Question

Average atomic mass of chlorine is 35.5. It occurs in atmosphere in two isotopic forms 17cl35 and 17cl37 . The percentage abundance of these isotopes are respectively
(1) 80% and20% (2)75% and25% (3) 70% and30% (4) 60% and 40%

Answer 1

When isotopes are present, atomic mass is taken as their weighted average.
Let percentage of 17c|35 chlorine = x%
      percentage of 17c|37 chlorine = (100-x)% (as only 2 isotopes are there)

Atomic weight = [(35 × x) + ( 37× (100-x))] / 100
⇒35.5 = [35x + 3700 -37 x ] / 100
⇒3550 = -2x + 3700
⇒ 3550-3700 = -2x
⇒ 2x = 150
⇒ x = 75
100 - x = 25

So percentage of 17c|35 chlorine = 75%
      percentage of 17c|37 chlorine = 25%

Answer is (2).

Answer 2

Answer :

Given,

Average atomic mass of chlorine = 35.5

There are two isotopes of Chlorine :-

1) 17Cl35

2) 17Cl37

To find,

The abundance in nature of each of the element.

Solution :

Let the abundance of 17Cl35 be x%

We know there are only two isotopes of Chlorine ( till date )

So

Abundance of 17Cl37 = (100 -x)%

We know,

Average atomic mass = [(percentage of 1st isotope × atomic mass)+(percentage of 2nd isotope × atomic mass)]/100

Putting the values ( that we know ) :-

35.5 = [(x × 35)+((100-x)×37)]/100

35.5 = [ 35x + 3700 - 37x]/100

35.5 = ( -2x + 3700 )/100

35.5 × 100 = -2x + 3700

3550 = -2x + 3700

-2x = 3550 - 3700

-2x = -150

x = -150/-2

x = 75

Percentage abundance of 17Cl35= 75%

Percentage abundance of 17Cl37 =( 100 - 75)% = 25%