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GATE 2026 CY – Question 20

Physical Chemistry · Kinetics and Reaction Dynamics: Elementary, parallel, opposing, and consecutive reactions. Steady state approximation. Mechanism of complex reactions. Unimolecular reactions. Potential energy surface and classical trajectories, Concept of saddle points, Transition state theory: Eyring equation, thermodynamic aspects. Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects. Fast reaction kinetics: relaxation and flow methods. Diffusion controlled reactions. Kinetics of unimolecular and bimolecular photophysical processes, Quantum yield calculation, static and dynamic quenching. · 1 mark · Multiple choice

For the reaction shown, if $\Delta^{\ddagger}U^\circ=5RT/2$, the value of $\Delta^{\ddagger}H^\circ$ is (X‡ is activated complex; the two deltas are standard activation internal energy and enthalpy; R is gas constant and T temperature)

A + B equilibrates with activated complex X‡, which forms product.
  1. $RT/2$
  2. $3RT/2$
  3. $7RT/2$
  4. $5RT/2$

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Correct answer: (B) $3RT/2$

Explanation

Relate the standard activation enthalpy and internal energy:
$$\Delta^\ddagger H^\circ=\Delta^\ddagger U^\circ+\Delta(PV)^\ddagger=\Delta^\ddagger U^\circ+\Delta n^\ddagger RT,$$
where $\Delta n^\ddagger$ is the change in the number of moles of gas on forming the activated complex.

**Here** two gaseous molecules A and B combine to give one activated complex $X^\ddagger$:
$$\Delta n^\ddagger=1-2=-1 .$$

**Numbers.**
$$\Delta^\ddagger H^\circ=\frac{5RT}{2}-RT=\frac{3RT}{2}\quad(\text{option B}).$$