Calculate the average atomic mass of iron. Its composition is 5.90
with a mass of 53.94 amu, 91.72
with a mass of 55.93 amu, 2.10
with a mass of 56.94 amu, and 0.280
with a mass of 57.93 amu.
The Correct Answer and Explanation is:
Correct Answer:
The average atomic mass of iron is calculated as:Average Atomic Mass=(5.90%×53.94)+(91.72%×55.93)+(2.10%×56.94)+(0.280%×57.93)\text{Average Atomic Mass} = (5.90\% \times 53.94) + (91.72\% \times 55.93) + (2.10\% \times 56.94) + (0.280\% \times 57.93)Average Atomic Mass=(5.90%×53.94)+(91.72%×55.93)+(2.10%×56.94)+(0.280%×57.93)
Convert Percentages to Decimal Form:
- 5.90% = 0.0590
- 91.72% = 0.9172
- 2.10% = 0.0210
- 0.280% = 0.00280
Substitute the values:(0.0590×53.94)+(0.9172×55.93)+(0.0210×56.94)+(0.00280×57.93)(0.0590 \times 53.94) + (0.9172 \times 55.93) + (0.0210 \times 56.94) + (0.00280 \times 57.93)(0.0590×53.94)+(0.9172×55.93)+(0.0210×56.94)+(0.00280×57.93)
Calculating each term:
- 0.0590×53.94=3.180.0590 \times 53.94 = 3.180.0590×53.94=3.18
- 0.9172×55.93=51.300.9172 \times 55.93 = 51.300.9172×55.93=51.30
- 0.0210×56.94=1.200.0210 \times 56.94 = 1.200.0210×56.94=1.20
- 0.00280×57.93=0.160.00280 \times 57.93 = 0.160.00280×57.93=0.16
Sum of all contributions:3.18+51.30+1.20+0.16=55.84 amu3.18 + 51.30 + 1.20 + 0.16 = 55.84 \, \text{amu}3.18+51.30+1.20+0.16=55.84amu
Final Answer:
The average atomic mass of iron is 55.84 amu.
Explanation:
The average atomic mass of an element is a weighted mean of the masses of its naturally occurring isotopes. Each isotope has its own mass and relative abundance. The relative abundance is expressed as a percentage, which shows how much of that isotope is present in a typical sample of the element.
To calculate the average atomic mass, you multiply the mass of each isotope by its fractional abundance (percentage divided by 100) and then sum those products. This approach gives more weight to isotopes that are more common in nature and less weight to those that are rare.
In this example, iron has four naturally occurring isotopes with the following details:
- An isotope with a mass of 53.94 amu and a 5.90% abundance
- An isotope with a mass of 55.93 amu and a 91.72% abundance
- An isotope with a mass of 56.94 amu and a 2.10% abundance
- An isotope with a mass of 57.93 amu and a 0.280% abundance
The most abundant isotope is the one with a mass of 55.93 amu, contributing significantly to the average. The other isotopes have lower abundances, so their impact on the average is smaller.
The calculated average atomic mass of iron is 55.84 amu, which matches the commonly accepted value found on the periodic table. This value is important for scientific calculations, especially in chemistry and physics, where precise mass values are necessary for reactions, equations, and conversions.
