The table below shows data for two isotopes of chlorine ([tex]$Cl$[/tex]). The data in the "\% Abundance" column represents the likelihood that any given atom of chlorine is a particular isotope.
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]
