Atomic And Molecular Mass
The average atomic mass of chlorine is 35.5 u. Given that chlorine exists as (^{35}\text{Cl}) (atomic mass 35 u) and (^{37}\text{Cl}) (atomic mass 37 u), what is the approximate percentage abundance of (^{35}\text{Cl})?
Select the correct option:
Solution
75%
Average atomic mass is the weighted mean of the isotopic masses, weighted by their fractional abundances. Let the fractional abundance of (^{35}\text{Cl}) be (x); then (^{37}\text{Cl}) has abundance ((1-x)). Setting up the equation: (35x + 37(1-x) = 35.5). Expanding: (35x + 37 - 37x = 35.5), so (-2x = -1.5), giving (x = 0.75) or 75%. Option 25% is the abundance of (^{37}\text{Cl}), not (^{35}\text{Cl}) — the student may have confused the two isotopes. Option 50% would give an average atomic mass of 36 u, not 35.5 u. Option 90% would give (35 \times 0.9 + 37 \times 0.1 = 31.5 + 3.7 = 35.2) u, which is less than 35.5 u. This is a classic NCERT problem on isotopes and average atomic mass appearing frequently in JEE. Plausibility check: since 35.5 is closer to 35 than to 37, (^{35}\text{Cl}) must be the more abundant isotope, confirming 75% is correct.
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About This Question
- Subject
- chemistry
- Chapter
- some basic concepts in chemistry
- Topic
- atomic and molecular mass
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
75%
Average atomic mass is the weighted mean of the isotopic masses, weighted by their fractional abundances. Let the fractional abundance of (^{35}\text{Cl}) be (x); then (^{37}\text{Cl}) has abundance ((1-x)). Setting up the equation: (35x + 37(1-x) = 35.5). Expanding: (35x + 37 - 37x = 35.5), so (-2x = -1.5), giving (x = 0.75) or 75%. Option 25% is the abundance of (^{37}\text{Cl}), not (^{35}\text{Cl}) — the student may have confused the two isotopes. Option 50% would give an average atomic mass of 36 u, not 35.5 u. Option 90% would give (35 \times 0.9 + 37 \times 0.1 = 31.5 + 3.7 = 35.2) u, which is less than 35.5 u. This is a classic NCERT problem on isotopes and average atomic mass appearing frequently in JEE. Plausibility check: since 35.5 is closer to 35 than to 37, (^{35}\text{Cl}) must be the more abundant isotope, confirming 75% is correct.
This medium difficulty chemistry question is from the chapter some basic concepts in chemistry, covering the topic of atomic and molecular mass. It appeared in the 2025 exam.
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