To calculate the atomic mass of sulfur, we use the weighted average method, which takes into account the atomic masses and the natural abundances of each isotope. Here's a step-by-step guide to solving this problem:
1. List the given data:
- Sulfur-32: Atomic mass = 31.97, Natural abundance = 94.93%
- Sulfur-33: Atomic mass = 32.97, Natural abundance = 0.76%
- Sulfur-34: Atomic mass = 33.97, Natural abundance = 4.29%
- Sulfur-36: Atomic mass = 35.97, Natural abundance = 0.02%
2. Calculate the contribution of each isotope to the atomic mass:
- For Sulfur-32: Multiply the atomic mass by its proportion in nature
[tex]\[
\text{Contribution of Sulfur-32} = 31.97 \times \frac{94.93}{100} = 30.349121
\][/tex]
- For Sulfur-33: Multiply the atomic mass by its proportion in nature
[tex]\[
\text{Contribution of Sulfur-33} = 32.97 \times \frac{0.76}{100} = 0.25057199999999996
\][/tex]
- For Sulfur-34: Multiply the atomic mass by its proportion in nature
[tex]\[
\text{Contribution of Sulfur-34} = 33.97 \times \frac{4.29}{100} = 1.457313
\][/tex]
- For Sulfur-36: Multiply the atomic mass by its proportion in nature
[tex]\[
\text{Contribution of Sulfur-36} = 35.97 \times \frac{0.02}{100} = 0.007194000000000001
\][/tex]
3. Sum the contributions of all isotopes:
[tex]\[
\text{Total atomic mass} = 30.349121 + 0.25057199999999996 + 1.457313 + 0.007194000000000001 = 32.0642
\][/tex]
Therefore, the atomic mass of sulfur, considering the given natural abundances and atomic masses of its isotopes, is 32.0642.
