ATOMIC AND MOLECULAR MASSES
Atoms are too light and small to be weighed individually. The mass of an atom, therefore, is expressed with respect to a standard or reference, when it is called the relative atomic mass or, simply, the atomic mass.
The relative atomic mass of an element is a number which shows how many times an atom of the element is heavier than an atom of a reference element.
Thus, the atomic mass should never be confused with the absolute mass of an atom, which can only be calculated but not directly determined.
Depending upon the reference element, different scales of atomic mass of an atom time to time. All of them contributed significantly to the development of chemistry.
The Hydrogen Scale
Hydrogen, being the lightest element, was first chosen as the reference, and the atomic mass was defined as follows.
The atomic mass of an element is the number of times an atom of element is heavier than an atom of hydrogen.
Atomic mass =
Thus, on the hydrogen scale, a hydrogen atom is assigned a mass of exactly 1 and the masses of the atoms of other elements are determined accordingly.
The Oxygen Scale
From Gay-Lussac’s law of combining volumes, we know that one atom of O combines with two atoms of H to form a molecule of water (steam). We also know that 16 parts by mass of oxygen combine with two parts by mass of hydrogen to form 18 parts by mass of water. So that atomic mass of O may be treated as 16.
Considering the greater reactivity of oxygen than hydrogen, chemists shifted the reference from H = 1.000 to O = 16.000. On this scale, an atom of O is granted a mass of exactly 16 and the masses of the other atoms are determined accordingly.
However, when isotopes (atoms of the same element differing in mass number) were discovered, the oxygen scale became incontinent. It was discovered that a natural sample of oxygen has three isotopes = 16O, 17O and 18O with abundances of 99.759, 0.037 and 0.204% respectively. Hence an atom of natural sample of oxygen as a reference has no significance.
Aston, therefore, proposed a scale based on oxygen – 16 (16O = 16.000) as the standard. This scale required the revision of all atomic-mass data compiled earlier on the natural-O scale.
From Aston’s work, it was clear that, instead of a natural sample of an element, only a definite isotope could be chosen as a standard. And, for convenience, the choice of the isotope should be such that minimal correction is required in the previously determined atomic masses.
The Carbon-12 Scale
Carbon has three isotopes – 12C, 13C and 14C – of which 14C is present in negligible amounts in natural samples. 12C and 13C have natural abundances of 98.89 and 1.11% respectively.
It was realised that carbon – 12 ( 12C = 12.000) could also be chosen as a good standard. If this was done, the amount of correction required in the earlier data would be minimal. The atomic masses determined according to the natural-O scale would have to be reduced only by 0.004% to make the them consistent with the carbon-12 scale. So the carbon-12 scale was finally adopted.
On this scale, one-twelfth the mass of an atom of the isotope 12C is treated as the atomic mass unit (amu), and relative atomic masses are determined accordingly. Relative atomic mass is defined as follows.
The relative atomic mass of an element is the ratio of the mass of an atom of the element to one-twelfth the mass of an atom of carbon-12.
In other words, it is a number that shows how many times an atom of an element is heavier than one-twelfth the mass of an atom of this isotope carbon-12.
Relative atomic mass =
of the mass of 1 atom 12C, i.e., 1 amu = 1.66 x 10 – 24 g = 1.66 x 10 –27 kg.
∴ mass of 1 atom of an element = relative atomic mass x 1.66 x 10 – 24 g.
The relative atomic mass of some important elements are given in the table.
| Element | Symbol | Atomic
number |
Atomic mass | Element | Symbol | Atomic
number |
Atomic mass | |
| Hydrogen | H | 1 | 1.0079 | Nickel | Ni | 28 | 58.693 | |
| Helium | He | 2 | 4.0026 | Copper | Cu | 29 | 63.546 | |
| Lithium | Li | 3 | 6.941 | Zinc | Zn | 30 | 65.409 | |
| Beryllium | Be | 4 | 9.0122 | Gallium | Ga | 31 | 69.723 | |
| Boron | B | 5 | 10.811 | Germanium | Ge | 32 | 72.64 | |
| Carbon | C | 6 | 12.011 | Arsenic | As | 33 | 74.922 | |
| Nitrogen | N | 7 | 14.007 | Selenium | Se | 34 | 78.96 | |
| Oxygen | O | 8 | 15.999 | Bromine | Br | 35 | 79.904 | |
| Fluorine | F | 9 | 18.998 | Krypton | Kr | 36 | 83.798 | |
| Neon | Ne | 10 | 20.180 | Rubidium | Rb | 37 | 85.468 | |
| Sodium | Na | 11 | 22.990 | Strontium | Sr | 38 | 87.62 | |
| Magnesium | Mg | 12 | 24.305 | Palladium | Pd | 46 | 106.42 | |
| Aluminium | Al | 13 | 26.982 | Silver | Ag | 47 | 107.87 | |
| Silicon | Si | 14 | 28.086 | Cadmium | Cd | 48 | 112.41 | |
| Phosphorus | P | 15 | 30.974 | Tin | Sn | 50 | 118.71 | |
| Sulphur | S | 16 | 32.065 | Antimony | Sb | 51 | 121.76 | |
| Chlorine | Cl | 17 | 35.453 | Tellurium | Te | 52 | 127.60 | |
| Argon | Ar | 18 | 39.948 | Iodine | I | 53 | 126.90 | |
| Potassium | K | 19 | 39.098 | Xenon | Xe | 54 | 131.29 | |
| Calcium | Ca | 20 | 40.078 | Cesium | Cs | 55 | 132.91 | |
| Scandium | Sc | 21 | 44.956 | Barium | Ba | 56 | 137.33 | |
| Titanium | Ti | 22 | 47.867 | Gold | Au | 79 | 196.97 | |
| Vanadium | V | 23 | 50.942 | Mercury | Hg | 80 | 200.59 | |
| Chromium | Cr | 24 | 51.996 | Lead | Pb | 82 | 207.20 | |
| Manganese | Mn | 25 | 54.938 | Bismuth | Bi | 83 | 208.98 | |
| Iron | Fe | 26 | 55.845 | Radium | Ra | 88 | 226 | |
| Cobalt | Co | 27 | 58.933 | Thorium | Th | 90 | 232.04 |
The Gram–atomic mass or gram–atom
The gram-atomic mass or the gram-atom of an element is its relative atomic mass expressed in grams.
For example, the relative atomic mass of H is 1.008 and its gram-atomic mass 1.008 g.
Illustration 1: How many gram–atoms are there in 80.0 g of oxygen (Ar of O = 16.0)?
Solution: The relative atomic mass of oxygen = 16.0
∴ the gram-atomic mass of oxygen = 16.0 g.
Given mass of oxygen = 80.0 g.
∴ the number of gram-atoms = 5.
Relative Molecular Mass
The relative molecular mass of a substance is the ratio of the mass of a molecule of the substance to one twelfth the mass of an atom of carbon-12.
Relative molecular mass =
Thus, the relative molecular mass of a substance is the number that shows how many times a molecule of the substance is heavier than an atom of 12C.
The unit of molecular mass is the same as that of atomic mass (i.e., 1/12 x mass a 12C atom). So the relative molecular mass of a substance – element or compound – can be easily calculated by adding the relative masses of all the individual atoms present in the molecule.
Gram–molecular mass
The gram-molecular mass of a substance is its relative molecular mass expressed in grams.
Examples
| Substance | Molecular Formula | Relative molecular mass | Gram–molecular mass |
| 1. Hydrogen | H2 | 2 x 1 = 2 | 2 g |
| 2. Oxygen | O2 | 2 x 16 = 32 | 32 g |
| 3. Ozone | O3 | 3 x 16 = 48 | 48 g |
| 4. Chlorine | Cl2 | 2 x 35.5 = 71 | 71 g |
| 5. Neon | Ne | 1 x 20 = 20 | 20 g |
| 6. Water | H2O | 2 x 1 + 16 = 18 | 18 g |
| 7. Carbon dioxide | CO2 | 12 + 2 x 16 = 44 | 44 g |
| 8. Methane | CH4 | 12 + 4 x 1 = 16 | 16 g |
| 9. Nitric acid | HNO3 | 1 + 14 + 3 x 16 = 63 | 63 g |
| 10. Ethanol | C2H5OH | 2 x 12 + 5 x 1 + 16 +1 = 46 | 46 g |
Formula Mass
Covalent substances like HCl, CO2 and CH4 exist as discrete molecules, but ionic solids do not. For example, a crystal of sodium chlorine does not contain discrete molecules of NaCl; rather it contains Na+ : Cl– ratio is 1 : 1 and the formula is NaCl. So, the relative mass of NaCl (58.5; Na = 23, Cl = 35.5) should be called the formula mass rather than the molecular mass.
The same is the case with all other ionic solids. Several covalent substances also do not exist in the form represented by their molecular formulae. For example, water molecules to form (H2O)n, both in the liquid and the solid state. However, the stoichiometry, i.e., the mass ratio of the elements in the compound, remains the same (1 : 8).
For all chemical calculations the formula mass is treated as the molecular mass as the stoichiometry is same in both cases. Also, the term ‘molecular mass’ is loosely used for formula mass.
| Substance | Formula | Formula mass (amu) |
| 1. Sodium chloride | NaCl | 23 + 35.5 = 58.5 |
| 2. Calcium chloride | CaCl2 | 40 + 2 x 35.5 = 111 |
| 3. Calcium oxide | CaO | 40 + 16 = 56 |
| 4. Sodium hydroxide | NaOH | 23 + 16 + 1 = 40 |
| 5. Sodium carbonate | Na2CO3 | 2 x 23 + 12 + 3 x 16 = 106 |
| 6. Calcium carbonate | CaCO3 | 40 + 12 + 3 x 16 = 100 |
