Question

calculate the atomic mass of sulfur if the four common isotopes of sulfur have masses of 31.972 amu (95.00% abundance), 32.971 amu (0.76%), 33.967 amu (4.22%), and 35.967 amu (0.014%)

Answer 1

To calculate the atomic mass of sulfur based on the given isotopes and their respective abundances, we can use the formula:

\[
\text{Atomic Mass} = \sum (\text{isotope mass} \times \text{fractional abundance})
\]

We'll first convert the percentages of abundance into fractional form by dividing by 100:

- For the first isotope (31.972 amu) with 95.00% abundance, the fractional abundance is \(0.9500\).
- For the second isotope (32.971 amu) with 0.76% abundance, the fractional abundance is \(0.0076\).
- For the third isotope (33.967 amu) with 4.22% abundance, the fractional abundance is \(0.0422\).
- For the fourth isotope (35.967 amu) with 0.014% abundance, the fractional abundance is \(0.00014\).

Now we calculate the contribution of each isotope to the atomic mass:

1. \(31.972 \, \text{amu} \times 0.9500 = 30.3734 \, \text{amu}\)
2. \(32.971 \, \text{amu} \times 0.0076 = 0.2506 \, \text{amu}\)
3. \(33.967 \, \text{amu} \times 0.0422 = 1.4325 \, \text{amu}\)
4. \(35.967 \, \text{amu} \times 0.00014 = 0.005036 \, \text{amu}\)

Now, we sum these contributions:

\[
\text{Atomic Mass} = 30.3734 + 0.2506 + 1.4325 + 0.005036
\]

Calculating the sum:

\[
\text{Atomic Mass} = 32.061536 \, \text{amu}
\]

Rounding to appropriate significant figures, the atomic mass of sulfur is approximately:

\[
\text{Atomic Mass} \approx 32.06 \, \text{amu}
\]