Avogadro's number atomic weight and molecular weight

The starting point is Avogadro's number, denoted N₀, and equal to:

N₀ = 6.022∙10²³

Why this number? It has been selected in order that, if N₀ carbon atoms are put on a balance, then the balance will show a weight of 12 grams (*see note). How to count N₀ atoms? Not a trivial experimental challenge.

The atomic weight of a chemical element is the weight of N₀ atoms of it. The atomic weights of the elements are included in the periodic table of the elements.

The molecular weight of a molecule is the weight of N₀ such molecules. The molecular weight of a molecule is equal to the sum of the atomic weights of its constituting atoms.

The weight in grams of a single atom is very small. It is only a matter of convenience to give the weight of N₀ atoms, instead of a single atom, in order to have a convenient measureable value. There is nothing more than that. The weight of a single atom can always be calculated back from the atomic weight by dividing by Avogadro's number. It is similarly true for molecules.

The molecular weight is calculated from the molecule's chemical formula and the atomic weights. For example, table salt is sodium chloride (NaCl). The atomic weight of sodium, given in the periodic table (see table below), is 22.990 gram, and of chlorine is 35.453 gram. The molecular weight of sodium chloride is, therefore:

M_w(NaCl) = 22.990 + 35.453 = 58.443 gram.

One mole is a quantity of N₀ atoms or molecules. Therefore, the atomic weight is the weight of one mole of atoms, and the molecular weight is the weight of one mole of molecules.

The molecular weight M_w of a molecule, multiplied by the number of moles n, is equal to the total weight W of the molecules:

W = n∙M_w

For example, the weight of 3.4 moles of sodium chloride is 3.4∙58.44 = 198.7 gram. Similarly, the number of moles is calculated from a given weight. For example, W = 33 grams of sodium chloride contain

n = W / M_w(NaCl) = 33 / 58.44 = 0.565 moles.

When a quantity of atoms or molecules is given in moles, then their absolute overall number can be calculated by multiplying by Avogadro's number N₀. It is never done, but good to know.

Another example: The formula of the water molecule is H₂O, that is, two atoms of Hydrogen and one of Oxygen. The atomic weight of Hydrogen, given in the periodic table of the elements, is 1.00794 gram, and the atomic weight of Oxygen is 15.9994 gram. Therefore, the molecular weight of water will be:

M_w(H₂O) = 2 ∙1.00794 + 15.9994 = 18.015 gram

How many moles of of water are there in one liter, about 1000 gram?

n = W / M_w = 1000 / 18.015 = 55.509 moles

and how many water molecules are there in one liter?

n ∙ N₀ =55.509 ∙ 6.022∙10²³ = 3.34 ∙10²⁵ molecules

Molar concentration of a solution is the number of moles dissolved in one liter of the solution. For example, the molar concentration of 33 grams sodium chloride in one liter of water, as calculated above, is 0.565 mol / liter, or 0.565 M, where M stands for mol / liter. When a salt molecule dissolves in water it disintegrates into two ions. Therefore, the ionic concentration is twice as that, 1.128 M. The salt concentration in seawater is approximately equal to this value. The salt concentration differs from sea to sea.

*note: There is nothing special about Avogadro's number and any other number could do. However, this selection is convenient since the numerical value of the atomic weight of a chemical isotope is (nearly) equal to its number of nucleons (protons and neutrons). Thus, the atomic weight of hydrogen with one proton is (nearly) one gram, and of carbon, with six protons and six neutrons, is twelve grams. The atomic weight of a chemical element is usually a non-integral number because it relates to its natural abundance of isotopes.

on the net: April 2000, updated February 2006.

Personal note:
Long time ago, when I was a boy, I looked for nails. There were no home-centers and the like, so I went to buy them in a small neighborhood shop. An old man with grim face stood behind a desk with scales on it, and I came in and asked for hundred nails. The man took a big cardboard box full of nails from a shelf behind him, counted ten nails on one scale and balanced it with a weight on the other scale. Suppose that the weight was twenty grams. He then replaced it with a two hundred grams weight and added more nails on the other side until the scales balanced again, and I got my hundred nails. Long time after that I realized that it was my first lesson of atomic chemistry, since this Avogadro's business is just the same thing.

Why is that?
In this example "Avogadro's number" = 10. Since the man did not know the "molecular weight" of nails, he measured it by putting one "mole" of nails on the balance. So that "M_w"(nails) = 20 gram. The 100 nails that I asked are equal to 100 / 10 = 10 "moles" of nails, so that their weight is 10∙"M_w"(nails) = 200 gram. So the man weighed 200 gram of nails.

See: Osmosis Reverse Osmosis and Osmotic Pressure what they are.

By the author:

1. "Thermoelectric Effects Peltier Seebeck and Thomson",
   Abstract: https://urila.tripod.com/Thermoelectric_abstract.htm
   Full page: https://urila.tripod.com/Thermoelectric.pdf, February 2014.
2. "Osmosis Desalination and Carnot", https://urila.tripod.com/Osmosis_Carnot.htm, December 2012.
3. "Light Scattering", https://urila.tripod.com/scatter.htm, August (2011).
4. "The Sun and the Moon a Riddle in the Sky", https://urila.tripod.com/moon.htm, July (2011).
5. "Osmosis and thermodynamics", American Journal of Physics, Vol 75 (11), pp. 997-998, November (2007).
6. "van't Hoff's Evidence", https://urila.tripod.com/evidence.htm, October (2007).
7. "Osmosis and Thermodynamics", https://urila.tripod.com/osmotic.htm, January (2007).
8. "Expansion of an ideal gas", https://urila.tripod.com/expand.htm, December (2002).
9. "Optimizing the Efficiency of Reverse Osmosis Seawater Desalination", https://urila.tripod.com/Seawater.htm, May (2002).
10. "Boltzmann Transport Equation", https://urila.tripod.com/Boltzmann.htm, May (2002).
11. "Energy of Seawater Desalination", https://urila.tripod.com/desalination.htm, April (2000).
12. "Avogadro's number atomic weight and molecular weight", https://urila.tripod.com/mole.htm, April (2000).
13. "Vapor Pressure, Boiling and Freezing Temperatures of a Solution", https://urila.tripod.com/colligative.htm, December (1998).
14. "Osmosis Reverse Osmosis and Osmotic Pressure what they are", https://urila.tripod.com/index.htm, February (1998).
15. "Calculation of linear coefficients in irreversible processes by kinetic arguments", American Journal of Physics, Vol 46 (11), pp. 1163-1164, November (1978).
16. "Derivation of some basic properties of ideal gases and solutions from processes of elastic collisions", Journal of Chemical Education, Vol 55 (6), pp. 369-371, June (1978).

Links: