# Relative Mass and Calculating Relative Mass – HSC Chemistry

This is part of the HSC Chemistry course under the topic of Atomic Structure and Atomic Mass

### HSC Chemistry Syllabus

• Calculate the relative atomic mass from isotopic composition (ACSCH024)

### Relative Mass and Calculating Relative Mass

This video will explain what relative atomic mass is, and how to calculate it.

### What is Relative Atomic Mass?

The periodic table lists the atomic mass for each element, which might seem confusing considering that elements can have isotopes – variants with the same number of protons but different numbers of neutrons.

The mass that is provided on the periodic table is the element's relative atomic mass and is calculated by considering the relative abundances of an element's stable isotopes and their atomic masses.

Atomic mass unit (amu) is usually expressed as u1 amu is defined as 1/12th of the mass of a carbon-12 atom. Specifically, 1 amu or 1 u = 1.661 xx 10^{-27} \text{ kg}.

Since most of an atom's mass is due to proton(s) and neutron(s) in its nucleus, there is a correlation between the nucleon number of an atom and its mass. For example, hydrogen-1 atom which contains one proton, has an atomic mass close to 1 amu. Lithium-7 atom, which contains 7 nucleons (3 protons and 4 neutrons), has an atomic mass of approximately 7 amu.

The general formula for calculating an element's relative atomic mass is given by:

$$\text{Relative atomic mass} = MM_1 \times R_1 + MM_2 \times R_2 + ... + MM_n \times R_n$$

where

• MM is the atomic mass of an isotope
• R is the relative abundance of the isotope

### Example 1 Relative Atomic Mass of Hydrogen

Consider hydrogen's stable isotopes: Hydrogen-1 (1 proton) and hydrogen-2 (1 proton and 1 neutron). Other isotopes of hydrogen are not considered in the calculation of its relative atomic mass because they are unstable.

The two isotopes' exact atomic masses and relative abundances are shown in the table below.

 Isotope Atomic mass (u) Relative abundance H-1 1.0078 99.9855% H-2 2.0141 0.0145%

The average atomic mass calculated from these abundances and masses aligns with the value listed on the periodic table:

$$0.999855 \times 1.0078 + 0.000145 \times 2.0141 = 1.008 \, u$$

The relative abundance of hydrogen-2 isotope is so negligible that the relative atomic mass of hydrogen is approximately the atomic mass of hydrogen-1 isotope.

### Example 2 – Relative Atomic Mass of Chlorine

Consider chlorine's isotopes: Chlorine-35 (with 17 protons and 18 neutrons) and Chlorine-37 (17 protons and 20 neutrons).

The two isotopes' exact atomic masses and relative abundances are shown in the table below.

 Isotope Atomic mass (u) Relative abundance Cl-35 34.97 75.77% Cl-37 36.97 24.23%

The average atomic mass calculated from these abundances and masses aligns with the value listed on the periodic table:

$$0.7577 \times 34.97 + 0.2423 \times 36.97 = 35.45 \, u$$

Previous Section: Structure of the Atom, Atomic Symbols and Isotopes