Sunday, September 20, 2015

everyday life - How many atoms are in a piece of paper?


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


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



Answer



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$$ 0.02775 \, \mathrm{mol} \times 6.02214 \cdot {10}^{23} \, \frac{\mathrm{molecule}}{\mathrm{mol}} ~=~ 1.07 \cdot {10}^{22} \, \mathrm{molecule}.$$


As in one cellulose molecule there are 21 atoms, the number of atoms is $2.247 \cdot {10}^{23}$ atoms.


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