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How many atoms are there in a common sheet of paper?

The paper is A4, i.e. $210 \, \mathrm{mm} {\times} 297 \, \mathrm{mm}$ $\left(8.27 \, \mathrm{in} {\times} 11.7 \, \mathrm{in}\right).$

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  • $\begingroup$ Hi one way to think about this is to use the idea, very roughly speaking, that there are as many atoms inside an apple as there are apples that would fit inside the earth, so you could work from there, compare the volume of an apple to that of the earth see en.wikipedia.org/wiki/Atom then take it from there.. $\endgroup$
    – user74893
    Apr 6, 2015 at 19:04
  • $\begingroup$ Oh, I corrected a flaw in my answer, so now it is right. The answer is much bigger. $\endgroup$
    – Jimmy360
    Apr 6, 2015 at 19:36

2 Answers 2

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You can estimate number of atoms by finding out average molar mass of paper and mass of one sheet of paper.

If we assume that paper is mainly composed of cellulose, we can neglect other components as insignificant. Then we find out that cellulose's molar mass is approximately $162.14 \, \mathrm{g}/\mathrm{mol}$. Mass of one sheet of paper is about $4.5 \, \mathrm{g}$.

Doing the math you get that one sheet of paper is approximately $0.02775 \, \mathrm{mol}$. With Avogadro's constant, we can calculate that there are$$ 0.02775 \, \mathrm{mol} \times 6.02214 \cdot {10}^{23} \, \frac{\mathrm{molecule}}{\mathrm{mol}} ~=~ 1.67 \cdot {10}^{22} \, \mathrm{molecule}.$$

As in one cellulose molecule there are 21 atoms, the number of atoms is $3.509 \cdot {10}^{23}$ atoms.

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  • $\begingroup$ But that gives you the number of molecules... you need to know how many atoms per molecule... this is why your answer differs from zeldredge $\endgroup$
    – hft
    Apr 6, 2015 at 19:52
  • $\begingroup$ Cellulose has $C_6 H_{10} O_5$, says Wiki. So this calculation just needs to be multiplied by 21 to give you the atomic quantity. $\endgroup$
    – zeldredge
    Apr 6, 2015 at 19:55
  • $\begingroup$ True, i forgot that. Thanks for pointing out. I'll edit. $\endgroup$
    – Vaimsus
    Apr 6, 2015 at 20:02
  • $\begingroup$ Note that 162.14 g/mol is the molar mass of the monomer, not of the actual cellulose molecules, and correspondingly, $C_6 H_{10} O_5$ is the molecular formula of the glucose monomers. Cellulose molecules are polymeric chains composed out of several glucose units, of which both the molecular mass and the molecular formula can vary depending on the number of monomers. The answer now given turns out to be correct, however. $\endgroup$
    – Stijn B.
    Nov 14, 2018 at 16:25
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So, a piece of paper is made of wood, and wood is some organic substance. I don't know what the chemical formula is, but let's say it's mostly carbon. In fact, let's just pretend it's all carbon, since you only want order of magnitude. Wikipedia tells me a piece of A4 paper weighs about five grams, and then I divide by the atomic mass of carbon and get $\approx 10^{23}$ atoms. This is on the order of Avogadro's number, which is generally what you get for small but macroscopic numbers of atoms.

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  • $\begingroup$ This answer is better, so I tied to delete mine, but you cannot delete an accepted answer. $\endgroup$
    – Jimmy360
    Apr 6, 2015 at 19:39

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