Q49P - Chemistry: Molecular Nature Of Matter And Change

Question

Chlorine has two naturally occurring isotopes,${}^{\mathbf{35}}\mathit{C}\mathit{l}$(isotopic mass 34.9689 amu) and ³⁷Cl (isotopic mass 36.9659 amu). If chlorine has an atomic mass of 35.4527 amu, what is the percent abundance of each isotope?

Step-by-Step Solution

Answer

Percentage abundance of isotope ${}^{35}Cl$= 75.77 %

Percentage abundance of isotope ${}^{37}Cl$= 24.23 %

Step 1: Average atomic mass

Definition: Average atomic mass of an element is defined as the sum of masses of each isotope each multiplied by their natural fractional abundance.

Formula:

Step 2: Calculation of fractional abundance of isotope 35 Cl

³⁵Cl

Let the fractional abundance of isotope ³⁵Cl be `X`

So, fractional abundance of isotope ³⁷Cl  will be `1 – X`

For isotope ³⁵Cl :

Mass of isotope ³⁵Cl = 34.9689 amu

Fractional abundance of isotope ³⁵Cl  = X

For isotope ³⁷Cl :

Mass of isotope ³⁷Cl = 36.9659 amu 

Fractional abundance of isotope ³⁷Cl = 1 – X

Putting values in formula of average atomic mass 

Step 3 : Calculation of percentage abundance of isotopes

Percentage abundance of isotope ${}^{35}Cl$=

Percentage abundance of isotope ${}^{37}Cl$= 

Hence, the percentage abundance of isotope ${}^{35}Cl$and isotope ${}^{37}Cl$are 75.77% and 24.23 % respectively.