Average Atomic Mass of Chlorine from Isotope Data

Given

• Isotope 1: 35Cl, mass = 34.969 u, abundance = 75.78%

• Isotope 2: 37Cl, mass = 36.966 u, abundance = 24.22%

Find

The average atomic mass of natural chlorine in u.

Principle

The atomic mass on the periodic table is a weighted average: each isotope's mass is multiplied by its natural fractional abundance, and the products are added. A high-abundance isotope pulls the average toward its own mass, which is why chlorine's table value sits near 35 rather than 37.

Formula

Solution

1. Convert percentages to fractions: 75.78% = 0.7578 and 24.22% = 0.2422. Check they sum to 1: 0.7578 + 0.2422 = 1.0000.

2. Contribution of 35Cl: 0.7578 x 34.969 u = 26.500 u.

3. Contribution of 37Cl: 0.2422 x 36.966 u = 8.953 u.

4. Add the contributions: 26.500 + 8.953 = 35.453 u.

5. Rounded to four significant figures: 35.45 u, matching chlorine's standard atomic weight.

Unit check

Abundance fractions are unitless, so fraction x mass gives mass in u, and the sum stays in u — a mass-weighted average must carry the same mass unit as its components.

What this means physically

No single chlorine atom weighs 35.45 u — every atom is either 34.969 or 36.966 u. The 35.45 u figure is the blend average over a natural sample, and it sits closer to 35 because the lighter isotope is three times more abundant. This is exactly the number used on the periodic table.