Question

1. rhenium, re, is one of the rarest elements on earth. alloys containing rhenium are used for oven filaments and x - ray machines. the average atomic mass of naturally occurring rhenium is 186.21 amu. there are two common isotopes of naturally occurring rhenium. using the information given below, calculate the percent abundance of naturally occurring rhenium. isotope mass (amu) re - 185 184.95 re - 187 186.96

Explanation:

Step1: Let the abundance of Re - 185 be $x$, then the abundance of Re - 187 is $1 - x$.

Step2: Use the average - atomic - mass formula: $186.21=184.95x + 186.96(1 - x)$.

Step3: Expand and solve for $x$.

$186.21=184.95x+186.96 - 186.96x$.
$186.21 - 186.96=(184.95 - 186.96)x$.
$- 0.75=- 2.01x$.
$x=\frac{0.75}{2.01}\approx0.373$.
The abundance of Re - 185 is about $37.3\%$, and the abundance of Re - 187 is about $1 - 0.373 = 0.627$ or $62.7\%$.

Answer:

The abundance of Re - 185 is approximately $37.3\%$ and the abundance of Re - 187 is approximately $62.7\%$.