How big is a mole? Daniel Dulek @ TED-Ed

Video: https://www.youtube.com/watch?v=TEl4jeETVmg

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 the unit of measurement for amount of substance in the International System of Units (SI). A mole of a substance or a mole of particles is defined as containing exactly 6.02214076×1023 particles, which may be atoms, molecules, ions, or electrons. In short, 1 mol contains 6.02214076×1023 of the specified particles.The current definition was adopted in November 2018 as one of the seven SI base units, revising the previous definition that specified one mole as the amount of substance in 12 grams of carbon-12 (12C), an isotope of carbon. The number 6.02214076×1023 (the Avogadro number) was chosen so that the mass of one mole of a chemical compound in grams is numerically equal, for most practical purposes, to the average mass of one molecule of the compound in daltons. Thus, for example, one mole of water contains 6.02214076×1023 molecules, whose total mass is about 18.015 grams – and the mean mass of one molecule of water is about 18.015 daltons. The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2H2 + O2 → 2H2O can be interpreted to mean that for each...
Definition from Wikipedia – Mole (unit)

Molar mass

In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance in that sample, measured in moles. 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 weight is very commonly used as a synonym of molar mass, particularly for molecular compounds; however, the most authoritative sources define it differently (see molecular mass). 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 substance, that does not depend on the size of the sample. In the International System of Units (SI), the base unit of molar mass is kg/mol. However,...
Definition from Wikipedia – Molar mass

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