8. what is the calculated average atomic mass for the mystery element given? round to the nearest hundredth

Explanation:

Step1: Recall average - atomic - mass formula

The formula for the average atomic mass of an element with isotopes is $Average\ atomic\ mass=\sum_{i}(m_i\times p_i)$, where $m_i$ is the atomic mass of the $i$ - th isotope and $p_i$ is the percent - abundance of the $i$ - th isotope (expressed as a decimal).

Step2: Convert percent - abundances to decimals

For Mg - 24 with abundance 78.99%, $p_1 = 0.7899$; for Mg - 25 with abundance 10.00%, $p_2=0.1000$; for Mg - 26 with abundance 11.01%, $p_3 = 0.1101$. The atomic masses are $m_1 = 23.99$, $m_2 = 24.99$, $m_3 = 25.98$.

Step3: Calculate the weighted sums

$m_1\times p_1=23.99\times0.7899 = 23.99\times(0.79 - 0.0001)=23.99\times0.79-23.99\times0.0001=18.9521 - 0.002399 = 18.949701$. $m_2\times p_2=24.99\times0.1000 = 2.499$. $m_3\times p_3=25.98\times0.1101=25.98\times(0.11+0.0001)=25.98\times0.11 + 25.98\times0.0001=2.8578+0.002598 = 2.860398$.

Step4: Sum up the weighted sums

$Average\ atomic\ mass=m_1\times p_1 + m_2\times p_2+m_3\times p_3=18.949701+2.499+2.860398 = 24.309099\approx24.31$.

Answer:

24.31