Average atomic mass problem

Question

An element consists of three isotopes. The abundance of one isotope is 92.21% and its atomic mass is 27.97693 amu. The abundance of the second isotope is 4.70% and its atomic mass is 28.97649 amu. The atomic mass of the third isotope is 29.97376 u. What is the average atomic mass of the element?

a. 28.98 amu

b. 29.87 amu

c. 28.09 amu

d. 29.07 amu

e. 28.96 amu

I got C. I wnt o know what went wrong and why that isn't the correct answer. formula I used

( 27.97693 * .9221) + (28.97649 * .047) + (29.97376 * .0309)

the percent for the third isotope is 100 - 92.21 - 4.7 = 3.09

Answer 1

Since we know the % abundance of the first two isotopes, we can easily find the % abundance of the third isotope (as you have shown):

Abundance of third isotope = 100% - 92.21% - 4.70% = 3.09%

Now, we'll do the calculations and see if we come to the same answer that you did:

(0.9221 x 27.97693) + (0.0470 x 28.97649) + (0.0309 x 29.97376) =

25.7975 + 1.3619 + 0.9262 = 28.09 amu = answer (c)

So, why do you say that isn't the correct answer? If your answer key says something else, perhaps they made the mistake, and not you.