Question

Sulfur is composed of three isotopes: 32S, 33S, and 34S. The atomic masses of these isotopes are given below. 32S: 31.97207 amu 33S: 32.97146 amu 34S: 33.96786 amu The abundance of 34S is 4.22%. Given the average atomic mass of sulfur (32.07 amu), determine the abundance of 32S to two decimal places.

Answer 1

Abundance of 32S is 94.41%

Step-by-step explanation:

The average atomic mass is defined as the sum of the atomic masses of each isotope times its abundance:

Average atomic mass = ∑ Atomic mass istope*Abundance

For the sulfur:

32.07amu = 31.97207X + 32.97146Y + 33.96786*0.0422 (1)

Where X is abundance of 32S and Y abundance of 33S

Also we can write:

1 = X + Y + 0.0422 (2)

0.9578 - X = Y

Because the sum of the abundances = 1

Replacing (2) in (1):

32.07amu = 31.97207X + 32.97146(0.9578 - X) + 33.96786*0.0422

32.07 = 31.97207X + 31.58006 - 32.97146X + 1.43344

-0.9435 = -0.99939X

0.9441 =X

In percentage, abundance of 32S is 94.41%