Oxygen (atomic mass = 15.9949 amu) has three isotopes with masses 15.9949 amu, 16.9993 amu, and 17.9992 amu. The abundance of the last isotope is 0.204%.

Question

Oxygen (atomic mass = 15.9949 amu) has three isotopes with masses 15.9949 amu, 16.9993 amu, and 17.9992 amu. The abundance of the last isotope is 0.204%. Estimate the abundance of the other two isotopes.

Please help! It would be much appreciated if someone could explain the whole process, thank you!

Answer 1

There's a typo in your question, Oxygen has an Atomic Mass of 15.9994 not 15.9949.

Atomic mass of an element is calculated by taking the atomic mass of isotope #1 times the percentage of that isotope found in the world (called its "abundance") plus the atomic mass of isotope #2 times its abundance plus the atomic mass of isotope #3 times its abundance . . . until all naturally occurring isotopes are covered. So it's a weighted average. Consequently, the sum of all the "abundances" must add up to 100% or 1.00.

So, if we identify isotope #1 as the one with weight 15.9949 and say its abundance is a₁ and if we say isotope #2 is the one with weight 16.9993 and say its abundance is a₂ then we can say the following:

1) a₁ + a₂ + 0.00204 = 1.000000 (notice I converted percent to a decimal)

and

2) 15.9994 = (15.9949)(a₁) + (16.9993)(a₂) + (17.9992)(0.00204)

Solving equation 1) above for a₂, we get a₂ = (0.99796)(a₁)

Substituting "(0.99796)(a₁)" for a₂ in equation 2) above, we get:

15.9994 = (15.9949)(a₁) + (16.9993)(0.99796)(a₁) + (17.9992)(0.00204)

and then we can solve for a₁ to get a₁ = 0.99755 or 99.755%

Then plugging 0.99755 in for a₁ into equation 1), we get a₂ = 0.000409 or 0.0409%