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.
Smallest grain
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.
Biggest grain
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.
Conclusion
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.
Mole (unit)
The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for amount of substance, a quantity proportional to the number of elementary entities of a substance. One mole contains exactly 6.02214076×1023 elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, or other particles. The number of particles in a mole is the Avogadro number (symbol N0) and the numerical value of the Avogadro constant (symbol NA) expressed in mol-1. The value was chosen based on the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12 grams of 12C, which made the mass of a mole of a compound expressed in grams numerically equal to the average molecular mass of the compound expressed in daltons. With the 2019 redefinition of the SI base units, the numerical equivalence is now only approximate but may be assumed for all practical purposes.
The mole is widely used in chemistry as a convenient way to express amounts of reactants and amounts of products of chemical reactions. For example, the chemical equation 2 H2 + O2 → 2 H2O can be interpreted to...
Definition from Wikipedia – Mole (unit)
Molar mass
In chemistry, the molar mass (M) of a chemical compound is defined as the ratio between the mass and the amount of substance (measured in moles) of any sample of said compound. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.
The molecular mass and formula mass are commonly used as a synonym of molar mass, particularly for molecular compounds; however, the most authoritative sources define it differently. The difference is that molecular mass is the mass of one specific particle or molecule, while the molar mass is an average over many particles or molecules.
The formula weight is a synonym of molar mass that is frequently used for non-molecular compounds, such as ionic salts.
The molar mass is an intensive property of the...
Definition from Wikipedia – Molar mass