To find the weighted average mass of chlorine, we need to consider the mass and abundance of each of its isotopes. The isotopes provided are [tex]\({}^{35}Cl\)[/tex] and [tex]\({}^{37}Cl\)[/tex]. The formula for calculating the weighted average mass is:
[tex]\[ \text{Weighted Average Mass} = ( \text{Mass of Isotope 1} \times \text{Abundance of Isotope 1} ) + ( \text{Mass of Isotope 2} \times \text{Abundance of Isotope 2} ) \][/tex]
Here are the steps for solving the problem:
1. Identify the masses and abundances of the isotopes:
- Mass of [tex]\({}^{35}Cl\)[/tex]: [tex]\(34.97 \, \text{amu}\)[/tex]
- Percent abundance of [tex]\({}^{35}Cl\)[/tex]: [tex]\(75.78\%\)[/tex]
- Mass of [tex]\({}^{37}Cl\)[/tex]: [tex]\(36.97 \, \text{amu}\)[/tex]
- Percent abundance of [tex]\({}^{37}Cl\)[/tex]: [tex]\(24.22\%\)[/tex]
2. Convert the percent abundances to decimal form:
- Abundance of [tex]\({}^{35}Cl\)[/tex]: [tex]\(75.78\% = 0.7578\)[/tex]
- Abundance of [tex]\({}^{37}Cl\)[/tex]: [tex]\(24.22\% = 0.2422\)[/tex]
3. Substitute the values into the weighted average mass formula:
[tex]\[
\text{Weighted Average Mass} = (34.97 \times 0.7578) + (36.97 \times 0.2422)
\][/tex]
4. Calculate each term separately:
- For [tex]\({}^{35}Cl\)[/tex]:
[tex]\[
34.97 \times 0.7578 = 26.499266
\][/tex]
- For [tex]\({}^{37}Cl\)[/tex]:
[tex]\[
36.97 \times 0.2422 = 8.955134
\][/tex]
5. Add the calculated terms together:
[tex]\[
26.499266 + 8.955134 = 35.4544
\][/tex]
The weighted average mass of chlorine is [tex]\(35.4544 \, \text{amu}\)[/tex].
