Calculate the average atomic mass for iron. 15.2% iron-55, 84.8% iron-56. AAM = 55(0.152) + 56(0.848)
The Correct Answer and Explanation is:
To calculate the average atomic mass (AAM) of iron, we need to consider the isotopes and their respective percentages. The formula for average atomic mass is:AAM=(m1×p1)+(m2×p2)AAM = (m_1 \times p_1) + (m_2 \times p_2)AAM=(m1×p1)+(m2×p2)
Where:
- m1m_1m1 and m2m_2m2 are the masses of the isotopes (in atomic mass units, amu),
- p1p_1p1 and p2p_2p2 are the relative abundances of each isotope (as decimals).
In this case:
- Iron-55 has a mass of 55 amu and an abundance of 15.2%, or 0.152,
- Iron-56 has a mass of 56 amu and an abundance of 84.8%, or 0.848.
Now, substitute these values into the formula:AAM=(55×0.152)+(56×0.848)AAM = (55 \times 0.152) + (56 \times 0.848)AAM=(55×0.152)+(56×0.848)
First, calculate each part:55×0.152=8.3655 \times 0.152 = 8.3655×0.152=8.3656×0.848=47.48856 \times 0.848 = 47.48856×0.848=47.488
Now, sum the results:AAM=8.36+47.488=55.848 amuAAM = 8.36 + 47.488 = 55.848 \, \text{amu}AAM=8.36+47.488=55.848amu
So, the average atomic mass of iron is approximately 55.85 amu.
Explanation:
The average atomic mass of an element is a weighted average based on the relative abundances and masses of its isotopes. Iron has two stable isotopes, iron-55 and iron-56. The atomic mass we calculated reflects the fact that iron-56 is much more abundant than iron-55, which is why the average atomic mass is closer to 56 than 55. This value is crucial because the atomic mass of an element is used in various chemical calculations, including determining the number of moles or grams in a given sample of iron.
