Question

question 6 (2 points) average atomic masses listed by iupac are based on a study of experimental results. ms. leung discovered an element that has two isotopes, 79 - le and 81 - le, whose masses (78.9183 and 80.9163 amu). calculate the percent abundances of both isotopes of le (leungstonium). the weighted average of the two isotopes is 80.357 amu. write your answers to 2 decimal places and include units.

Explanation:

Step1: Recall the weighted - average formula

The formula for the weighted - average atomic mass ($A$) of an element with two isotopes is $A = m_1x_1 + m_2x_2$, where $m_1$ and $m_2$ are the masses of the isotopes and $x_1$ and $x_2$ are their respective fractional abundances. Given that the sum of the fractional abundances of two isotopes is 1, if the fractional abundance of the first isotope is $x$, the fractional abundance of the second is $1 - x$. Let the mass of the first isotope $m_1=78.9183$ amu and the mass of the second isotope $m_2 = 80.9163$ amu. The weighted - average atomic mass $A = 80.357$ amu.

Step2: Set up the equation

$80.357=78.9183x+(80.9163)(1 - x)$

Step3: Expand the equation

$80.357=78.9183x + 80.9163-80.9163x$

Step4: Combine like - terms

$80.357-80.9163=78.9183x-80.9163x$
$- 0.5593=-1.998x$

Step5: Solve for $x$

$x=\frac{0.5593}{1.998}\approx0.28$
The fractional abundance of the first isotope with mass 78.9183 amu is $x\approx0.28$, and the fractional abundance of the second isotope with mass 80.9163 amu is $1 - 0.28 = 0.72$.

Answer:

The percent abundances of the two isotopes are approximately 28.00% and 72.00% (rounded to two decimal places).