Calculating the Number of Aluminum Atoms in a Can

Given a 15.8-gram aluminum can, the question is how many aluminum atoms are contained within it. To answer this, we need to employ some basic principles of chemistry, specifically the concepts of molar mass and Avogadro's number.

In this article, we'll explain the step-by-step process to determine the number of aluminum atoms in the can, ensuring a clear understanding of the underlying mathematical and chemical principles.

Step-by-Step Solution

Determining the Molar Mass of Aluminum

The molar mass of aluminum (Al) is approximately 26.98 grams per mole. This value represents the mass of one mole of aluminum atoms.

Calculating the Number of Moles of Aluminum in the Can

The first step in calculating the number of aluminum atoms is to determine the number of moles of aluminum in the can. We do this by dividing the mass of the aluminum can by its molar mass.

Using the formula:

[ n frac{mass}{molar mass} ]

We input the given mass and molar mass:

[ n frac{15.8 , text{g}}{26.98 , text{g/mol}} 0.5856 , text{moles} ]

Using Avogadro's Number to Find the Number of Atoms

Avogadro's number is approximately (6.022 times 10^{23}) atoms per mole. This number represents the number of atoms in one mole of any substance. By multiplying the number of moles by Avogadro's number, we can find the total number of aluminum atoms in the can.

Using the formula:

[ text{Number of atoms} text{Number of moles} times text{Avogadro's number} ]

We calculate:

[ text{Number of atoms} 0.5856 , text{moles} times 6.022 times 10^{23} , text{atoms/mole} approx 3.522 times 10^{23} , text{atoms} ]

Conclusion

The closest answer from the provided options is (3.53 times 10^{23}) atoms, which matches our calculated result. This demonstrates the importance of understanding molar mass and Avogadro's number in chemistry and their practical applications.

Additional Insights

Key Concepts: Using molar mass to convert between mass and moles, and Avogadro's number to convert between moles and atoms.

Related Keywords: aluminum atoms, atomic mass, Avogadro's number, molar mass

Further Reading: Explore more about the principles of stoichiometry, molarity, and chemical reactions involving aluminum. Understanding these concepts will help deepen your knowledge of chemistry and its applications in various fields.