Atoms and Molecules : Atomic and Molecular Masses

 

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 Gramatomic mass or gramatom

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 gramatoms 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.

 

Grammolecular mass

The gram-molecular mass of a substance is its relative molecular mass expressed in grams.

 

Examples

Substance Molecular Formula Relative molecular mass Grammolecular 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

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Atoms and Molecules : Moles

 

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