Atomic And Molecular Mass

Question

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 $^{35}\text{Cl}$?

RankGuru · Accepted Answer

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.

Atomic And Molecular Mass

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