Search the World of Chemistry

×

Atomic Weight

09th Jul 2019 @ 20 min read

Physical Chemistry

The atomic weight (also known as relative atomic mass) is a quantity used to express the average weight of an atom. Atoms consist of electrons, protons, and neutrons. Protons and neutrons are mainly responsible for the mass of an atom. For a given element, the proton number (more commonly known as the atomic number) is fixed, but the neutron number can vary. Such elements are called isotopes. Because of this variance in the neutron number, an atom of the same element can have a different atomic mass.

Consider an example of chlorine, which has two naturally-occurring isotopes: 35Cl and 37Cl. The atomic mass of these isotopes is 34.969 u and 36.966 u respectively. The dilemma here is which atomic mass to consider. To solve this problem and have better accuracy in calculations, we average out atomic masses. This average atomic mass is called the atomic weight.

isotopes of chlorine
Figure 1: Chlorine has two naturally-occurring isotopes: 35Cl, 75.76 %; 37Cl, 24.24 %. The weighted average of their atomic masses gives the atomic weight of chlorine.

Definition of Atomic Weight

The Atomic weight is defined as the average atomic mass of isotopes of an element in a given sample. It is the weighted average atomic mass calculated using the relative abundance of isotopes of an element. The atomic weight is also known as the relative atomic mass.

Notation

The atomic weight is denoted by the symbol Ar.

Unit

Unlike the atomic mass, the atomic weight does not have any unit. It is a dimensionless quantity.

Formula

The formula of atomic weight can be formulated based on the above definition.

A_\text{r} =\frac{\sum p_im_i}{1\,\text{u}}

where pi is the percentage or relative abundance of an isotope i of atomic mass mi.

The numerator in the above formula gives the average atomic mass, which has a unit of the dalton or the unified atomic mass (u). In order to make the result dimensionless we divide it by 1 u.

1 u is also defined as the one-twelfth atomic mass of carbon-12, 1 u = 112 m(12C). So, we can also define the atomic weight in terms of carbon-12 as the ratio of the average atomic mass to the one-twelfth atomic mass of carbon-12.

A_\text{r} =\frac{\sum p_im_i}{\frac{1}{12}m_{(^{12}\text{C})}}

Standard Atomic Weight

When the atomic weight of an element is calculated using the relative abundance based on the Earth, we called it the standard atomic weight Ar, std Thus, the standard atomic weight considers naturally occurring isotopes. It is more specific than the atomic weight. The values of the standard atomic weight are published and maintained by the Commission on Isotopic Abundances and Atomic Weights (CIAAW), which is a committee of the IUPAC.

Atomic Weight and Atomic Mass

The atomic weight and the atomic mass are often confused as the same quantity, but they are different. The notion of the atomic weight was discovered prior to the atomic mass. In fact, John Dalton calculated atomic weights of different elements using hydrogen, which is the lightest element, as the reference standard, not atomic masses. The atomic mass came to known with the discovery of isotopes. It was English scientist Francis Aston who accidentally discovered the existence of isotopes. The table below helps to distinguish the differences between both.

Table 1: Comparison between Atomic Weight and Atomic Mass
Atomic WeightAtomic Mass
The atomic weight is weighted average atomic mass of isotopes.The atomic mass is the mass of an atom of an element. It does not account isotopes.
It is a dimensionless quantity.The dalton or the unified mass unit (u) or the atomic mass unit (amu) is the unit used to express the atomic mass.
The atomic weight is more practical and often used by chemists.It is used when we are dealing with an isotopic atom. It is more likely used by physicists.
The atomic weight is estimated from the atomic mass of isotopes of an element.It is determined from the atomic number and the mass number. It is the sum of the mass of electrons, protons, and neutrons present in an atom.
The atomic weight depends on the relative abundance of isotopes of an element in a given sample. So, it can vary from sample to sample.The atomic mass of an isotopic atom is unique. It does not change from sample to sample.
It is usually expressed in fewer decimal figures.It is mentioned in large significant figures.

When we deal with elements which are mono-isotopic i.e., have only one isotope, the atomic mass and the atomic weight are the same. The difference in the atomic mass and the atomic weight increases when there is a large variance in atomic masses of isotopes. The difference also depends on the relative abundance of isotopes.

Note: The values mention in the periodic table are atomic weights, not atomic masses.

uranium ore enriched uranium-235
Figure 2: The natural uranium ore (on the left) consists of isotopes 234U, 0.005 %; 235U, 0.720 %; and 238U, 99.274 % having the atomic weight of 238.028. While enriched uranium 235U (on the right) have the atomic mass of 235.043 929 9(20) u.
[Image Source: Stanford University]

Atomic Weight and Atomic Number

Russian chemist Dmitri Mendeleev used the atomic weight to form the raw version of the periodic table. But the atomic weight was found inconsistent to define an element. Later, it was replaced by the atomic number, which uniquely defines an element. Elements in the modern periodic table are arranged with increasing order of the atomic number. The below graph shows the trend of the atomic weight to the atomic number.

Graph of Atomic Number vs Atomic Weight
Figure 3: Graph of Atomic Number vs Atomic Weight (The red line in the figure is plotted for twice the atomic number and the blue is for the atomic weight.)

As we can see from the above graph, initially for lighter elements, the atomic weight is almost twice the atomic number. For heavier elements, as the atomic number increases, the atomic weight exceeds twice the atomic number. This divergence in the graph is due to an increase in the neutron number. For heavier elements, the number of neutrons in the nucleus is more than the number of protons which increases the mass of an atom.

We can also notice from the above graph the atomic weight does not always increases with rise in the atomic number. In between there are small dips in the atomic weight. Examples are 18Ar, 39.948 and 19K, 39.098; 27Co, 58.933 and 28Ni, 58.693; 52Te, 127.6 and 53I, 126.904.

Uncertainties in Atomic Weight

There are always uncertainties in the values reported by the CIAAW. They are discussed below.

igneous rock sedimentary rock
Figure 4: Igneous Rock (on the left) and Sedimentary Rock (on the right)
[Image Source: Metropolitan Community College Library1 2 ]

Formats of Atomic Weight

The atomic weight is reported in many formats based on the requirement. The below mentions some of the common formats.

  1. Abridged: The abridged format published by the CIAAW. It mentions the atomic weight in five significant figures. For example, Ar, abridged of 10Ne is 20.180.
  2. Interval: When the average atomic mass of an element vary significantly from different sources, we preferably use interval to mention the atomic weight. For example, Ar of 5B is [10.806, 10.821].
  3. Conventional: The conventional format is commonly used format. The values are approximated to fewer decimal points. For example, Ar, conv of 5B is 10.81.
  4. Standard: The standard format is more precise with mentioning of uncertainty. For example, Ar, std of 2He is 4.002 602(2).

Molecular Weight

The molecular weight is the weight of a molecule. It can be calculated by adding the atomic weights of each element in the molecule. The molecular weight of any molecule can be determined by knowing its molecular formula and atomic weights of its elements. It is synonymous with the relative molar mass. Consider an example of methane, which has the molecular formula CH4. So, we can calculate the molecular weight of methane as:

\text{Mol.Wt.} &=A_{\text{r}(\text{C})}+4 A_{\text{r}(\text{H})} \\ &=12.010\,7+4\times 1.007\,9 \\ &=16.042\,3

To Calculate Atomic Weight

The atomic weight of any element can be calculated by knowing the individual atomic mass and the relative abundance of isotopes.

Example 1: To Calculate Atomic Weight of Hydrogen

Hydrogen has three naturally occurring isotopes. The data of the isotopes is mentioned in the below table.

Table 2: Isotopes of Hydrogen with Relative Abundance
IsotopeAtomic Mass (u)Relative Abundance (%)
Hydrogen (1H)1.007 82599.98
Deuterium (2H)2.014 1020.02
Tritium (3H)3.016 049trace

Since tritium presence in very small, we can simply ignore it. Thus, the atomic weight accurate up to three decimal figures is calculates as follows:

A_\text{r} &=\frac{\sum p_im_i}{1\,\text{u}} \\ &=\frac{99.98\,\% \times 1.007\,825+0.02\,\% \times 2.014\,102}{1\,\text{u}} \\ &=1.008

Example 2: To Calculate Atomic Weight of Carbon

Carbon has around 15 known isotopes of which only two are stable. The data of these two isotopes is mentioned in the below table.

Table 3: Isotopes of Carbon with Relative Abundance
IsotopeAtomic Mass (u)Relative Abundance (%)
Carbon-12 (12C)1298.9
Carbon-13 (13C)13.003 3551.1

The atomic mass of carbon-12 is exactly 12 u. The atomic weight accurate up to three decimal figures is calculates as follows:

A_\text{r} &=\frac{\sum p_im_i}{1\,\text{u}} \\ &=\frac{98.9\,\% \times 12 + 1.1\,\% \times 13.003 \,355}{1\,\text{u}} \\ &=12.011

Example 3: To Calculate Atomic Weight of Oxygen

Oxygen has three naturally-occurring isotopes. The data of the isotopes is mentioned in the below table.

Table 4: Isotopes of Oxygen with Relative Abundance
IsotopeAtomic Mass (u)Relative Abundance (%)
Oxygen-16 (16O)15.994 91599.76
Oxygen-17 (17O)16.999 1320.04
Oxygen-18 (18O)17.999 1590.20

Since tritium presence in very small, we can simply ignore it. Thus, the atomic weight accurate up to three decimal figures is calculates as follows:

A_\text{r} &=\frac{\sum p_im_i}{1\,\text{u}} \\ &=\frac{99.76\,\% \times 15.994 \,915+0.04\,\% \times 16.999 \,132+0.20\,\% \times 17.999 \,159}{1\,\text{u}} \\ &=15.999

Example 4: To Calculate Atomic Weight of Zinc

Zinc has five stable isotopes. The data of the isotopes is mentioned in the below table.

Table 5: Isotopes of Zinc with Relative Abundance
IsotopeAtomic Mass (u)Relative Abundance (%)
Zinc-64 (16Zn)63.929 14249.17
Zinc-66 (17Zn)65.926 03327.73
Zinc-67 (18Zn)66.927 1274.04
Zinc-68 (18Zn)67.924 84418.45
Zinc-70 (18Zn)69.925 3190.61

Since tritium presence in very small, we can simply ignore it. Thus, the atomic weight accurate up to three decimal figures is calculates as follows:

\,A_\text{r} &=\frac{\sum p_i m_i}{1\,\text{u}} \\ &=\frac{\splitfrac{49.17\,\% \times 63.929 \,142+27.73\,\% \times 65.926 \,033+4.04\,\% \times 66.927 \,127}{+18.45\,\% \times 67.924 \,844+0.61\,\% \times 69.925 \,319}}{1\,\text{u}} \\ &=65.378

List of Elements by Atomic Weight

The table below lists the atomic weights of all 118 elements with their atomic numbers.

Table 6: List of Elements by Atomic Weight

Atomic Number

Element

Symbol

Atomic Weight

1

Hydrogen

H

1.008

2

Helium

He

4.002 602

3

Lithium

Li

6.94

4

Beryllium

Be

9.012 183 1

5

Boron

B

10.81

6

Carbon

C

12.011

7

Nitrogen

N

14.007

8

Oxygen

O

15.999

9

Fluorine

F

18.998 403 16

10

Neon

Ne

20.179 7

11

Sodium

Na

22.989 769 28

12

Magnesium

Mg

24.305

13

Aluminium

Al

26.981 538 4

14

Silicon

Si

28.085

15

Phosphorus

P

30.973 762

16

Sulphur

S

32.06

17

Chlorine

Cl

35.45

18

Argon

Ar

39.948

19

Potassium

K

39.098 3

20

Calcium

Ca

40.078

21

Scandium

Sc

44.955 908

22

Titanium

Ti

47.867

23

Vanadium

V

50.941 5

24

Chromium

Cr

51.996 1

25

Manganese

Mn

54.938 043

26

Iron

Fe

55.845

27

Cobalt

Co

58.933 194

28

Nickel

Ni

58.693 4

29

Copper

Cu

63.546

30

Zinc

Zn

65.38

31

Gallium

Ga

69.723

32

Germanium

Ge

72.63

33

Arsenic

As

74.921 595

34

Selenium

Se

78.971

35

Bromine

Br

79.904

36

Krypton

Kr

83.798

37

Rubidium

Rb

85.467 8

38

Strontium

Sr

87.62

39

Yttrium

Y

88.905 84

40

Zirconium

Zr

91.224

41

Niobium

Nb

92.906 37

42

Molybdenum

Mo

95.95

43

Technetium

Tc

98

44

Ruthenium

Ru

101.07

45

Rhodium

Rh

102.905 49

46

Palladium

Pd

106.42

47

Silver

Ag

107.868 2

48

Cadmium

Cd

112.414

49

Indium

In

114.818

50

Tin

Sn

118.71

51

Antimony

Sb

121.76

52

Tellurium

Te

127.6

53

Iodine

I

126.904 47

54

Xenon

Xe

131.293

55

Caesium

Cs

132.905 452

56

Barium

Ba

137.327

57

Lanthanum

La

138.905 47

58

Cerium

Ce

140.116

59

Praseodymium

Pr

140.907 66

60

Neodymium

Nd

144.242

61

Promethium

Pm

145

62

Samarium

Sm

150.36

63

Europium

Eu

151.964

64

Gadolinium

Gd

157.25

65

Terbium

Tb

158.925 354

66

Dysprosium

Dy

162.5

67

Holmium

Ho

164.930 328

68

Erbium

Er

167.259

69

Thulium

Tm

168.934 218

70

Ytterbium

Yb

173.045

71

Lutetium

Lu

174.966 8

72

Hafnium

Hf

178.49

73

Tantalum

Ta

180.947 88

74

Tungsten

W

183.84

75

Rhenium

Re

186.207

76

Osmium

Os

190.23

77

Iridium

Ir

192.217

78

Platinum

Pt

195.084

79

Gold

Au

196.966 57

80

Mercury

Hg

200.592

81

Thallium

Tl

204.38

82

Lead

Pb

207.2

83

Bismuth

Bi

208.980 4

84

Polonium

Po

209

85

Astatine

At

210

86

Radon

Rn

222

87

Francium

Fr

223

88

Radium

Ra

226

89

Actinium

Ac

227

90

Thorium

Th

232.037 7

91

Protactinium

Pa

231.035 88

92

Uranium

U

238.028 91

93

Neptunium

Np

237

94

Plutonium

Pu

244

95

Americium

Am

243

96

Curium

Cm

247

97

Berkelium

Bk

247

98

Californium

Cf

251

99

Einsteinium

Es

252

100

Fermium

Fm

257

101

Mendelevium

Md

258

102

Nobelium

No

259

103

Lawrencium

Lr

266

104

Rutherfordium

Rf

267

105

Dubnium

Db

268

106

Seaborgium

Sg

269

107

Bohrium

Bh

270

108

Hassium

Hs

270

109

Meitnerium

Mt

278

110

Darmstadtium

Ds

281

111

Roentgenium

Rg

282

112

Copernicium

Cn

285

113

Nihonium

Nh

286

114

Flerovium

Fl

289

115

Moscovium

Mc

290

116

Livermorium

Lv

293

117

Tennessine

Ts

294

118

Oganesson

Og

294

[Data Source: Royal Society of Chemistry]

Associated Articles

If you appreciate our work, consider supporting us on ❤️ patreon.
Atom

Copy Article Cite

Thanks for your response!
Write a response


Join the Newsletter

Subscribe to get latest content in your inbox.

newsletter

We won’t send you spam.