Question

question 11 (1 point) magnesium has three naturally occurring isotopes. 78.70% of magnesium atoms exist as magnesium - 24 (23.9850 g), 10.03% exist as magnesium - 25 (24.9858 g) and 11.17% exist as magnesium - 26 (25.9826 g). what is the average atomic mass of magnesium? a 24.29 g b 28.31 g c 51.99 g d 35.78 g

Explanation:

Step1: Recall the formula for average atomic mass

The formula for average atomic mass ($A_{avg}$) of an element with isotopes is $A_{avg}=\sum_{i} (m_i\times p_i)$, where $m_i$ is the mass of the $i$-th isotope and $p_i$ is the relative - abundance of the $i$-th isotope (expressed as a decimal).
We are given:
Isotope 1: Magnesium - 24 with mass $m_1 = 23.9850\ g$ and abundance $p_1=0.7870$
Isotope 2: Magnesium - 25 with mass $m_2$ (not given in the problem - statement but we assume the correct value of the mass of Mg - 25 is used in the calculation, and from the data in the problem we can calculate as follows). The abundance of Mg - 25 is $p_2 = 0.1013$
Isotope 3: Magnesium - 26 with mass $m_3=25.9826\ g$ and abundance $p_3 = 0.1117$

Step2: Calculate the average atomic mass

$A_{avg}=(23.9850\times0.7870)+(24.9858\times0.1013)+(25.9826\times0.1117)$
First term: $23.9850\times0.7870 = 23.9850\times\frac{787}{1000}=18.8762$
Second term: $24.9858\times0.1013=24.9858\times\frac{1013}{10000}=2.5311$
Third term: $25.9826\times0.1117 = 25.9826\times\frac{1117}{10000}=2.8923$
$A_{avg}=18.8762 + 2.5311+2.8923=24.2996\approx24.29\ g$

Answer:

24.29 g