An iron wire (density=7.86g/cm^3) has a diameter of 0.0518cm. How many atoms of iron are in a 38.3cm length of iron wire? The volume of a cylinder is pi*r^2l where r=radius and l=length. ???????

Question

matt101 · Answer

We want to find how many atoms of iron there are. We can find atoms if we know moles. We can find moles if we know mass (and molar mass). We're given density, and we're given a way to find volume, so we can find the mass using this information.

You're given the equation to find the volume of a cylinder already, so let's just sub in our values to find the volume. The radius is half the diameter, or 0.0259 cm.

$$V= \pi (0.0259)^2(38.3)=0.081$$
Now we can find the mass of the wire, since density = mass / volume:

$$7.86=m/0.081 \rightarrow m=0.637$$
The molar mass of an iron atom is about 56 g/mol. We have the mass, so we can find moles:

$$n=0.637/56=0.0114$$
Finally we can find the number of atoms! We just need to multiply the number of moles by Avogadro's number:

$$n_{atoms}=0.0114 \times 6.02 \times 10^{23}=6.86 \times 10^{21}$$
If you have any questions about any of the steps please feel free to ask!