Question

The element chlorine has two stable isotopes, chlorine-35 with a mass of 34.97 amu and chlorine-37 with a mass of 36.95 amu. From the atomic weight of Cl = 35.45 one can conclude that:

Answer 1

Answer: One isotope has a percentage abundance of 75.75 % and the percentage abundance of another isotope is 24.24%.

Explanation:

We are given the two stable isotopes of chlorine with their respective masses. The average atomic mass of chlorine is also given.

Average atomic mass of chlorine = 35.45 amu.

Let us assume the fractional abundance of one isotope be 'x' and the fractional abundance for another isotope will be (1 - x) because the total fractional abundance is always equal to 1.

• For Chlorine-35 isotope:

Fractional abundance = x

Mass = 34.97 amu

• For Chlorine-37 isotope:

Fractional abundance = 1 - x

Mass = 36.95 amu

The formula for the calculation of average atomic mass is given by:

$\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i$

Putting values in above equation, we get:

$35.45=34.97(x)+36.95(1-x)\\\\35.45=34.97x+36.95-36.95\\\\-1.5=-1.98x\\\\x=\frac{-1.5}{-1.98}=0.7575$

$1-x=1-0.7575=0.2424$

Converting these two fractional abundances into percentage abundances by multiplying it with 100.

$x=0.7575\times 100=75.75\%\\\\1-x=0.2424\times 100=24.24\%$

Hence, one isotope has a percentage abundance of 75.75 % and the percentage abundance of another isotope is 24.24%.