Calculate the average atomic mass in units of amu for iron (Fe) given that the naturally occurring element exists mainly as a mixture of Fe-56 (91.754%0), Fe-54 (5.845%), and Fe-57 (2.119%). Does your value agree with that shown in the periodic table?
The Correct Answer and Explanation is :
The average atomic mass of iron (Fe), calculated from its isotopic distribution, is approximately 55.68 amu. This value is very close to the value typically listed in the periodic table for iron, which is about 55.845 amu.
Explanation:
Iron (Fe) is a naturally occurring element that exists as a mixture of several isotopes. The isotopes of iron relevant to this calculation are Fe-56, Fe-54, and Fe-57. Each isotope has a different atomic mass and a specific natural abundance.
The atomic mass of an element listed in the periodic table is a weighted average of the masses of its isotopes, based on their natural abundances. To calculate the average atomic mass, we multiply the atomic mass of each isotope by its relative abundance (expressed as a percentage), and then divide by 100 to account for the percentage form.
- Fe-56 has an atomic mass of 55.9349375 amu and an abundance of 91.754%.
- Fe-54 has an atomic mass of 53.939610 amu and an abundance of 5.845%.
- Fe-57 has an atomic mass of 56.935398 amu and an abundance of 2.119%.
The average atomic mass is calculated as:
[
\text{Average Atomic Mass} = (55.9349375 \times 91.754\%) + (53.939610 \times 5.845\%) + (56.935398 \times 2.119\%)
]
[
\text{Average Atomic Mass} \approx 55.68 \text{ amu}
]
This value is very close to the standard atomic weight of iron (Fe) listed in the periodic table, which is approximately 55.845 amu. The slight difference can be attributed to rounding and differences in the precision of the values used in various sources.
Now, I will generate an image that visually represents this isotopic distribution.
Here is a bar graph illustrating the isotopic distribution of iron (Fe), showing the relative abundances of Fe-56, Fe-54, and Fe-57. As you can see, Fe-56 has the highest abundance, followed by Fe-54, and Fe-57 with the lowest.
This distribution was used to calculate the average atomic mass of iron, which is approximately 55.68 amu, a value that closely matches the one found in the periodic table (around 55.845 amu).
