Answer to Question #124471 in General Chemistry for Japhet Mtalai

Question

Nitrogen is made up ot two isotopes, N-14 and N-15. Given nitrogen's atomic weight of 14.007, What is the percent abundance of each of isotopes?

Answer 1

Assuming atomic masses of N-14 and N-15 to be exactly 14 and 15 amu respectively,

14x + 15 (1 - x) = 14.007,

where x*100% is the percent abundance of N-14, and (1 - x)*100% is the percent abundance of N-15.

From the equation above, x = 0.993 => percent abundance of N-14 is 99.3%, and the percent abundance of N-15 is 0.7%.

However, the actual masses of N-14 and N-15 isotopes rounded to three decimal places are 14.003 and 15.000 amu respectively. In this case

14.003x + 15.000 (1 - x) = 14.007;

x = 0.996.

=> percent abundance of N-14 is 99.6%, and the percent abundance of N-15 is 0.4%.

Answer: N-14 - 99.3%, N-15 - 0.7% assuming isotope masses to be 14 and 15 respectively;

N-14 - 99.6%, N-15 - 0.4% considering their real (actual) masses.