To determine the correct answer, let's go through the process of calculating the average atomic mass of chlorine using the given data:
1. Identify the relevant data:
- The atomic mass of Chlorine-35 ([tex]\( ^{35}\text{Cl} \)[/tex]) is 34.969 amu.
- The relative abundance of Chlorine-35 is 75.78 percent, which can be converted to a decimal as [tex]\(0.7578\)[/tex].
- The atomic mass of Chlorine-37 ([tex]\( ^{37}\text{Cl} \)[/tex]) is 36.966 amu.
- The relative abundance of Chlorine-37 is 24.22 percent, which can be converted to a decimal as [tex]\(0.2422\)[/tex].
2. Apply the formula for the weighted average atomic mass:
- The formula to calculate the average atomic mass is given by:
[tex]\[
\text{Average Atomic Mass} = (\text{Mass of } ^{35}\text{Cl} \times \text{Abundance of } ^{35}\text{Cl}) + (\text{Mass of } ^{37}\text{Cl} \times \text{Abundance of } ^{37}\text{Cl})
\][/tex]
3. Substitute the given values into the formula:
- Mass of [tex]\(^{35}\text{Cl}\)[/tex]: 34.969 amu
- Abundance of [tex]\(^{35}\text{Cl}\)[/tex]: 0.7578
- Mass of [tex]\(^{37}\text{Cl}\)[/tex]: 36.966 amu
- Abundance of [tex]\(^{37}\text{Cl}\)[/tex]: 0.2422
[tex]\[
\text{Average Atomic Mass} = (34.969 \times 0.7578) + (36.966 \times 0.2422)
\][/tex]
4. Perform the multiplication and addition:
[tex]\[
\text{Average Atomic Mass} = 26.4916182 + 8.9610552
\][/tex]
5. Sum the two results to find the average atomic mass:
[tex]\[
\text{Average Atomic Mass} = 35.4526734
\][/tex]
6. Round to an appropriate number of significant figures:
- Typically, atomic masses are given to significant figures that reflect the precision of the provided data. Here, we will match the significant figures in the data provided.
Therefore, the average atomic mass of chlorine is approximately [tex]\(35.453 \, \text{amu}\)[/tex].
Hence, the correct answer is:
[tex]\[
\boxed{35.453 \, \text{amu}}
\][/tex]
