Question

recall that all isotopes of an element have the same physical and chemical properties, with the exception of atomic mass (and for unstable isotopes, radioactivity). therefore, the periodic table lists a weighted - average atomic mass for each element. in order to calculate this quantity, the natural abundance and atomic mass of each isotope must be provided.

1. use one of the methods in model 3 that gave the correct answer for average atomic mass to calculate the average atomic mass for oxygen. isotope information is provided below. show all of your work and check your answer against the mass listed on the periodic table.

isotope	natural abundance on earth (%)	atomic mass (amu)
$^{17}$o	0.04	16.9991
$^{18}$o	0.20	17.9992

(99.76)(15.9949)+(0.04)(16.9991)+(0.20)(17.9992)

1. consider the individual atomic masses for magnesium isotopes given in model 2.

a. which isotope has an atomic mass closest to the average atomic mass listed on the periodic table?
b. give a mathematical reason for your answer to part a.
boron has two naturally - occurring isotopes: boron - 10 and boron - 11. which isotope is more abundant on earth? use grammatically correct sentences to explain how your group determined the answer.

Explanation:

Step1: Recall average atomic mass formula

The average atomic mass ($A_{avg}$) of an element is calculated as $A_{avg}=\sum_{i = 1}^{n}(x_i\times m_i)$, where $x_i$ is the natural - abundance (in decimal form) of the $i$ - th isotope and $m_i$ is the atomic mass of the $i$ - th isotope.

Step2: Convert percentages to decimals

For $^{16}O$: $x_1 = 0.9976$, $m_1=15.9949$ amu; for $^{17}O$: $x_2 = 0.0004$, $m_2 = 16.9991$ amu; for $^{18}O$: $x_3=0.0020$, $m_3 = 17.9992$ amu.

Step3: Calculate average atomic mass

$A_{avg}=(0.9976\times15.9949)+(0.0004\times16.9991)+(0.0020\times17.9992)$
$A_{avg}=15.9949\times0.9976+16.9991\times0.0004 + 17.9992\times0.0020$
$A_{avg}=15.9564+0.0068+0.0360$
$A_{avg}=15.9992$ amu

Answer:

The average atomic mass of oxygen is approximately $15.9992$ amu.