Question- Chlorine has two isotopes,35Cl and 37Cl; 75.77 % of chlorine is 35Cl, and 24.23% is 37Cl. The atomic mass of 35Cl is 34.969 amu, and the atomic mass of 37Cl is 36.966 amu. What is the atomic weight of Chlorine?
(Hint: atomic mass = the weighted average mass of the isotopes in the element)
Solution
The atomic mass and atomic weight are synonyms that consider the weighted average of naturally occurring isotopes of all the atoms of an element.
An isotope’s contribution to the element’s atomic weight is given a ‘weightage’ or a ‘value’ derived from its natural abundance and the isotopic atomic mass. The results are then added to obtain the average atomic mass.
Weightage of 35Cl= percentage abundance of isotope 35Cl x atomic mass of isotope 35Cl
= 75.77/100 x 34.969 = 0.7577 x 34.969 = 26.496
Weightage of 37Cl= percentage abundance of isotope 37Cl x atomic mass of isotope 37Cl
= 24.23/100 x 36.966 = 0.2423 x 36.966 = 8.956
Average atomic weight of Cl= 26.496+ 8.956= 35.45
Solution using Log Table
The Atomic mass of 35Cl =34.969 amu
The Atomic mass of 37Cl = 36.966 amu
Percentage abundance of 35Cl =75.77 %
Percentage abundance of 37Cl =24.23 %
Atomic weight of Cl = Atomic mass of 35Cl x % abundance of 35Cl/100 + Atomic mass of 37Cl x % abundance of 37Cl/100
Atomic weight (A) = 34.969 x 75.77/100 + 36.966 x 24.23/100
= (34.969 x 0.7577) + (36.966 x 0.2423)
= 26.496 + 8.956
Taking log on both sides
log10A = log (26.496 + 8.956)
= log (35.45) = 1. 5496
A = antilog (1.5496) = 35.45 amu
Therefore, the atomic weight of the Cl atom is 35.5 amu.
Related Read : How to Calculate Average atomic mass