What is the average atomic mass of the element in the data table?
| Mass (amu) | Abundance (%) |
|---|---|
| 10.0 | 19.9 |
| 11.0 | 80.1 |
A. 21.0 amu
B. 41.2 amu
C. 10.8 amu
D. 35.5 amu
Answer (2)
Convert the abundance percentages to fractional abundances.
Multiply the mass of each isotope by its fractional abundance.
Sum the weighted masses to find the average atomic mass.
The average atomic mass of the element is 10.801 amu .
Explanation
Understanding the Problem We are given the mass and abundance of two isotopes of an element and asked to calculate the average atomic mass of the element. The average atomic mass is the sum of the products of each isotope's mass and its fractional abundance.
Converting Percentages to Decimals First, we need to convert the abundance percentages to fractional abundances by dividing by 100. So, 19.9% becomes 0.199 and 80.1% becomes 0.801.
Calculating Weighted Masses Next, we multiply the mass of each isotope by its fractional abundance: Isotope 1: 10.0 amu * 0.199 = 1.99 amu Isotope 2: 11.0 amu * 0.801 = 8.811 amu
Summing Weighted Masses Finally, we sum the weighted masses to find the average atomic mass: Average atomic mass = 1.99 amu + 8.811 amu = 10.801 amu
Final Answer Therefore, the average atomic mass of the element is 10.801 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 chemical reactions. In material science, understanding the isotopic composition and average atomic mass is vital for predicting the properties of materials, such as density and thermal conductivity. Moreover, in environmental science, the isotopic analysis and average atomic mass are used to trace the origin and fate of pollutants in the environment. For example, if you are trying to determine the mass of carbon dioxide produced in a reaction, you need to know the average atomic mass of carbon to calculate the molar mass of carbon dioxide ( C O 2 ).
The average atomic mass of the element is calculated to be 10.801 amu. Therefore, the correct choice from the options is C: 10.8 amu.
;
