# 1.3B: Relative Atomic Mass

The actual mass of an atom basically depends on the numbers of protons and neutrons in its nucleus. Since the rest mass of proton and neutrons are too small to regard, to calculate the actual mass of an atom seems inconvenient for scientists. In order to solve this problem, relative atomic mass (Ar), which unit is defined as 1/12th of the mass of carbon-12 atom, is introduced.

## Introduction

The calculated relative atomic mass is not the mass of exact atom. It is a ratio of actual mass respect to the 1/12th of the mass of carbon-12 atom. Relative atomic mass has unit of "1" according to the equation since "kg" at the top cancels with the bottom one. The introduction of using relative mass, to a great extend, makes scientists calculate mass of large molecules much more convenient.

## Way to calculate Relative atomic mass (Ar) for standard atoms

In order to calculate Ar, first of all, is to calculate the 1/12 of carbon-12: 1.993x10-26/12=1.661x10-27 Kg; then, compare this value with any other atom which needs to be calculated and the obtained ratio is relative atomic mass for that atom. For example, for the oxygen atom, its rest mass is 2.657x10-26, divide it by 1.661x10-27 (2.657x10-26/1.661x10-27 ) and the answer will approximately be 16--that is the relative atomic mass for oxygen. The contribution of this value is to make calculation much easier.

## Calculating relative atomic mass of an element with isotopes

Most of the elements in the world have isotopes; therefore, relative atomic mass for one element is expanded to the average mass of the naturally occurring isotopes of the element. This quantity takes into account the percentage abundance of all the isotopes of an element which exist. For example, there are two naturally occurring isotopes of chlorine, 35Cl and 37Cl; hence, the Ar for Cl should be the average of value of each isotope's mass times its percentage abundance.

## Relative Atomic Mass of some common atoms

• H 1.007 94
• C 12.017
• N 14.006 7
• O 15.999 4
• F 18.998 403 2
• Na 22.989 769 28
• Mg 24.305 0
• Al 26.981 538 6
• Si 28.085 5
• P 30.973 762
• S 32.065
• Cl 35.453
• K 39.098 3
• Ca 40.078

## References

1. IUPAC Quantities, Units and Symbols in Physical Chemistry. Second Edition, Blackwell Scientific Publications, Oxford, 1993.
2. Williams, Andrew. Origin of the Formulas of Dihydrogen and Other Simple Molecules. J. Chem. Ed. 2007.