Calculating Nickel Atoms in a Specific Alloy Composition

When dealing with alloys, understanding the composition by mass percent is a common and useful approach. Consider an alloy that has a density of 8.31 g/cm3 and consists of 56.0% copper, 33.0% nickel, and 11.0% manganese. The question at hand is: how many nickel atoms are present in a block measuring 10.0 cm x 20.0 cm x 42.0 cm?

Determining the Volume of the Block

To start, we first need to determine the volume of the block:

Volume Length × Width × Height

Volume 10.0 cm × 20.0 cm × 42.0 cm 8,400 cm3

Calculating the Mass of the Block

Next, we calculate the mass of the block using the density of the alloy:

Mass Volume × Density

Mass 8,400 cm3 × 8.31 g/cm3 69,804 grams

Calculating the Mass of Nickel in the Block

Now that we know the total mass of the block, we can determine the mass of nickel by using its percentage composition:

Mass of Nickel Mass of Block × Percentage of Nickel

Mass of Nickel 69,804 g × 0.33 23,035.32 grams

Converting Mass to Moles of Nickel

We then convert the mass of nickel to moles by using its molar mass:

Molar Mass of Nickel (Ni) 58.693 g/mol

Moles of Nickel Mass of Nickel ÷ Molar Mass of Nickel

Moles of Nickel 23,035.32 g ÷ 58.693 g/mol 392.47 moles

Converting Moles to Number of Atoms

Finally, we need to find out the number of nickel atoms in the block by using Avogadro's number:

Number of Nickel Atoms Moles of Nickel × Avogadro's Number

Number of Nickel Atoms 392.47 moles × 6.022 × 1023 atoms/mole ≈ 2.363 × 1026 atoms

Conclusion

Therefore, the block described above contains approximately 2.363 × 1026 nickel atoms. This method is a practical application of density and mass percent composition in the context of alloy composition, providing insights into the atomic makeup of materials.

Keywords: density, mass percent composition, molar mass