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


Avogadro's number atomic 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 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).

Links:

  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