# The atomic weight of a newly discovered element is 110.352 amu. It has two naturally occurring isotopes. One has a mass of 111.624 amu. The other has an isotopic mass of 109.75 amu. What is the percent abundance of the last isotope (109.75 amu)?

##### 1 Answer

#### Explanation:

The idea here is that each isotope will contribute to the average atomic mass of the element **proportionally** to their respective abundance.

Now, the key to this problem lies in how you can write the abundances of the two isotopes.

Let's assume that the *decimal abundance*, which is simply the percent abundance divided by

Since you only have **two isotopes**, it follows that their decimal abundances must **add up to give**

The average atomic mass of the element can be calculated using

#color(blue)("avg. atomic mass" = sum_i("isotope"_i xx "abundance"_i))#

In your case, you would have

#"110.352 u" = "111.624 u" xx (1-x) + "109.75 u" xx x#

This is equivalent to

#110.352 = 111.624 - 111.624 * x + 109.75 * x#

#1.874 * x = 1.272 implies x = 1.272/1.874 = 0.67876#

The *percent abundances* of the two isotopes will be

#"111.624 u " -> " 32.124%# #"109.75 u " -> " 67.876%#