# Illustrating moles with sand grains, Are there more moles of SiO2 in a grain than moles of sand on the earth

I have been trying to understand the scale of atoms, thinking about sand grains as an example.

With approximately $$7.5\times10^{18}$$ grains of sand on the earth that is $$1.25\times10^{-5}$$ moles of sand grains. Source

I've found that a beach sand has approximate density $$2.5\times10^{3}$$ grams/litre or 2.5g/cm$$^3$$. Assuming a quartz grain of diameter 0.05cm, so volume of approx $$5\times10^{-4}cm^3$$ and mass of approx 0.001g. Source

With moelcular mass 60, then there are $$2.2\times10^{-5}$$ moles of $$\ce{SiO2}$$ per grain.

This surprised me. Are there really more moles of $$\ce{SiO2}$$ in a grain of sand than moles of sand on the Earth? And is there any verfication of this by a more serious study?

• Actually, I do mean moles I think here. – EdL Aug 3 '20 at 10:46
• This site reports heavier sand grains, averaging 0.0044 grams. So by that measure the SiO2 entities win by a wider margin. Lots of atoms fit into a little space. – Oscar Lanzi Aug 3 '20 at 10:56
• Your question should be: Are there really more moles of $\ce{SiO2}$ in a grain of sand than amount of sand grains on the Earth (in mols)? Seemingly, yes. Similar to number of molecules in 10 drops of water, which is even bigger than that. – Mathew Mahindaratne Aug 3 '20 at 11:13
• what-if.xkcd.com/83 – Karl Aug 3 '20 at 11:25
• What "more serious" study do you want? The math is correct, the assumption for the sand grain weight makes sense, and if you doubt that number for the amount of sand on earth, I fear you are in the wrong SE. ;-) – Karl Aug 3 '20 at 11:39