Question

1. the pie - graph shows the abundance of the two kinds of silver atoms found in nature. the more abundant isotope has an atomic mass of a little less than 107, but the average atomic mass of silver on the periodic table is about 107.9. explain why it is higher.

calculate the average atomic masses using the following data for #5 - 14.

1. isotope mass (u) fractional abundance

mg - 24 23.985 78.7%
mg - 25 24.986 10.13%
mg - 26 25.983 11.17%
average atomic mass of magnesium =

1. isotope mass (u) fractional abundance

ir - 191 191.0 37.58%
ir - 193 193.0 62.42%
average atomic mass for iridium =

1. isotope mass (u) fractional abundance

li - 6 6.015 7.59%
li - 7 7.016 92.41%
average atomic mass of lithium =

1. isotope mass (u) fractional abundance

cr - 50 49.946 4.35%
cr - 52 51.941 83.8%
cr - 53 52.941 9.5%
cr - 54 53.939 2.35%
average atomic mass of chromium =

Explanation:

Step1: Recall average atomic mass formula

The average atomic mass of an element is calculated as the sum of the products of the mass of each isotope and its fractional abundance, i.e., $Average\ atomic\ mass=\sum_{i} (mass_{i}\times fractional\ abundance_{i})$.

Step2: Calculate average atomic mass of magnesium

$Average\ atomic\ mass\ of\ Mg=(23.985\times0.787)+(24.986\times0.1013)+(25.983\times0.1117)$
$=18.8762+2.5311+2.9023$
$=24.3096\ u$

Step3: Calculate average atomic mass of iridium

$Average\ atomic\ mass\ of\ Ir=(191.0\times0.3758)+(193.0\times0.6242)$
$=71.7778+120.4706$
$=192.2484\ u$

Step4: Calculate average atomic mass of lithium

$Average\ atomic\ mass\ of\ Li=(6.015\times0.0759)+(7.016\times0.9241)$
$=0.4565+6.4894$
$=6.9459\ u$

Step5: Calculate average atomic mass of chromium

$Average\ atomic\ mass\ of\ Cr=(49.946\times0.0435)+(51.941\times0.838)+(52.941\times0.095)+(53.939\times0.0235)$
$=2.1727+43.5266+5.0294+1.2676$
$=51.9963\ u$

Answer:

Average atomic mass of magnesium = $24.3096\ u$
Average atomic mass for iridium = $192.2484\ u$
Average atomic mass of lithium = $6.9459\ u$
Average atomic mass of chromium = $51.9963\ u$