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Abstract: Thermoelectric Effect Peltier Seebeck and Thomson
Full page: Thermoelectric Effect Peltier Seebeck and Thomson

Avogadro's number atomic weight and molecular weight

Uri Lachish, guma science

Chemical measures and units

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:

Mw(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 Mw of a molecule, multiplied by the number of moles n, is equal to the total weight W of the molecules:

W = n∙Mw

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 / Mw(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:

Mw(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 / Mw = 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 "Mw"(nails) = 20 gram. The 100 nails that I asked are equal to 100 / 10 = 10 "moles" of nails, so that their weight is 10∙"Mw"(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: http://urila.tripod.com/Thermoelectric_abstract.htm
Full page: http://urila.tripod.com/Thermoelectric.pdf, February 2014.
2. "Osmosis Desalination and Carnot", http://urila.tripod.com/Osmosis_Carnot.htm, December 2012.
3. "Light Scattering", http://urila.tripod.com/scatter.htm, August (2011).
4. "The Sun and the Moon a Riddle in the Sky", http://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", http://urila.tripod.com/evidence.htm, October (2007).
7. "Osmosis and Thermodynamics", http://urila.tripod.com/osmotic.htm, January (2007).
8. "Expansion of an ideal gas", http://urila.tripod.com/expand.htm, December (2002).
9. "Optimizing the Efficiency of Reverse Osmosis Seawater Desalination", http://urila.tripod.com/Seawater.htm, May (2002).
10. "Boltzmann Transport Equation", http://urila.tripod.com/Boltzmann.htm, May (2002).
11. "Energy of Seawater Desalination", http://urila.tripod.com/desalination.htm, April (2000).
12. "Avogadro's number atomic weight and molecular weight", http://urila.tripod.com/mole.htm, April (2000).
13. "Vapor Pressure, Boiling and Freezing Temperatures of a Solution", http://urila.tripod.com/colligative.htm, December (1998).
14. "Osmosis Reverse Osmosis and Osmotic Pressure what they are", http://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).

1. Thermodynamics Research Laboratory, http://www.uic.edu/~mansoori/Thermodynamics.Educational.Sites_html
2. Thermodynamik - Warmelehre, http://www.schulphysik.de/thermodyn.html
3. The Blind Men and the Elephant
4. My Spin on Lunacy
5. Five Weeks in a Balloon
6. The first man I saw
7. "Faster, Faster!"
8. Perfection can't be rushed
9. The man higher up
10. Brains
11. The First-Class Passenger
12. other

Table-1: Atomic numbers and atomic weights (gram / mole) of common elements
 Element Symbol Atomic number Atomic weight Aluminum Al 13 26.982 Antimony Sb 51 121.760 Argon A 18 39.948 Arsenic As 33 74.922 Barium Ba 56 137.327 Beryllium Be 4 9.012 Bismuth Bi 83 208.980 Boron B 5 10.811 Bromine Br 35 79.904 Cadmium Cd 48 112.411 Calcium Ca 20 40.078 Carbon C 6 12.0107 Cesium Cs 55 132.905 Chlorine Cl 17 35.453 Chromium Cr 24 51.996 Cobalt Co 27 58.933 Copper Cu 29 63.546 Fluorine F 9 18.998 Gallium Ga 31 69.723 Germanium Ge 32 72.61 Gold Au 79 196.97 Helium He 2 4.0026 Hydrogen H 1 1.00794 Indium In 49 114.818 Iodine I 53 126.904 Iron Fe 26 55.845 Krypton Kr 36 83.80 Lead Pb 82 207.21 Lithium Li 3 6.941 Magnesium Mg 12 24.305 Manganese Mn 25 54.938 Mercury Hg 80 200.59 Molybdenum Mo 42 95.94 Neon Ne 10 20.1797 Nickel Ni 28 58.693 Nitrogen N 7 14.0067 Osmium Os 76 190.23 Oxygen O 8 15.9994 Palladium Pd 46 106.42 Phosphor P 15 30.974 Platinum Pt 78 195.078 Potassium K 19 39.098 Radium Ra 88 226.025 Radon Rn 86 222.018 Selenium Se 34 78.96 Silicon Si 14 28.086 Silver Ag 47 107.868 Sodium Na 11 22.990 Sulfur S 16 32.066 Tantalum Ta 73 180.948 Tellurium Te 52 127.60 Thallium Tl 81 204.383 Tin Sn 50 118.710 Titanium Ti 22 47.867 Tungsten W 74 183.84 Uranium U 92 238.029 Vanadium V 23 50.941 Xenon Xe 54 131.29 Zinc Zn 30 65.39 Zirconium Zr 40 91.224

Table-2: Molecular weights (gram / mole) of common molecules
 Name Formula Molecular weight Ammonia NH3 17.032 Carbon dioxide CO2 44.0098 Chlorine Cl2 70.906 Ethyl Alcohol C2H5OH 46.0688 Fluorine F2 37.997 Glucose C6H12O6 180.2 Hydrogen H2 2.016 Methane CH4 16.043 Methyl Alcohol CH3OH 32.04 Nitrogen N2 28.013 Oxygen O2 32.00 Ozone O3 47.98 Sucrose C12H22O11 342.3 Table Salt NaCl 58.443 Water H2O 18.015