Rhenium has two naturally occurring isotopes: Re-185 with a natural abundance of 37.40% and Re-187 with a natural abundance of 62.60%. The sum of the masses of the two isotopes is 371.9087 amu. Find the masses of the individual isotopes.
Solution 116P
Explanation:
The atomic weight of Rhenium (Re) as found on the periodic table of the elements is 186.207. Let x = the atomic weight of Re-185 and (371.9087 - x) = the atomic weight of Re-187.
Known/Given:
atomic weight of Re = 186.207 amu
x = atomic weight of Re-185 in amu
(371.9087 - x) = atomic weight of Re-187 in amu
abundance of Re-185 = 37.40% = 0.3740
abundance of Re-187 = 62.60% = 0.6260
Unknown:
atomic masses of Re-185 and Re-187
Solution:
Note: In order to reduce rounding errors, I will include guard digits and round to the proper number of significant figures at the end.
Step 1:
Multiply x times the abundance of Re-185 and multiply (371.9087 - x) times the abundance of Re-187.
Re-185: (0.3740)(x) = 0.3740x
Re-187: (0.6260)(371.9087 - x) = 232.8148462 - 0.6260x
