How do you calculate atomic weight?

The atomic weight of an element is calculated as the weighted average of the masses of its isotopes, considering their relative abundances. Here's a breakdown of the process:

Steps to Calculate Atomic Weight

1. Determine the Isotopes and Their Masses: Identify all the isotopes of the element and their exact masses (usually given in atomic mass units, amu).
2. Find the Percent Abundances: Obtain the percent abundance of each isotope. This indicates how frequently each isotope occurs naturally.
3. Convert Percent Abundances to Decimal Fractions: Divide each percent abundance by 100 to convert it to a decimal fraction, representing the mass fraction of each isotope.
4. Calculate the Weighted Mass of Each Isotope: Multiply the exact mass of each isotope by its corresponding decimal fraction (mass fraction). This gives the weighted mass for each isotope.
5. Sum the Weighted Masses: Add up all the weighted masses calculated in the previous step. The result is the atomic weight of the element.

Formula

The formula for calculating atomic weight is:

Atomic Weight = (Mass of Isotope 1 × Abundance of Isotope 1) + (Mass of Isotope 2 × Abundance of Isotope 2) + ... + (Mass of Isotope n × Abundance of Isotope n)

Where:

• Mass of Isotope is the exact mass of the isotope.
• Abundance of Isotope is the decimal fraction representing the isotope's abundance.

Example

Let's say we want to calculate the atomic weight of chlorine (Cl). Chlorine has two naturally occurring isotopes:

• Chlorine-35 (³⁵Cl): Mass = 34.96885 amu, Abundance = 75.77%
• Chlorine-37 (³⁷Cl): Mass = 36.96590 amu, Abundance = 24.23%

Here's how we calculate the atomic weight:

1. Convert Percent Abundances to Decimal Fractions:

   • ³⁵Cl: 75.77% / 100 = 0.7577
   • ³⁷Cl: 24.23% / 100 = 0.2423

2. Calculate the Weighted Mass of Each Isotope:

   • ³⁵Cl: 34.96885 amu × 0.7577 = 26.496 amu
   • ³⁷Cl: 36.96590 amu × 0.2423 = 8.957 amu

3. Sum the Weighted Masses:

   • Atomic Weight of Cl = 26.496 amu + 8.957 amu = 35.453 amu

Therefore, the atomic weight of chlorine is approximately 35.453 amu.

Key Considerations

• Isotopes: Atoms of the same element with different numbers of neutrons.
• Exact Mass: The precise mass of an isotope, usually measured using mass spectrometry.
• Weighted Average: A type of average where some elements of the data set contribute more than others to the final average. In this case, isotopes with higher abundances contribute more to the atomic weight.