Answer to Question #190473 in General Chemistry for isabelle cunha

Question

The metal rhenium (Re) was predicted to exist by Dmitri Mendeleev but was not discovered until 1925. Rhenium is composed of two isotopes, Re-185 (mass 184.95 amu) and Re-187 (mass 186.96 amu). Given that the average atomic mass rhenium is 186.21 u, calculate the percent abundance of each of these isotopes.  Show a full solution and round the final answer to 1 decimal place. 

Answer 1

We know that

average atomic mass of Rhenium =$m_1P_1+m_2P_2$

m= mass

P= percentage of abundance

Let x% for Re-185

And (100-x)% for Re-187

Now

$186.21=(184.95){x\over100} + (186.96){(100-x)\over100}$

$186.21×100=184.95x-186.96x+186.96×100$

$75=2.01x$

Percentage of abundance i.e

$x=37.3\% \ Re -185 \\ 100-x=62.7\% \ Re-187$