Atomic Masses and Isotopic Calculations in GOB Chemistry

Atomic Masses

Definition and Determination

The atomic mass of an element is the weighted average mass of all its naturally occurring isotopes. It is a fundamental property that can be found on the periodic table and is essential for chemical calculations.

• Units: Atomic mass is typically expressed in grams per mole (g/mol), atomic mass units (amu), or daltons (Da).

• Isotopes: Atoms of the same element with different numbers of neutrons, resulting in different masses.

• Periodic Table: The atomic mass of each element is listed, usually as a decimal number below the element symbol.

Example: The element with the greatest atomic mass in the first column (Group 1A) of the periodic table is Cesium (Cs).

Units and Conversion

• Atomic mass unit (amu): A standard unit for expressing atomic and molecular weights. 1 amu = $1.66 \times 10^{-27}$ kg.

• Dalton (Da): Another name for the atomic mass unit; 1 Da = 1 amu.

Comparing Atomic Masses

When comparing atomic masses, use the value provided in the periodic table or convert between units as needed.

• Practice Example: Given several elements with different atomic masses, the one with the highest value (e.g., 0.350 kg) has the greatest atomic mass.

Calculating Atomic Mass

Isotopic Masses and Percent Abundances

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

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

• Percent Abundance: The percentage of each isotope present in a natural sample of the element.

• Fractional Abundance: The percent abundance divided by 100.

Atomic Mass Formula

The atomic mass is calculated using the following formula:

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

Step-by-Step Calculation

1. Convert percent abundances to fractional abundances: Divide each percent abundance by 100.

2. Multiply each isotope's mass by its fractional abundance.

3. Add the results to obtain the atomic mass.

Example Calculation

Gallium has two naturally occurring isotopes:

• Ga-69: Mass = 68.9256 amu, Abundance = 60.11%

• Ga-71: Mass = 70.9247 amu, Abundance = 39.89%

Convert percent abundances:

• Ga-69: $\frac{60.11}{100} = 0.601$

• Ga-71: $\frac{39.89}{100} = 0.399$

Calculate atomic mass:

$\text{Atomic Mass} = (68.9256 \times 0.601) + (70.9247 \times 0.399)$

$= 41.397 + 28.325 = 69.722$ amu

Practice Problems

Isotopic Calculations

• Magnesium Isotopes: Three isotopes exist: $^{24}\text{Mg}$ (78.70%, 23.98504 amu), $^{25}\text{Mg}$ (10.13%, unknown mass), $^{26}\text{Mg}$ (11.17%, 25.98259 amu). Use the atomic mass formula to solve for the unknown mass.

• Silver Isotopes: Given atomic mass of silver (107.868 amu), Ag-109 (108.905 amu, 48.16% abundance), solve for the mass of the other isotope.

Summary Table: Key Terms and Definitions

Term	Definition	Units
Atomic Mass	Weighted average mass of all isotopes of an element	g/mol, amu, Da
Isotopic Mass	Mass of a specific isotope	amu
Percent Abundance	Percentage of a specific isotope in a natural sample	%
Fractional Abundance	Percent abundance divided by 100	Unitless

Additional info:

• Atomic mass values are essential for stoichiometric calculations in chemistry.

• Understanding isotopic composition helps explain variations in atomic mass for elements with multiple naturally occurring isotopes.