To find the weighted average mass of chlorine based on the given isotopes and their abundances, follow these steps:
1. Identify the masses and abundances:
- Isotope [tex]\({}^{35}Cl\)[/tex] has a mass of 34.97 amu and an abundance of 75.78%.
- Isotope [tex]\({}^{37}Cl\)[/tex] has a mass of 36.97 amu and an abundance of 24.22%.
2. Convert the percentages to decimals:
- For [tex]\({}^{35}Cl\)[/tex]: 75.78% becomes 0.7578
- For [tex]\({}^{37}Cl\)[/tex]: 24.22% becomes 0.2422
3. Calculate the contribution of each isotope to the weighted average mass:
- Contribution of [tex]\({}^{35}Cl\)[/tex]: [tex]\( 34.97 \times 0.7578 \)[/tex]
- Contribution of [tex]\({}^{37}Cl\)[/tex]: [tex]\( 36.97 \times 0.2422 \)[/tex]
4. Sum these contributions to get the weighted average mass:
[tex]\[
(34.97 \times 0.7578) + (36.97 \times 0.2422)
\][/tex]
5. Perform the calculations:
- [tex]\( 34.97 \times 0.7578 = 26.502866 \)[/tex]
- [tex]\( 36.97 \times 0.2422 = 8.951534 \)[/tex]
6. Add these values together:
[tex]\[
26.502866 + 8.951534 = 35.4544
\][/tex]
Therefore, the weighted average mass of chlorine is [tex]\( 35.4544 \, \text{amu} \)[/tex].
The correct answer is:
C. 35.45
