3.4 Relative Atomic Mass and Atomic Mass Unit

This topic explains how the masses of atoms are measured and compared. Since atoms are extremely small, scientists use a relative scale based on a standard atom — carbon-12.

Definition

Relative Atomic Mass

The mass of an atom of an element relative to the mass of an atom of C-12 is called its relative atomic mass.

Simple explanation: Relative atomic mass tells you how heavy an atom is compared to a carbon-12 atom.

Atomic Mass Unit (amu)

One atomic mass unit (amu) is defined as a mass exactly equal to one-twelfth the mass of one C-12 atom.

Simple explanation: The amu is the unit we use to measure atomic masses. It is based on carbon-12.

Main Idea

An atom is an extremely small particle. Therefore, we cannot determine the mass of a single atom directly in grams in a convenient way. However, it is possible to determine the mass of one atom of an element relative to another experimentally.

This is done by assigning a value to the mass of one atom of a given element, so that it can be used as a standard.

• By international agreement in 1961, the light isotope of carbon, C-12, has been chosen as the standard.
• This isotope of carbon (C-12) has been assigned a mass of exactly 12 atomic mass units.
• This value has been determined accurately using a mass spectrometer.

The masses of atoms of all other elements are compared to the mass of C-12.

Core Concept

The Standard: Carbon-12

Key Formula

1 amu = mass of one C-12 atom12

Mass of one C-12 atom = 12 amu

Detailed Explanation

Why Carbon-12 Was Chosen

Carbon-12 was chosen as the standard because:

• It is a stable isotope.
• It is readily available.
• It can be measured accurately using a mass spectrometer.
• It gives convenient values for other elements.

How Relative Atomic Mass Is Calculated

Example from the book:

A hydrogen atom is 8.40% as massive as the standard C-12 atom. Therefore:

Relative atomic mass of hydrogen = 8.40100 × 12 amu

= 1.008 amu

Simple explanation: Hydrogen is only 8.40% as heavy as carbon-12. So its relative atomic mass is 8.40% of 12 = 1.008 amu.

Relative Atomic Masses of Some Elements

Table 3.1 from the book:

Simple explanation: These numbers tell you how heavy each atom is compared to carbon-12. For example, an oxygen atom is about 16 times heavier than 112 of a carbon-12 atom.

Mass Spectrometer

A mass spectrometer is an instrument used to measure atomic masses accurately. It:

• Separates atoms or molecules by mass.
• Measures the relative abundance of each isotope.
• Gives very precise values of atomic masses.

Intermediate Level

Why "Relative" Atomic Mass?

The word "relative" is important because:

• We are not measuring absolute mass in grams.
• We are comparing masses to a standard (C-12).
• The values are ratios, so they have no units (though we often write "amu").

Why Not Just Use Grams?

• Extremely small (10⁻²³ to 10⁻²² grams)
• Inconvenient to use in calculations
• Impossible to measure directly with ordinary balances

The relative scale gives convenient numbers (like 1.008, 16.00, 23.00) that are easy to work with.

Relation to Moles

The relative atomic mass in amu is numerically equal to the molar mass in grams per mole (g/mol).

• Carbon: relative atomic mass = 12 amu → molar mass = 12 g/mol
• Oxygen: relative atomic mass = 16 amu → molar mass = 16 g/mol
• Sodium: relative atomic mass = 23 amu → molar mass = 23 g/mol

This is why 1 mole of carbon weighs 12 grams, 1 mole of oxygen weighs 16 grams, etc.

Why Atomic Masses Are Not Whole Numbers

Most relative atomic masses are not whole numbers because:

• Elements exist as mixtures of isotopes.
• Each isotope has a different mass.
• The relative atomic mass is a weighted average of the isotope masses.

• Cl-35 (about 75%)
• Cl-37 (about 25%)
• Average = 35.453 amu

Important Points

• - Relative atomic mass: mass of an atom of an element relative to the mass of an atom of C-12.
• - Atomic mass unit (amu): mass exactly equal to one-twelfth the mass of one C-12 atom.
• - C-12 is the standard — assigned a mass of exactly 12 amu.
• - C-12 was chosen by international agreement in 1961.
• - Mass spectrometer is used to measure atomic masses accurately.
• - Most relative atomic masses are not whole numbers because they are weighted averages of isotopes.
• - Examples:
• - H = 1.008 amu
• - N = 14.0067 amu
• - O = 15.9994 amu
• - Na = 22.9898 amu
• - Al = 26.9815 amu
• - S = 32.06 amu
• - Cl = 35.453 amu
• - Fe = 55.847 amu

Remember

• - Relative atomic mass = mass compared to C-12.
• - **amu** = 112 mass of one C-12 atom.
• - C-12 = standard; assigned mass = 12 amu.
• - Mass spectrometer = instrument for measuring atomic masses.
• - Most atomic masses are not whole numbers (due to isotopes).
• - **H = 1.008 amu**, **O = 15.9994 amu**, **Na = 22.9898 amu**.

Common Mistakes

• 1. Thinking relative atomic mass is the actual mass in grams. It is a relative value, not an absolute mass.
• 2. Thinking C-12 has a mass of 12 grams. It has a mass of 12 amu.
• 3. Confusing relative atomic mass with mass number. Mass number is a whole number (protons + neutrons); relative atomic mass is a weighted average (may be decimal).
• 4. Thinking all atomic masses are whole numbers. They are not, because of isotopes.
• 5. Forgetting the standard. The standard for atomic masses is carbon-12, not hydrogen or oxygen.
• 6. Thinking amu is a unit of grams. amu is its own unit, based on C-12.

Quick Revision

• Relative atomic mass: mass of an atom of an element relative to the mass of an atom of C-12.
• Atomic mass unit (amu): mass exactly equal to one-twelfth the mass of one C-12 atom.
• Standard: Carbon-12, assigned a mass of exactly 12 amu.
• Chosen by: international agreement in 1961.
• Measured using: mass spectrometer.
• **Examples:** H = 1.008 amu; O = 15.9994 amu; Na = 22.9898 amu; Cl = 35.453 amu.
• Most relative atomic masses are not whole numbers because they are weighted averages of isotopes.

60-Second Revision

• Relative atomic mass = mass compared to C-12.
• **amu** = 112 mass of one C-12 atom.
• C-12 = standard; mass = exactly 12 amu.
• Mass spectrometer measures atomic masses.
• **H = 1.008 amu**, **O = 15.9994 amu**, **Na = 22.9898 amu**.
• Warning: relative atomic mass is not the same as mass number.