JEE Main · 2020 · Shift-IIeasyMOLE-112

The average molar mass of chlorine is 35.5\,g mol-1. The ratio of 35Cl to 37Cl in naturally occurring chlorine is close…

Some Basic Concepts (Mole Concept) · Class 11 · JEE Main Previous Year Question

Question

The average molar mass of chlorine is $35.5\,\text{g mol}^{-1}$ . The ratio of ${}^{35}\text{Cl}$ to ${}^{37}\text{Cl}$ in naturally occurring chlorine is close to:

Options

a
$4:1$
b
$3:1$
✓
c
$2:1$
d
$1:1$

Correct Answerb

$3:1$

Detailed Solution

🧠 The average pulls toward the more abundant isotope $35.5$ sits much closer to $35$ than to $37$ . So $^{35}\text{Cl}$ must be the bigger share.

🗺️ Alligation method Distance from average to lighter isotope: $35.5 - 35 = 0.5$ . Distance from average to heavier isotope: $37 - 35.5 = 1.5$ .

Ratio of abundances $=$ inverse of distances $= 1.5 : 0.5 = 3 : 1$ .

So $^{35}\text{Cl} : ^{37}\text{Cl} = 3 : 1$ .

⚡ Quick sanity check $75\%$ of $35$ plus $25\%$ of $37 = 26.25 + 9.25 = 35.5$ . ✓

$\boxed{\text{Answer: (b)}}$

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