Question

Calculate the atomic mass of magnesium (Mg). Magnesium has three stable isotopes: 24Mg, 25Mg, and 26Mg. Magnesium-24 has a relative abundance of 78.99 %. Magnesium-25 has a relative abundance of 10.00 %. Magnesium-26 has a relative abundance of 11.01 %.

*Show your work to receive full credit.

Answer 1

To calculate the atomic mass of magnesium (Mg), we can use the formula for the weighted average based on the relative abundances and atomic masses of its stable isotopes. The atomic mass of an isotope is typically expressed in atomic mass units (amu).

The steps to calculate the atomic mass are as follows:

1. List the isotopes with their atomic masses and relative abundances:
- \(^{24}\text{Mg}\): atomic mass = 24 amu, relative abundance = 78.99% or 0.7899
- \(^{25}\text{Mg}\): atomic mass = 25 amu, relative abundance = 10.00% or 0.1000
- \(^{26}\text{Mg}\): atomic mass = 26 amu, relative abundance = 11.01% or 0.1101

2. Convert the relative abundances from percentages to fractions by dividing by 100:
- \(^{24}\text{Mg}\): \(0.7899\)
- \(^{25}\text{Mg}\): \(0.1000\)
- \(^{26}\text{Mg}\): \(0.1101\)

3. Calculate the contribution of each isotope to the atomic mass using the formula:

\[
\text{contribution} = (\text{relative abundance}) \times (\text{atomic mass})
\]

4. Sum the contributions from all isotopes to get the total atomic mass:

\[
\text{Atomic mass of Mg} = (0.7899 \times 24 \text{ amu}) + (0.1000 \times 25 \text{ amu}) + (0.1101 \times 26 \text{ amu})
\]

5. Performing the calculations:

- Contribution from \(^{24}\text{Mg}\):
\[
0.7899 \times 24 = 18.9576 \text{ amu}
\]

- Contribution from \(^{25}\text{Mg}\):
\[
0.1000 \times 25 = 2.5000 \text{ amu}
\]

- Contribution from \(^{26}\text{Mg}\):
\[
0.1101 \times 26 = 2.8626 \text{ amu}
\]

6. Summing the contributions:
\[
\text{Atomic mass of Mg} = 18.9576 + 2.5000 + 2.8626 = 24.3202 \text{ amu}
\]

Thus, the atomic mass of magnesium (Mg) is approximately **24.32 amu**.