3.2 Relative masses of atoms and molecules

2026 Syllabus Objectives

  1. Core: Describe relative atomic mass, ArA_r, as the average mass of the isotopes of an element compared to 1/12th of the mass of an atom of 12C^{12}\text{C}
  2. Core: Define relative molecular mass, MrM_r, as the sum of the relative atomic masses. Relative formula mass, MrM_r, will be used for ionic compounds
  3. Core: Calculate reacting masses in simple proportions. Calculations will not involve the mole concept

The Need for Relative Atomic Mass

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The mass of a single hydrogen atom is incredibly small when measured in grams (g):

mass of one hydrogen atom=1.7×10−24 g=0.0000000000000000000000017 g\text{mass of one hydrogen atom} = 1.7 \times 10^{-24} \, \text{g} = 0.0000000000000000000000017 \, \text{g}

Such tiny masses are impractical to work with. Instead, it is much more useful and convenient to measure the masses of atoms relative to each other.

🔑 The Standard Atom

To establish a relative scale, a standard atom has been chosen against which all other atoms are compared:

Standard atom: An atom of the carbon-12 isotope (12C^{12}\text{C}), which is given a mass value of exactly 12.

All other atomic masses are compared to one-twelfth of the mass of a carbon-12 atom.

Visual representation: If we balance one carbon atom (mass 12 units) on a scale, it would balance twelve hydrogen atoms (each with mass 1 unit). Similarly, one helium atom balances four hydrogen atoms.

Relative Atomic Mass (ArA_r)

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Definition

Relative atomic mass (ArA_r) is the average mass of an atom of an element, taking into account the different natural isotopes of that element, compared to 1/12th of the mass of an atom of 12C^{12}\text{C}.

Understanding Isotopes

The mass spectrometer first revealed the existence of isotopes - atoms of the same element that have different masses because they contain different numbers of neutrons in the nucleus.

Since elements exist as mixtures of isotopes in nature, the relative atomic mass is an average value weighted by the natural abundance of each isotope.

Key Points ⚡

  • Most relative atomic masses are not whole numbers due to the averaging of isotope masses
  • In many cases, values are rounded to the nearest whole number to simplify calculations
  • Exception: Chlorine has Ar=35.5A_r = 35.5 (reflecting its two main isotopes: 35Cl^{35}\text{Cl} and 37Cl^{37}\text{Cl})
  • The mass of an ion is essentially the same as the parent atom (the mass of electrons gained or lost is negligible)

Examples of Isotopes

Different elements have varying numbers of naturally occurring isotopes:

  • Fluorine (F): Only one isotope with mass number 19
  • Lithium (Li): Two isotopes with mass numbers 6 and 7
  • Chlorine (Cl): Two main isotopes with mass numbers 35 and 37
  • Krypton (Kr): Multiple isotopes with mass numbers 82, 83, 84, 86
  • Tin (Sn): Multiple isotopes with mass numbers 116, 117, 118, 119, 120, 122, 124

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