3.8-9 Isotopes—Atomic Mass or Relative Atomic Mass

• Definition: Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, leading to different mass numbers.

• Example: Hydrogen has seven isotopes: H, H1, H2, H3, H4, H5, H6. Three of these isotopes occur in nature, and the others are synthetic.

Natural Isotopes of Hydrogen:

Name Symbol Proton Number (Z) Mass Number (A) Neutron Number

Hydrogen H 1 1 0

Deuterium H1 1 2 1

Tritium H3 1 3 2

3.9 Atomic Mass or Relative Atomic Mass

• Mass Number: The mass number of an atom is the sum of its protons and neutrons. It is usually an integer.

• Relative Atomic Mass: This is the weighted average mass of atoms of an element, calculated relative to 1/12 of the mass of a carbon-12 atom.

Why Relative Atomic Mass is Necessary:

• Atoms have very small masses (e.g., Fluorine = 3.16×10^-23 g, Aluminium = 4.482×10^-23 g).

• It’s impractical to use these small numbers directly. Therefore, we use the mass of carbon-12 as a standard reference.

Carbon-12 as the Standard:

• The mass of 1/12 of a carbon-12 isotope = 1.66×10^-24 g.

• To calculate the relative atomic mass of any atom, divide the actual mass of the atom by the mass of 1/12 of a carbon-12 atom.

Example Calculation:

• Mass of an Al (Aluminium) atom = 4.482×10^-23 g.

• Relative atomic mass of Al = (4.482×10^-23 g) ÷ (1.66×10^-24 g) = 27 (no unit, since it’s a ratio).

3.9.1 Determining the Average Relative Mass of an Element from Percentage of Isotopes

• Many elements have more than one isotope. The average relative mass is calculated using the percentage of each isotope present in nature.

Steps:

1. Multiply the mass number of each isotope by its natural abundance percentage.

2. Sum the results from step 1.

3. Divide the total by 100 to get the average relative mass.

Formula:

• Average relative atomic mass = (p × m + q × n) / 100

• p = mass number of the first isotope

• m = percentage of the first isotope

• q = mass number of the second isotope

• n = percentage of the second isotope

Example: Chlorine has two isotopes:

• 35Cl: 75% abundance

• 37Cl: 25% abundance

• Average relative atomic mass = (35×75 + 37×25) / 100 = 35.5

3.9.2 Getting the Relative Molecular Mass from Relative Atomic Mass

• The relative molecular mass is calculated by summing the products of the relative atomic mass of each element in a molecule and the number of atoms of that element.

Example 1: Hydrogen molecule (H2):

• The relative atomic mass of Hydrogen = 1.

• H2 contains two hydrogen atoms, so relative molecular mass = 1×2 = 2.

Example 2: Sulfuric acid (H2SO4):

• Relative atomic mass of Hydrogen = 1, and there are 2 atoms → 1×2 = 2.

• Relative atomic mass of Sulfur = 32, and there is 1 atom → 32×1 = 32.

• Relative atomic mass of Oxygen = 16, and there are 4 atoms → 16×4 = 64.

• Relative molecular mass = 2 + 32 + 64 = 98.