass of $\text{Cl}$ is $35.45\text{ amu}$ and the mass of $1\text{ mol}$ of $\text{Cl}$ is $35.45\text{ g}$. The atomic mass of $\text{Cl}$ is numerically equivalent to the mass of $\text{1 mol}$ of $\text{Cl}$ expressed in grams. The relation between $\text{amu}$ and $\text{g/mol}$ for $\text{Cl}$ atoms is as follows:

$35.45\text{ amu}\equiv 35.45\text{ g/mol}$

The expression to calculate the mass of $\text{Cl}$ is as follows:

$\begin{array}{c}\text{Mass of Cl}\left(\text{g}\right)=\left(2\text{ mol Cl}\right)\left(\frac{35.45\text{ g Cl}}{1\text{ mol Cl}}\right)\\ =70.90\text{ g Cl}\end{array}$

Conclusion

The mass of $3\text{ mol}$ of $\text{Al}$ atoms is $80.94\text{ g}$ and the mass of $\text{2 mol}$ of $\text{Cl}$ atoms is $70.90\text{ g}$.