How many atoms and molecules are in a grain of sand?
One can combine the atomic weights of all involved elements to determine the molecular mass (the individual mass of a element can be found in the periodic table). Given for simplicity sand as silicon dioxide (SiO2) at 28.09 + 2 x 16 = 60.09 units of mass we get M(SiO2) * 1 g/mol with 60.09 g/mol. So that is about 60g for one mole of sand.
Now a grain of sand may vary in size and weight so I used the range (smallest, biggest) that classifies a grain (derived in the Article/Essay from Marina Theodoris). This gives use 0,00067 g for the smallest grain (0.06mm Ø) and 0,023 g for the biggest grain (2.1mm Ø) of sand.
0,00067 / 60.09 * 6.022140857×1023 = 6,71465197901481×1018 = 6.714.651.979.014.810.000 molecules of SiO2 in the smallest grain of sand. Given that there are 3 atoms per sand molecule we would have 20.143.955.937.044.400.000 atoms in there.
0,023 / 60.09 * 6.022140857×1023 = 2,3050297838409×1020 = 230.502.978.384.090.000.000 molecules of SiO2 in the biggest grain of sand. Given that there are 3 atoms per sand molecule we would have around 691.508.935.152.271.000.000 atoms in there.
The numbers are so incredibly big that one can’t even imagine them properly. Given an estimate of 1011 stars (much likely even more) in our galaxy one can say there are many more atoms in a small grain of sand then stars in our galaxy (about 200 million times more). Also the progression from the smallest to the biggest grain size isn’t linear as it depends on the volume of the grain sphere. Furthermore this approximation is based on an ideal mathematical sphere. In reality the grain may vary in shape, form and size hence the range from smallest to biggest grain.
The mole is the base unit of amount of substance in the International System of Units (SI). Effective 20 May 2019, the mole is defined as the amount of a chemical substance that contains exactly 6.02214076×1023 (Avogadro constant) constitutive particles, e.g., atoms, molecules, ions or electrons.This definition was adopted in November 2018, revising its old definition based on the number of atoms in 12 grams of carbon-12 (12C) (the isotope of carbon with relative atomic mass 12 Da by definition).
Definition from Wikipedia – Mole (unit)
In chemistry, the molar mass M is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance.
Definition from Wikipedia – Molar mass