What is the average atomic mass of the element in the data table?
| Mass (amu) | Abundance (%) |
| :---------- | :------------- |
| 35.0 | 75.77 |
| 37.0 | 24.23 |
A. 63.9 amu
B. 21.0 amu
C. 41.2 amu
D. 35.5 amu
Answer (2)
Convert percentages to decimals.
Multiply the mass of each isotope by its decimal abundance.
Add the results to obtain the average atomic mass.
The average atomic mass is approximately 35.5 amu.
Explanation
Understanding the Problem We are given the mass and abundance of two isotopes of an element and asked to find the average atomic mass of the element. The average atomic mass is the weighted average of the masses of the isotopes, where the weights are the abundances of the isotopes.
Converting Percentages to Decimals First, we need to convert the percentages to decimals. To do this, we divide each percentage by 100. So, 75.77% becomes 0.7577 and 24.23% becomes 0.2423.
Multiplying Mass by Abundance Next, we multiply the mass of each isotope by its decimal abundance. For the first isotope, this is 35.0 amu * 0.7577 = 26.5195 amu. For the second isotope, this is 37.0 amu * 0.2423 = 8.9651 amu.
Adding the Results Finally, we add the results to obtain the average atomic mass: 26.5195 amu + 8.9651 amu = 35.4846 amu.
Final Answer Therefore, the average atomic mass of the element is approximately 35.4846 amu. Rounding to one decimal place, we get 35.5 amu.
Examples
The concept of average atomic mass is crucial in various fields. For instance, in chemistry, it helps in determining the molar mass of compounds, which is essential for stoichiometric calculations. In environmental science, understanding isotopic abundances can aid in tracing the origin and fate of pollutants. Moreover, in nuclear medicine, isotopes with specific average atomic masses are used for diagnostic and therapeutic purposes, highlighting the practical significance of this concept.
To find the average atomic mass, we converted the abundance percentages to decimals, multiplied each isotope's mass by its decimal abundance, and then added those values together. The result, rounded to one decimal place, is approximately 35.5 amu. Therefore, the correct answer is option D: 35.5 amu.
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