Average Atomic Mass & Relative Atomic Mass Calculations

An element that exists in two or more isotopes will have atoms with different mass numbers. The relative atomic mass of such an element is the average of the mass numbers of its naturally occurring isotopes. To calculate this value, you have to take into account the relative abundances of the isotopes.

So by definition,

It has no unit (since it's a relative value).

Also Check: Difference between Relative Atomic Mass and Mass Number

Example: The relative atomic mass of chlorine is 35.5 because chlorine has two main isotopes:

• Cl-35 (about 75%)
• Cl-37 (about 25%)

Ar=(35×0.75)+(37×0.25)=35.5

If you've been following along, you may have noticed that we've been discussing relative atomic mass. However, there's also average atomic mass.

While the relative atomic mass (Aᵣ) and average atomic mass are closely related, they have distinct meanings. We've already covered relative atomic mass above. Now, let's look at average atomic mass.

The average atomic mass is the actual mass of an element’s atoms, taking into account the natural abundances of its isotopes. It is expressed in atomic mass units (amu or u). Essentially, it is the same as the relative atomic mass, but with the unit included.

For example, the average atomic mass of chlorine is 35.5 amu.

In everyday chemistry, both terms are often used interchangeably because they refer to the same calculated value, but technically, the relative atomic mass is a ratio, while the average atomic mass is a measured mass in amu.

How Relative Atomic Mass & Average Atomic Mass Are Calculated

The average atomic mass or relative atomic mass is calculated using the following formula:

Average Atomic Mass=∑(Isotope Mass × Relative Abundance)

Where:

• Isotope Mass is the mass of a specific isotope of the element.
• Relative Abundance is the fraction or percentage of that isotope in nature.

Steps to calculate:

1. Identify the isotopes: Determine the masses of all naturally occurring isotopes of the element.
2. Find their relative abundances: These are usually given as percentages or fractions.
3. Multiply each isotope's mass by its relative abundance.
4. Sum the results to get the average atomic mass.

Example:

Consider chlorine, which has two naturally occurring isotopes:

• Chlorine-35: mass = 34.96885 amu, abundance = 75.78% (or 0.7578)
• Chlorine-37: mass = 36.96590 amu, abundance = 24.22% (or 0.2422)

The average atomic mass is calculated as:

Average Atomic Mass=(34.96885×0.7578)+(36.96590×0.2422)

Average Atomic Mass=26.50+8.95=35.45 amu

Thus, the average atomic mass of chlorine is approximately 35.45 amu.

This weighted average reflects the contribution of each isotope to the overall mass of the element as it occurs in nature.

Using Our Calculator to Calculate Average Atomic Mass Or Relative Atomic Mass

Our calculator is a user-friendly tool designed to calculate both relative and average atomic mass of an element based on the masses and relative abundances of its isotopes. The tool is ideal for students, educators, and professionals in chemistry who need to quickly and accurately determine the relative atomic mass of an element.

How to use the calculator

Step 1: Add Isotopes

• Click the "Add Isotope" button to create input fields for a new isotope.
• Each isotope requires:
  • Mass (amu): The atomic mass of the isotope.
  • Abundance (%): The percentage abundance of the isotope in nature.
• You can add up to 10 isotopes.

Step 2: Enter Data

• Fill in the mass and abundance for each isotope.
• Ensure that the total abundance of all isotopes adds up to 100%.

Step 3: Calculate RAM

• Click the "Calculate RAM" button to compute the Relative Atomic Mass.

Average Atomic Mass Problems and Solutions

Put our calculator to the test by trying these 10 Relative/Average Atomic Mass quizzes!