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. 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. 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. ## 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.

 Atomic Weight Atomic 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. 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. 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. You can extract data from the above graph (atomic weight vs atomic number) using PlotDigitizer.

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.

• Measurement Limits: The measurement limits are always present in experimental results. There is a limit to which we measure the atomic mass of an isotope. This results in uncertainty in the atomic mass itself. For example, the atomic mass of sodium-23 is 22.989 769 282 0(19), where “(19)” represents uncertainty in the atomic mass. It can also be represented as 22.989 769 282 0 ± 000 000 001 9.
• Sampling Error: The sampling error results when a given sample may not represent the original source. This may be due to negligence from the human side.
• Unequal Distribution: The relative abundance of an isotope can vary from the source. Since the Earth is a huge giant, the distribution of an isotope can differ in air, ocean, soil, crust, volcanoes. For example, the presence of lighter isotopes of thallium is more in igneous rocks compare to sedimentary rocks. 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: ## 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.

 Isotope Atomic Mass (u) Relative Abundance (%) Hydrogen (1H) 1.007 825 99.98 Deuterium (2H) 2.014 102 0.02 Tritium (3H) 3.016 049 trace

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: ### 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.

 Isotope Atomic Mass (u) Relative Abundance (%) Carbon-12 (12C) 12 98.9 Carbon-13 (13C) 13.003 355 1.1

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

 Isotope Atomic Mass (u) Relative Abundance (%) Oxygen-16 (16O) 15.994 915 99.76 Oxygen-17 (17O) 16.999 132 0.04 Oxygen-18 (18O) 17.999 159 0.20

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: ### Example 4: To Calculate Atomic Weight of Zinc

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

 Isotope Atomic Mass (u) Relative Abundance (%) Zinc-64 (16Zn) 63.929 142 49.17 Zinc-66 (17Zn) 65.926 033 27.73 Zinc-67 (18Zn) 66.927 127 4.04 Zinc-68 (18Zn) 67.924 844 18.45 Zinc-70 (18Zn) 69.925 319 0.61

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: ## List of Elements by Atomic Weight

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

 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 