JEE Main · 2021 · Shift-ImediumTHERMO-111

At 298.2 K the relationship between enthalpy of bond dissociation (in kJ mol-1) for hydrogen (EH) and its isotope,…

Thermodynamics · Class 11 · JEE Main Previous Year Question

Question

At 298.2 K the relationship between enthalpy of bond dissociation (in kJ mol1\text{kJ mol}^{-1}) for hydrogen (EHE_H) and its isotope, deuterium (EDE_D), is best described by:

Options
  1. a

    EH=12EDE_H=\frac{1}{2}E_D

  2. b

    EH=EDE_H=E_D

  3. c

    EH=ED7.5E_H=E_D-7.5

  4. d

    EH=2EDE_H=2E_D

Correct Answerc

EH=ED7.5E_H=E_D-7.5

Detailed Solution

🧠 Heavier isotope → lower zero-point energy → stronger bond Vibrational frequency scales as 1/μ1/\sqrt{\mu} where μ\mu is reduced mass. Deuterium is heavier, so D-D vibrates more slowly, has lower zero-point energy, sits deeper in the potential well, and needs more energy to dissociate than H-H.

The experimental difference in bond dissociation enthalpies is approximately 7.5 kJ mol1^{-1}, giving:

EH=ED7.5E_H = E_D - 7.5

⚠️ Trap: Students often assume isotopes have identical chemical bond strengths. The kinetic isotope effect is small but measurable — deuterium bonds are genuinely stronger.

Answer: (c) EH=ED7.5\boxed{\text{Answer: (c) } E_H = E_D - 7.5}

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At 298.2 K the relationship between enthalpy of bond dissociation (in kJ mol-1) for hydrogen (EH)… (JEE Main 2021) | Canvas Classes