Atomic Mass: Concepts, Calculations, and Practice

Atomic Mass (Simplified)

Definition and Periodic Table Application

The atomic mass of elements can be found by looking at the Periodic Table. Atomic mass is the weighted average of all the isotopes of an element, expressed in atomic mass units (amu) or grams per mole (g/mol).

• 1 amu is defined as $1.66 \times 10^{-27}$ kg.

• The atomic mass listed on the periodic table is not always a whole number because it reflects the average mass of all naturally occurring isotopes of that element.

Example: Identifying Greatest Atomic Mass in a Group

Which of the following represents an element from the first column with the greatest atomic mass?

• Li (Lithium)

• Na (Sodium)

• K (Potassium) ← Correct Answer

• H (Hydrogen)

Explanation: As you move down a group (column) in the periodic table, atomic mass increases.

Practice Question

Which of the following choices has the greatest atomic mass?

• a) Element B (3.24 × 102 kg)

• b) Element C (2.10 kg)

• c) Element D (5.14 × 104 Da)

Note: 1 Da (Dalton) = 1 amu

Calculating Atomic Mass

The atomic mass of an element can be calculated if you know the isotopic masses and percent abundances of its isotopes.

• Isotopic Mass: The mass of a specific isotope of an element.

• Percent Abundance: The percentage of each isotope found in nature for a given element.

Atomic Mass Formula

The atomic mass is calculated as the sum of the products of each isotope's mass and its fractional abundance:

Formula:

$\text{Atomic Mass} = (\text{Isotopic Mass}_1 \times \text{Fractional Abundance}_1) + (\text{Isotopic Mass}_2 \times \text{Fractional Abundance}_2) + \ldots$

Where fractional abundance is percent abundance divided by 100.

Example: Calculating Atomic Mass of Gallium

• Ga-69: 68.926 amu, 60.11%

• Ga-71: 70.925 amu, 39.89%

Step 1: Convert percent abundances to decimals (fractional abundances):

• Ga-69: 0.6011

• Ga-71: 0.3989

Step 2: Plug into the formula:

$\text{Atomic Mass} = (68.926 \times 0.6011) + (70.925 \times 0.3989) = 69.72$ amu

Practice Problem

Three isotopes of magnesium exist on earth. Mg-24 is the most common form at 78.70% natural abundance with a mass of 23.98504 amu. Mg-25 has an 11.17% natural abundance, while Mg-26 has a natural abundance of 11.13% and a mass of 25.98259 amu. What is the mass of the Mg-25 isotope?

Answer: 24.99090 amu

Practice Problem: Silver Isotopes

Silver has an atomic mass of 107.868 amu. The Ag-109 isotope (108.905 amu) is 48.16%. What is the amu of the other isotope?

• Answer: 106.905 amu

Summary Table: Key Terms in Atomic Mass Calculations

Term	Definition
Atomic Mass	Weighted average mass of all isotopes of an element
Isotopic Mass	Mass of a specific isotope
Percent Abundance	Percentage of a specific isotope in a natural sample
Fractional Abundance	Percent abundance divided by 100

Additional info:

• Atomic mass is crucial for stoichiometric calculations in chemical reactions.

• Understanding isotopic composition helps in fields such as geochemistry and radiometric dating.