Answer :
To determine the average atomic mass of sulfur using the information provided in the table, we will follow these steps:
1. Multiply the relative abundance of each isotope by its atomic mass.
2. Sum these values.
3. Divide the result by 100 to account for the percentage scale of relative abundance.
Here are the calculations for each isotope of sulfur:
1. For S-32:
[tex]\[ 94.93\% \times 31.972 \, \text{amu} = 30.3739956 \, \text{amu} \][/tex]
2. For S-33:
[tex]\[ 0.76\% \times 32.971 \, \text{amu} = 0.2505796 \, \text{amu} \][/tex]
3. For S-34:
[tex]\[ 4.29\% \times 33.967 \, \text{amu} = 1.4570643 \, \text{amu} \][/tex]
4. For S-36:
[tex]\[ 0.02\% \times 35.967 \, \text{amu} = 0.0071934 \, \text{amu} \][/tex]
Next, we add up these contributions:
[tex]\[ 30.3739956 + 0.2505796 + 1.4570643 + 0.0071934 = 32.088833 \][/tex]
Finally, since the relative abundances are given in percentage, we adjust the sum by dividing by 100:
[tex]\[ \frac{32.088833}{100} = 32.0659769 \, \text{amu} \][/tex]
Thus, the average atomic mass of sulfur is approximately 32.0659769 amu.
Among the multiple-choice options given:
A. \(31.972 \, \text{amu}\)
B. \(32.060 \, \text{amu}\)
C. \(33.71 \, \text{amu}\)
D. \(34.090 \, \text{amu}\)
E. \(35.967 \, \text{amu}\)
The correct answer is \(32.060 \, \text{amu}\), which rounds up the computed result \(32.0659769 \, \text{amu}\).
Thus, the correct answer is B. [tex]\(32.060 \, \text{amu}\)[/tex].
1. Multiply the relative abundance of each isotope by its atomic mass.
2. Sum these values.
3. Divide the result by 100 to account for the percentage scale of relative abundance.
Here are the calculations for each isotope of sulfur:
1. For S-32:
[tex]\[ 94.93\% \times 31.972 \, \text{amu} = 30.3739956 \, \text{amu} \][/tex]
2. For S-33:
[tex]\[ 0.76\% \times 32.971 \, \text{amu} = 0.2505796 \, \text{amu} \][/tex]
3. For S-34:
[tex]\[ 4.29\% \times 33.967 \, \text{amu} = 1.4570643 \, \text{amu} \][/tex]
4. For S-36:
[tex]\[ 0.02\% \times 35.967 \, \text{amu} = 0.0071934 \, \text{amu} \][/tex]
Next, we add up these contributions:
[tex]\[ 30.3739956 + 0.2505796 + 1.4570643 + 0.0071934 = 32.088833 \][/tex]
Finally, since the relative abundances are given in percentage, we adjust the sum by dividing by 100:
[tex]\[ \frac{32.088833}{100} = 32.0659769 \, \text{amu} \][/tex]
Thus, the average atomic mass of sulfur is approximately 32.0659769 amu.
Among the multiple-choice options given:
A. \(31.972 \, \text{amu}\)
B. \(32.060 \, \text{amu}\)
C. \(33.71 \, \text{amu}\)
D. \(34.090 \, \text{amu}\)
E. \(35.967 \, \text{amu}\)
The correct answer is \(32.060 \, \text{amu}\), which rounds up the computed result \(32.0659769 \, \text{amu}\).
Thus, the correct answer is B. [tex]\(32.060 \, \text{amu}\)[/tex].
