Chapter 3, Problem 1PE

How many moles of aluminum are there in a 3.47 gram sheet of aluminum foil used to wrap your sandwich for lunch today? (Hint: Recall the tool that relates the mass of an element to moles of that element.)

Interpretation Introduction

Interpretation:

The number of moles of aluminum present in $3.47\text{ g}$ of aluminum foil is to be calculated.

Concept Introduction:

One mole of an element is equal to the atomic mass of the element in grams.

The moles of an element are calculated by using the conversion factor as follows:

$\frac{1\text{ mol of element}}{\text{Atomic mass of element in g }}$

Answer to Problem 1PE

Solution: $0.129\text{ mol}$

Explanation of Solution

Given information: Mass of $\text{Al}$ is $3.47\text{ g}$.

The mass of $\text{1 mol}$ of atoms is equal to its atomic mass. For $\text{Al}$, it is expressed as follows:

$1\text{ mol Al}=\text{26}\text{.98 g Al}$

The conversion factor used to convert the mass of $\text{Al}$ into its moles is $\frac{1\text{ mol Al}}{\text{26}\text{.98 g Al}}$.

Multiply the conversion factors with the given mass of $\text{Al}$ and cancel the units to get the moles of $\text{Al}$ as follows:

$\left(3.47\cancel{\text{g Al}}\times \frac{1\text{ mol Al}}{\text{26}\text{.98 }\cancel{\text{g Al}}}\right)=0.129\text{ mol Al}$

Conclusion

The number of moles of aluminum present in $3.47\text{ g}$ of aluminum foil is $0.129\text{ mol}$.