Question

What amount of iron is contained in the bar and how many atoms of iron?
Iron bar:
length: 10.5 cm
square ends: 1.25 cm
Density: 7.874 g/cm^3

Answer 1

First figure out the volume.\[
Mass = Volume \times Density
\]

Answer 2

Then figure out the mass of an iron bar and divide the total mass by that number.

Answer 3

figure out the mass of an iron atom^

Answer 4

you mean multiply the volume by the given density to obtain the mass

Answer 5

Yeah

Answer 6

Then divide the total mass by the mass of an iron atom to find the number of atoms.

Answer 7

that process would give us the number of moles in the bar, not the number of atoms.
the number of atoms can be obtained by multiplying the number of moles by the Avogadro's constant 6.022 x 10^23

Answer 8

agree or disagree?

Answer 9

Let us do some dimensional analysis.
\[D = \frac{ m }{ v }\]
First, figure out the volume of the bar. Our dimensions are 10.5 cm long and 1.25 cm square ends.
\[v=10.5 cm \times 1.25cm \times 1.25cm=16.4 cm^{3}\]

Given the density \[\frac{ 7.874g }{1 cm^3 }\] we can solve for our mass.
\[m=v \times D\] \[m=16.4cm^3 \times \frac{7.874g }{ 1cm^3 }=129g\]
And in order for us to find out how many atoms in 129g of bar, we need to find the number of moles in it. Mole is defined such that a sample of a natural element with a mass equal to the element’s atomic mass expressed in grams contains 1 mole of atoms. Using the periodic table as our reference \[^{55.845}_{26}Fe\]
A mole of Fe has a mass of 55.845g
We have 129 g of Fe, therefore it has a mole of
\[129g Fe \times \frac{ 1 molFe }{ 55.845gFe }=2.31molFe\]
One mole of something consists of 6.022 x 10^23 units of that substance. Just as a dozen eggs is 12 eggs, a mole of eggs is 6.022 x10^23 eggs.
Atoms of Fe
\[2.31molFe \times \frac{ 6.22\times10^{23}atomsFe }{ 1 mol Fe }= 1.39 \times 10^{24}atoms Fe\]

Answer 10

Hmm... I have read about this in dimensional analysis, but I forgot!

Answer 11

I couldn't remember it. I think there was this carbon isotope on which the mole is based. :-\

Answer 12

Dimensional analysis is just your regular math with conversions and with proper units attached. Yes, a mole is based on the average mass, which is the sum of the fractional abundance of isotopes of Carbon.

Answer 13

regular arithmetic, I should say :)

Answer 14

Guys, look at this book. It's really freaky in a good way.

http://libgen.org/get?nametype=orig&md5=A1F255962D377ABE7BB5D37A191ECB38

Answer 15

could you make that a proper attachment so it doesn't download automatically?

Answer 16

Sure.

Answer 17

http://libgen.org/book/index.php?md5=A1F255962D377ABE7BB5D37A191ECB38

Answer 18

\(\TeX\) is not working for me. :-\

Answer 19

it sure is taking a long time for a very small file to download. I am going to terminate it for possible malware content

Answer 20

No malware at all.

Answer 21

http://libgen.org doesn't have any malware on any of their books, so you can trust 'em.

Answer 22

@ParthKohli I realized it is the website that is slow.
Have you read the whole content or even the first few pages of that book?
Knowing your level of geekery (no pun intended) apply the knowledge of dimensional analysis to turn a rabbit into a frog.

Answer 23

lol, yes. I have read the dimensional analysis chapter but that was about a month ago.

Answer 24

And a little bit of the second one.

Answer 25

turn a rabbit into a frog using dimensional analysis technique

Answer 26

I don't remember anything. >_<

Answer 27

Seriously, it may look like an excuse, but I don't remember anything... just a little.

Answer 28

\[Rabbit \times \frac{ Frog }{ Rabbit }=Frog\]