Why chlorine weighs 35.5 u

The idea

The average atomic mass of an element is found by multiplying the mass of each isotope by its percent relative abundance and adding the results; unlike a simple average, it reflects the element as it occurs in nature.

Two kinds of chlorine

Chlorine has two isotopes, one of mass 35 u and one of mass 37 u. They are not equally common.

What should we take as the mass of chlorine as it occurs in nature?

• A value between 35 u and 37 u, worked out from how common each isotope is
• Exactly 35 u
• Exactly 37 u

Mix the isotopes

Slide the share of ³⁵Cl. The rest is ³⁷Cl. The coloured dots show 20 atoms as an example.

A weighted average

A simple average treats both isotopes as equally common. The weighted average multiplies each mass by its share and adds them. For chlorine, it is 35 × 0.75 + 37 × 0.25 = 35.5 u.

The average atomic mass is found by multiplying the mass of each isotope by its percent relative abundance and adding the results. Unlike a simple average, this weighted average reflects the element as it occurs in nature.

Notes

Average atomic mass = (mass of each isotope × its percent abundance), added up. Unlike a simple average, it reflects the element as it occurs in nature, for example 35.5 u for chlorine.

Check yourself

Chlorine: ³⁵Cl (35 u) is 75 % and ³⁷Cl (37 u) is 25 %. What is the weighted average atomic mass in u?

Answer: 35.5

35 × 0.75 + 37 × 0.25 = 26.25 + 9.25 = 35.5 u.

Why is 36 u not the accurate average mass of chlorine?

An example (not from the book): an element has isotopes of 10 u (60 %) and 20 u (40 %). What is the weighted average atomic mass in u?

Answer: 14

10 × 0.60 + 20 × 0.40 = 6 + 8 = 14 u.

Does the value 35.5 u mean that one chlorine atom has a mass of 35.5 u?

• The isotope ³⁷Cl does not occur in nature. Chlorine occurs in two isotopic forms, ³⁵Cl and ³⁷Cl.
• The heavier isotope should be ignored. Both isotopes count, each in proportion to how common it is.
• It treats both isotopes as equally common, but they are not — correct. Yes!
• No. Each atom is 35 u or 37 u, and 35.5 u is the average over many atoms — correct. Yes!
• Yes, every chlorine atom has a mass of 35.5 u. Chlorine atoms are either ³⁵Cl or ³⁷Cl, with masses 35 u or 37 u.
• No, because chlorine has only one isotope. Chlorine occurs in two isotopic forms, 35 u and 37 u.