Particles in Sand Grain
Name: Carol B.
Date: Monday, January 20, 2003
About how many particles (atoms or ions) would be in an
average grain of sand?
Assuming an average grain of sand is about 1 cubic millimetre in volume and
it is composed of silicon dioxide (SiO2, molar mass = 60 g / mol) with a
density of about 2.4 g / cm^3:
A 1mm^3 grain would have a mass of (2.4 g / cm^3) / ( 1000 cubes / cm^3) =
2.4 x 10^-3 grams
That mass per grain divided by 60 g / mol = 4 x 10^-5 moles
Then (4 x 10^-5 moles)(6.02 X 10 ^23 formula units per mole ) = 2.4 x 10^19
units of SiO2 per sand grain.
Since there are 3 atoms in one SiO2 unit, there would be (3 atoms per
unit)(2.4 x 10^19 units) =
7.2 x 10^19 atoms present in one grain of sand.
If the grain of sand is a cube 0.1 mm on a side that is 0.001 mm^3. Assume
a density of 2 gm/mm^3 (just about any number will do) that is 0.002 gm. If
the sand is SiO2 the molecular weight is 60 gm/mole or is
0.002/60 = 3.3x10^-5 moles. There are 6x10^23 units / mole, so the number of
SiO2 units is about 2x10^19. Each SiO2 unit contains 3 atoms/ions so there
are about 6x10^19 atoms/ions.
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Update: June 2012