Average Atomic Mass Calculations - Chemistry

1. Fundamental Concepts

Definition: Average atomic mass is the weighted average of the masses of all naturally occurring isotopes of an element.
Isotopes: Atoms of the same element with different numbers of neutrons and, consequently, different masses.
Natural Abundance: The percentage of each isotope found in nature.

2. Key Concepts

Formula for Average Atomic Mass: $${\text{Average Atomic Mass}} = \sum ( \text{fractional abundance} \times \text{isotopic mass} )$$

Fractional Abundance: $${\text{Fractional Abundance}} = \frac{\text{natural abundance}}{100}$$

Application: Used to determine the average atomic mass of elements in the periodic table, which is crucial for stoichiometric calculations in chemistry.

3. Examples

Easy
Problem:

An element has two isotopes:

10 amu (50%)

12 amu (50%)

Solution:

$(10)(0.50) + (12)(0.50) = 5 + 6 = 11 \text{ amu}$

Medium

Problem:

Chlorine has two isotopes:

Cl-35 (34.97 amu, 75%)

Cl-37 (36.97 amu, 25%)

Solution:

$(34.97)(0.75) + (36.97)(0.25) = 26.23 + 9.24 = 35.47 \text{ amu}$

Hard
Problem:

An element has three isotopes:

| Isotope | Mass (amu) | Abundance |

| ------- | ---------- | --------- |

| A | 24.0 | 78.99% |

| B | 25.0 | 10.00% |

| C | 26.0 | 1.01% |

Solution:

$(24.0)(0.7899) + (25.0)(0.1000) + (26.0)(0.0101)$

$= 18.96 + 2.50 + 0.26 = 21.72 \text{ amu}$

4. Problem-Solving Techniques

Organize Data: List the isotopes, their masses, and their natural abundances in a table.
Convert Percentages: Always convert natural abundances from percentages to decimal form (fractional abundances).
Use a Calculator: Use a scientific calculator to handle the multiplication and addition accurately.
Check Units: Ensure that the final answer is in atomic mass units (amu).
Verify Results: Compare your calculated average atomic mass with the standard values provided in the periodic table.